ECO4000 - REVIEW word
docx
keyboard_arrow_up
School
Baruch College, CUNY *
*We aren’t endorsed by this school
Course
4000
Subject
Economics
Date
Jan 9, 2024
Type
docx
Pages
56
Uploaded by CoachDolphinPerson1012
1.
Given the equation Inyi= B0 + B1 In(xi), which of the following represents the after equation?
a)
In(yi+Δyi) = B0 + B1 In(xi+Δxi)
b)
yi+Δyi = B0 + B1 In(xi+Δxi)
c)
In(yi+Δyi) = ^B0 + ^B1 In(xi+Δxi)
d)
In(yi+Δyi) = ^B0 + ^B1 In(xi+Δxi)
Answer: a) In(yi+Δyi) = B0 + B1 In(xi+Δxi)
2.
A 1% increase in X (multiplying X by 1.01) is associated with a a) .01 B
1 change in Y
b) .01 B
1 change in X
c) .01 B
1 change in X and Y
d) None of the above Answer : A
Explanation:A 1% increase in X (multiplying X by 1.01) is associated with a .01
B
1 change in Y. (
1% increase in X → .01 increase in in(x) → .01 B
1 increase in Y )
3.
The natural logarithm is the inverse of
a) The exponential function b) Regression line c) Price elasticity d)The t-statistic Answer: a 4.
What are the three logarithmic regression models?
I. Linear-Log Model II. Log-Linear Model III. Log Normal Distribution IIII. Log-Log Model A) I, II, IIII B) II,III,IIII
C) I, III, IIII D) None of above Answer A 5.
How is a random variable called when it is the natural logarithm of a normal random variable? A. lognormal random variable
B. Standard normal distribution C. Logarithmic transformation
D. None of the above
Answer : A. lognormal random variable
6.
Fill in the blank: Models which are nonlinear in either one or multiple parameters are to be estimated by _____________.
A) Ordinary Least Squares (OLS)
B) Nonlinear Least Squares (NLS)
C) Both A and B, doesn’t matter
D) Neither A or B
ANSWER : B
7. Which of the following is an example of two continuous independent variables?
A. Gender and height
B. Age and occupation
C. Marital status and education level
D. Work experience and years of education
Answer: D.
8. What is the purpose of the interaction term in a linear regression model with two continuous independent variables?
A. To make the regression model non-linear
B. To account for measurement error in the independent variables
C. To allow the effect of one independent variable to depend on the value of the other independent variable
D. To reduce multicollinearity between the independent variables
Answer: C. 9. What is the interpretation of the coefficient on the interaction term in a linear regression model with two continuous independent variables?
A. The effect of one independent variable on the dependent variable, holding the other independent variable constant
B. The extra effect on the dependent variable from changing both independent variables, beyond the sum of the effects of changing each independent variable separately
C. The amount of variation in the dependent variable that is explained by the independent variables
D. The degree of association between the independent variables
Answer: B.
10. In x of polynomials which one is the regression function approximated by?
A. Cubic
B. Calculating Percentage
C. Log Lig Function
D. None of the Above
Answer A.
11. Models that are in the parameter that are linear can be estimated by the A. OLS
B. NLS
C. Slope
D. None of the Above
Answer: A. 12.
Which of the following statements about nonlinear least squares is true?
A. Nonlinear least squares can only be used to estimate linear regression models.
B. Nonlinear least squares is a method for estimating the parameters of a linear regression model.
C. Nonlinear least squares is a method for estimating the parameters of a nonlinear regression model.
D. Nonlinear least squares can only be used to estimate the parameters of a logistic regression model. Answer :B.
Nonlinear least squares is a method for estimating the parameters of a linear regression model.
13. What are the potential drawbacks of using a high learning rate in a neural network?
a. The model may converge slowly.
b. The model may overfit to the training data.
c. The model may underfit to the training data.
d. The model may get stuck in a local minimum.
Answer: b.
The model may overfit to the training data.
14.
In a regression analysis, if the error term is heteroskedastic, which of the following statements is correct about the resulting t-statistics for the regression coefficients?
a) The t-statistics will also be heteroskedastic.
b)The t-statistics will be homoskedastic.
c) The t-statistics will not be affected by the heteroskedastic error term.
d) The t-statistics will not be valid.
Answer: D The t-statistics will not be valid
15. What is true about heteroscedasticity?
a. It makes the residuals left skewed b. It decreases the sample size
c. It makes the residuals left skewed d.
It leads to a swayed results of the regression coefficients
Answer: 4. It leads to a swayed results of the regression coefficients
16.
Which of the following best describes the purpose of including fixed effects in panel data regression?
A) Controlling for changes in the dependent variable over time
B) Controlling for changes in the independent variables over time
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
C) Controlling for differences in the dependent variable across individuals or groups
D) Controlling for differences in the independent variables across individuals or groups
Answer: C) Controlling for differences in the dependent variable across individuals or groups
17.
Which of the elements below is not included in the 5 elements of the general approach to modeling nonlinear regression functions? a)
Specify a nonlinear function, and estimate its parameters by OLS. b)
Determine whether the linear model improves upon a nonlinear model. c)
Identify a possible nonlinear relationship d)
Estimate the effect on Y of a change in X. Correct Answer - B 18.
What is the interpretation of β1 when the regression specification is Yi = β0 + β1ln(Xi)+ui a)
A 1% change in X is associated with a change in Y of 0.01β1 b)
A change in X by one unit 1∆X = 12 is associated with a 100β1% change in Y. c)
A 1% change in X is associated with a b1% change in Y, so b1 is the elasticity of Y with respect to X. d)
A 1% change in X is not associated with a change in Y of 0.01β1 Correct answer - A. 19. Which pair of methods can be used together to enhance the fitting of a regression model? A) Utilizing polynomial terms for both Y and X along with applying logarithmic transformations
B) Applying logarithms to Y and incorporating logarithmic transformations
C) Combining polynomial terms for X and incorporating logarithmic transformations D) None of the above
Answer: C)
Combining polynomial terms for X and incorporating logarithmic transformations 20. Which option is not part of the typical process for constructing a nonlinear regression model? a) Visualizing the fitted nonlinear regression curve
b) Recognizing potential nonlinear associations
c) Calculating the coefficients for a linear regression
d) Assessing the impact of an X variable change on the Y variable Answer: c)
Calculating the coefficients for a linear regression
21. In various situations, the relationship between binary and continuous predictors in regression analysis can be interpreted differently. Which equation enables the impact on the continuous predictor to rely on the binary predictor? A. Yi = β0 + β1Di + β2Xi + β3(Di * Xi) + ui B. Yi = β0 + β1X1i + β2X2i + ui C. Yi = β0 + β1D1i + β2D2i + ui D. Yi = β0 + β1Di + β2Xi + ui The correct answer is A. 22. What would happen if the relation between Y and X was nonlinear?
a.
The effect on Y of a change in X depends on the value of the value of X.
b.
A linear regression is mis- specified.
c.
The estimator of the effect on Y and X is biased.
d.
The solution is to estimate a regression function that is nonlinear in X.
1.
a and b
2.
a, b, and c
3.
a, c, and d
4.
a,
b,
c,
and
d
23. Which of the following is true for the error term when using a nonlinear
regression function?
a)
It is assumed that the error term is regularly distributed.
B)
It
is
assumed
that
the
error
term is
independent
and
identically
distributed
(i.i.d.).
c)
The error term will remain constant regardless of the independent variable's values.
d)
The dependent variable and error term are thought to be linearly related.
24. Which of the following statements is incorrect regarding polynomial regression functions?
a)
Individual coefficients have complicated interpretations
b)
Hypotheses concerning degree r can be tested by t- and F-tests on the appropriate blocks of variables
c)
To interpret the estimated regression function: plot predicted values as a function of
x and compute predicted
for different values of x
d)
Permits
modeling
relations
in
“percentage”
terms
(like
elasticities),
rather
than linearly
25.
To
interpret
the
estimated
regression
function:
a.
Plot predicted values as a function of x
b.
Plot predicted values as a function of y
c.
Compute predicted Y/
X
Δ
Δ
for different values of x
d.
Compute predicted Y/
X
Δ
Δ
for different values of x
e.
The
exact
answer
choice
is
not given
26.
Which of the following statements about polynomial regression functions is true?
a)
They are not suitable for fitting nonlinear data
B)
They can only fit curves with a single bend.
b)
They
are
a
type
of
linear
regression
e)
They are a type of logistic regression.
27. if the relation between Y and X is nonlinear, then - .
a.
the
effect
on
Y
depends
on
the
marginal
effect
of
X
b.
the effect of X is consistent
c.
the effect on X depends on the effect of Y - 1
d.
the effect of Y is consistent
28. Logothorims can transform independent Y variables, dependent X variables, or both. However,
a.
The variable being transformed must be negative.
b.
The
variable
being
transformed
must
be
positive.
c.
The variable being transformed must be a value between 0 and 1.
d.
It must be a random variable.
29.
Which of the following best describes the result of fitting data using a degree-4 polynomial regression model?
a.
The model perfectly explains the data.
b.
The
model
is
overfit
to
the
data.
c.
The model is underfit to the data.
d.
The model cannot explain the data.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
30
For the polynomial regression model:
a.
you need new estimation techniques since the OLS assumptions do not apply any longer.
b.
the
techniques
for
estimation
and
inference
developed
for
multiple
regression
can be applied.
c.
you can still use OLS estimation techniques, but the t-statistics do not have an asymptotic normal distribution.
d.
the critical values from the normal distribution have to be changed to 1.96^2, 1.96^3, etc.
Answer:B
31.
Which of the following studies is most likely to be wrong using the log regression
A.
Study about the max speed ? motor vehicle and it’s engine’s max power output ?
?
?
B.
Study about the interest rate ? and inflation rate ?
?
?
C.
Study about the income of someone ? and his/her intelligence level ?
?
?
D.
Study
about
the
the
time
for
someone
to
finish
study
a
chapter
of
text
?
and
his/her
?
intelligence
level
?
?
32.
What is the interpretation of the regression specification: ln(
? ) = β + β ?
+
?
?
0
1 ?
?
a.
A 1% change in X is associated with a change in Y of 0.01
β .
1
b.
A
change
in
X
by
one
unit
(∆X
=
1)
is
associated
with
a
100
β
%
change
in
Y.
1
c.
A 1% change in X is associated with a β % change in Y, so β
is the elasticity of Y with respect
1
1
to X.
d.
None of the above
Answer is B. A change in X by one unit (∆X = 1) is associated with a 100
β % change in Y.
1
As stated in Key Concept 8.2 Logarithms in Regression: Three Cases:
33.
You are an economic statistician working at Milbareel farms. During your research, you find that seniors in highschools in tight-knit communities of low populations are far
more likely to take up farming when compared to seniors in large cities with high populations. Upon further research, you recognize that at a certain point on your graph during the increase of population, the number of farmers needed to keep a community running curves and then levels off. Which function are your findings most likely to represent?
a.
Linear Regression Function
b.
Non
Linear
Regression
Function
c.
Negative Echo Regression Function
d.
Positive Foxtrot Regression Function
34.
Which nonlinear specification can be used to model the suspected difference in the effect on hours studied on test scores between students with high income and students
with low income?
A) TestScore = β0 + β1 * Hours + β2 * Income + β3 * Hours * Income + ε
B) TestScore = β0 + β1 * ln(Hours) + β2 * ln(Income) + ε
C) TestScore = β0 + β1 * Hours + β2 * Income^2 + ε
D) TestScore = β0 + β1 * Hours^2 + β2 * Income + ε
35.
What are some of the issues with implementing heteroskedasticity in OLS regressions?
A.
Biased estimates of regression dependent variables
A.
Inconsistent and biased estimates of regression coefficients
A.
Biased estimates of the independent variables
A.
Biased and inconsistent estimates of the intercept
36.
We are given a dataset of income and expenditure and are told to estimate the relationship between them using a linear regression model. But, when plotted the data shows a non-
linear relationship between the two variables, with the majority of the data points clustered at lower levels of income and expenditure, and a few data points scattered at higher levels. Which of the following statements below would be True about using a logarithmic transformation?
A) A logarithmic transformation is not useful when the data is clustered at lower levels.
B) A logarithmic transformation can only be used when both income and expenditure are negative.
C) A logarithmic transformation can only be used when the relationship between income and expenditure is already linear by nature.
D) A logarithmic transformation can be used to linearize the relationship between income and
expenditure.
37.
Which of these is not a possibility that occurs through the use of the interaction term Xi x Di, population regression line relating Yi, and the continuous variable Xi, and a slope depending on binary variable Di?
A.
Different intercepts, same slope / Yi =B0 +B1Xi +B2Di +ui;
A.
Different intercepts and slopes / Yi =B0 +B1Xi +B2Di +B3(Xi *Di)+ui; A.
Same intercept, different slopes / Yi =B0 +B1Xi +B2(Xi *Di)+ui.
A.
All of the above are all potential possibilities to occur
38.
Of the five elements used in the general approach to modeling nonlinear regression functions taken in this chapter, which would apply the use of t-statistics and F-statistics
to test the null hypothesis of the regression function being linear against the alternative hypothesis that it is linear?
A.
Identify a possible nonlinear relationship.
A.
Specify a nonlinear function, and estimate its parameters by OLS.
A.
Determine whether the nonlinear model improves upon a linear model.
A.
Plot the estimated nonlinear regression function.
A.
Estimate the effect on Y of a change in X.
39.
What is the purpose of using polynomials in multiple regression? (Kun Zhang)
A)
To improve model interpretability
B)
To introduce nonlinearity in the model
C)
To handle multicollinearity among the independent variables
D)
To reduce overfitting of the model
The correct answer is B. 40.
What happens when interaction terms are included as regressors?(Olumide Martins)
A.
Allows the regression slope of one variable to depend on the value of another variable.
B.
Makes it so regressions involving logarithms are used to estimate proportional changes and elasticities
C.
Small changes in logarithms can be interpreted as proportional or percentage changes in a variable.
D.
Allows the unknown coefficients to be estimated by OLS
The correct answer is A. 41. A hypothesis test was conducted to test whether the population regression is linear. The test resulted in rejecting the null hypothesis at the 1% significance level. What can be concluded from this test?
A)The population regression is definitely a polynomial of degree up to 3.
B) There is no evidence to reject the null hypothesis that the population regression is linear.
C) There is evidence that the population regression is not linear.
Option C
42. What is the best way to identify the difference between cubic and linear log specification in identical sample?
a)X
b)Y
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
c)R
2
d)B0
Answer: C Because the R
2
logarithmic regression is 0.561 and for the cubic regression it is 0.555.R
2
has the slightest edge so it’s a way to identify the difference between cubic and linear log. 43. In terms of the effect of student-teacher ratio on student test scores in nonlinear functions, how
will the effect of a change in X1 affect Y1 as X is becoming increasingly larger and how is this
represented graphically?
a) As X1 is becoming larger, the change in Y1 due to a change in X1 should be bigger than
the change when X1 is of a lower value, and as X1 is increasing, the graph will become
steeper
b) As X1 is becoming larger, Y1 will respond less to a change in X1 and the graph will
become flatter
c) Up to a certain X value, Y1 will respond with a constant slope, and thereafter, the slope
will become much flatter, and a have lower constant coefficient
e)
None of these are correct
Correct answer: b
44. Given the regression function Yi=607.3+3.85×Income−0.0423×Income^2, where Yi is test
scores. By how many points do test scores change as income changes from $8000 to $12000?
Note: X is assumed to be in thousands of dollars
a) -10.91
b) 11.06
c) 12.02
d) 9.66
Correct answer: c
45. Regarding the preceding question and the regression model:
Yi=607.3+3.85×Income−0.0423×Income^2. Select the correct computation of the standard error
of ΔYˆ based on the predicted change when income changes from $8000 to $12000.
a) SE(ΔYˆ)=SE(βˆ1+21βˆ2),
b) SE(ΔYˆ)=SE(4βˆ1+βˆ2).
c) SE(ΔYˆ)=SE(βˆ1+21βˆ2).
d) SE(ΔYˆ)=SE(4βˆ1+80βˆ2).
e) None of the above
Correc answer: d
46. Identify the correct interacted regressor based on the following non-interacted regressor:
Yi=β0+β1D1i+β2D2i+ui.
Hint: Di1 and Di2 are binary variables.
a) Yi=β0+β1D1i+β2D2i+β3(D1i+D2i)+ui
b) Yi=β0+β1D1i+β2D2i+β3(D1i×D2i)+ui
c) Yi=β0+β1D1i+β2D2i+β4(D1i×D2i)+ui
d) Yi=β1D1i+β2D2i+β3(D1i×D2i)+ui
e) None of the above are correct
Correct answer: b
47. Given the following equation, Yi=β0+β1Xi+β2Di+ui, assume Xi is a continuous variable and Di is
a binary variable that can take on the values 0 or 1. Select the correct Y-axis intercepts when
Di=1 and when Di=0, and select the accurate description regarding the slope.
a) β0+β2, β0, the slope is the same whether Di=1 or 0, meaning slope=β1
b) β0+β1, the slope changes depending on whether Di=1 or 0, but should be equal to β1
c) β0+β2, β0 the slope is β2 whether Di=1 or 0
d) β0+β2, β0, the slope is the same whether Di=1 or 0, meaning slope=β2
Correct answer: a
48.
What would be the change in test scores if you increase the district income from 5 to 6 ($5,000 per capita to $6,000 per capita)? Where 0, 1, and 2 are the B
̂
B
̂
B
̂
OLS estimators equaling 607.3, 3.85, and .0423 respectively. a.
3.4 points
b.
2.4 points c.
2.50 points d.
3.73 points 49.
Which of the following is one of the five elements of the general approach to modeling nonlinear regression functions? a.
Estimate the effect on X of a change in Y b.
Testing the null hypothesis c.
Identify a possible linear relationship d.
Determine whether the nonlinear model improves upon a linear model
50. Let f(x) be a nonlinear function of a single independent variable x. Which of the following statements is true about the behavior of f(x) as x approaches infinity? A) f(x) approaches a finite limit B) f(x) approaches infinity
C) f(x) approaches negative infinity D) The behavior of f(x) cannot be determined without more information 51. Which of the following statements is an accurate interpretation of a transformation under the lin-log model? a.) A 1% change in X leads to 0.01 ^β1 change in Y. b.) A 1% change in Y leads to 1% change in X c.) 1 unit change in X leads to 100% change in Y d.) 1 unit change in X leads to ^β1X100% change in Y 52. Which of the following statements is true about the 2nd case of Logarithms in Regression about B1 interpretation? a.
2% change in X is associated with a change in Y of 0.2%B1 b.
5% change in X is associated with a change in Y of 50%B1 c.
2% change in X will not change in Y d.
A change in X by one unit is associated with a 100B1% change in Y
53. What is the degree of a polynomial regression model? A) The number of independent variables included in the model.
B) The highest power of the polynomial terms included in the model.
C) The number of observations used to estimate the model. D) The sum of the coefficients in the regression equation. 54. Which of the following is NOT an element of the nonlinear regression model? a) Plotting the estimated nonlinear regression b) Identifying a possible nonlinear relationship c) Determining the polynomial X d) Estimating the effect on Y of a change in X 55. How do we compute predicted values of Y when Y is in logarithms ?
a) The t-statistic on a coefficient on the cubic term is 0.118 so the null hypothesis would be true for the coefficient
b) If a dependent variable Y has been transformed by taking logarithms, the estimated regression can be used to compute directly the predicted value of ln(Y). While also trying to compute the predicted value of Y itself. In which it gives us the expected value of Yi being given to Xi of the function in the y values. c) A regression model has b1 is the effect on log earnings of having a college degree while there's also a increase in the student teacher ratio test scores d) A binary value that equals 1 for the student teacher ratio to be 20 or more and then
the binary variable will equal to 10% of English learners 56. How can polynomials in X, approximate the population regression? a) They are approximated by a quadratic, cubic, or higher-degree polynomial. b) Keeping the old regressor and defining a new dependent variable, while. c) Make use of many different varieties of the coefficients that provide percentage interpretations. d) Utilizing logarithmic transformations. 57. How can panel datas become useful ? a) Helps data availability b) Allows organizations to review how variables are changing over time c) Allows researchers to collect a large amount of data
d) A, B & C. Explanation: Panel data is a very useful data because with panel data we can college
large amounts of data,
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
58. Which two can make a regression line have a zero coefficient? a) Same Slope & Large Group Size b) Large group size & Opposite Slope c) Same Intercept & Opposite Slope d) Same Slope & Same Intercept 59. Which one is linear-log molde a)
ln(Y
i
) = β
0 + β
1
X
i +u
i b)
Y
i =β
0
+β
1 ln(X
i
)+u
i c)
ln(Y
i
) = β
0 + β
1
In(X
i
)+u
i d)None of above Explanation:
X is in logarithms, Y is not. In the linear-log model, a 1% change in X is associated with a change in Y of 0.01
β
1 60. Which type of slope does this population regression function have? (GRAPH)
a) Slope depends on the value of X
1
b) Constant slope
c) Slope depends on the value of X
2
d) Slope depends on the value of Y
61, Which statement is correct about elasticity?
a) 1% increase in X cause β
１
% decrease in Y.
b) 1% decrease in X cause β
１
% decrease in Y.
c) 1% increase in Y cause β
１
% increase in X.
d) 1% decrease in Y cause β
１
% decrease in X.
62. What are the two complementary approaches:
a) Polynomials in Y and X and logarithmic transformations.
b) Logarithm in Y and logarithmic transformation
c) Polynomials in X and Logarithmic transformations
d) None of the above
63. How many log regression specifications are there?
a) 2
b) 3
c) 4
d) 5
64. What happens in a log-log model?
a)1% change in X associated with Y
b) 1% change in X only
c) 1% change in Y only
d) none of the above
65. How dependent is the population casual effect on the regression function f ?
a) independent
b) dependent
c) both a and b
d) none of the above
66.
You are a social economic statistician researching the increase in LSAT scores by income for law-school bound students in 2023. You find that for familial incomes below $30,000. The average LSAT score is calculated to be 142; for $60,000, it is calculated as 152. For $90,000, the jump is slightly smaller at 159. At the $1,000,000 to $4,000,000 mark, the score jumps very slightly: from 169 to 171 between them. What should you conclude upon these findings?
a.
Our values grow significantly at first, then level off at a higher income, making this a linear regression function
b.
Our
values
grow
significantly
at
first,
then
level
off
at
a
higher
income,
making
this a non linear regression function
c.
Our values’ growth remain constant throughout our research, making this a non linear regression function
d.
Our values’ growth remains constant throughout our research, making this a linear regression function.
Answer: B
67.
A researcher is studying the relationship between a company's production output (X) and its total cost (Y). After analyzing the data, the researcher finds that a nonlinear regression model best fits the relationship. Which of the following functions best represents a form of a
nonlinear regression model used to estimate this relationship?
a)
Y = + α
X
β
b)
Y = X + α
β
c)
Y = e^( X)
α
β
d)
Y
=
X^2
α
+
X
β
Answer
d) Y = αX^2 + βX
68.
Through the use of the interaction term Xi * Di, the population regression line relating Yi and the continuous variable Xi can have a slope that depends on the
binary variable Di. Which of these CANNOT be a possibility in Interactions Between Binary and Continuous Variables
A.
Different intercepts, same slope
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
B.
Different intercepts and slopes
C.
Same intercept, different slopes
D.
Same
intercept,
Same slopes Answer: D
69.
Which of the following statements is true about the polynomial regression model?
A.
The polynomial regression model does not make any assumptions regarding the functional structure of the connection between the independent and dependent variables. It is a nonparametric model.
B.
The polynomial regression model should only be used with multicollinear data
C.
The
polynomial
regression
model
is
a
linear
model
that
allows
for
a
nonlinear relationship between the independent and dependent variables
D.
Only data with linear relationships are eligible for the polynomial regression model.
Answer: C.
70. What is the homoskedasticity-only F-statistic? A. A statistic that can be computed using both homoscedastic and heteroskedastic error terms B. A statistic that measures the improvement in the fit of the regression when the error term is homoskedastic C. A statistic that measures the improvement in the fit of the regression when the error term is heteroskedastic D. A statistic that is only valid when the error term is heteroskedastic 71. If the t-statistic is greater than the critical value in a hypothesis test what do we do with the null hypothesis? A. Accept B. Reject C. Ignore D. None of the Above Answer: B
72. A joint hypothesis specifies a value for how many coefficients? A. Only 1 B. Only 2 C. 2 or more D. none of the above
73. How do you compute the homoskedasticity only F-statistic? Using the: A. squared residual of the restricted regression B. the residual of the unrestricted regression C
. the sum of the squared residuals of the restricted and unrestricted residuals D. the squared residual of the unrestricted regression Answer. C 74. How should one choose control variables: A. knowledge of how data was collected B. expert judgement C. economic theory D. all of the above Answer: D
75. Which of the following statements below are true
The R² and R
̅
² tells you
a) whether the regressors are good at predicting, or “explaining,” the values of the
dependent variable in the sample of data on hand.
b) An included variable is statistically significant,
c) The regressors are a true cause of the dependent variable
d) There is omitted variable bias
76. You are a cashier at a Mcdonald’s restaurant. You notice that this month’s happy meal toys are
based on the Super Mario Bros Movie and would like to find a relationship between the sales of
the Mario Happy meal toys, the ticket sales of the Mario Bros movie, and total sales of the store
to evaluate if total sales increased due to the popularity of the Mario Bros movie. You collect
data for a year and calculate a F-statistic using a multiple regression analysis. Your resulting
numbers are an F-statistic of 12.45 and a p-value of 0.002. What conclusion can you draw from
this analysis?
A) There is no significant relationship between the factors at the 5% significance level
B) There is a significant relationship between the factors at the 5% significance level
C) This model should not be used to evaluate the impact of sales
D) These numbers prove that critics did not enjoy the Mario Bros movie
77. You are a resident of Pallet Town, a town known for its far larger than average Coca-Cola
consumption rates compared to the rest of the United States. You find that Pallet Town’s Coca
Cola consumption rates are a result of multiple factors exclusive to Pallet Town’s community,
including its poor nutritional education standards, larger than average amounts of fast food
chains and convenience stores per capita, and disproportionate amount of soda-based marketing
directed towards Pallet town. To prove a significant relationship between these items, which
statistic are you most likely to calculate.
A) T-statistic
B) F-statistic
C) P- Statistic
D) G-Statistic
78. You are calculating a homoskedasticity-only F-statistic. Your values are given below
SSR (restricted) = 8
SSR (unrestricted) =2
q (number of restrictions) =2
n (sample size) =52
K (number of regressors in an unrestricted regression) = 49
What is your F-statistic
A) 1.23
B) 2.56
C) 4.89
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
D) 3
79. Which of the following statements is true regarding the F-Statistic ?
A) The f-statistic is used to test for heteroscedasticity on a regression model.
B) The f-statistic is used to determine if the error term in a regression model
is normally
distributed.
C) The f-statistic is used to test the significance of individual coefficients in a regression
model
D) The f-statistic is used to test the overall significance of a regression model.
80. While completing a multi-regression project for your econometrics class,
your peer Mark
suggests that you should test your joint hypothesis by using the usual t-
statistics to test the
restrictions one at a time. Should you take Mark up on his suggestion, and what should be your
reasoning?
A) Yes, this is a perfectly reliable method of testing your hypothesis. Multi-
regressions are the
same as linear regressions so there should be no issue.
B) No, one at a time approaches are unreliable, as there are many special cases where e
t-statistics are uncorrelated and thus are independent in large samples.
C) Yes, you can take Mark’s suggestion and use the Bonferroni method; it will never fail.
D) No, Mark is seedy and you don’t trust him.
81. Which test is utilized to compare the variances of two independent samples?
a) t-test
b) Chi-square test
c) F-test
d) Wilcoxon rank-sum test
82) What is the confidence set for a joint confidence set
A) 90% with a 10% incorrect null hypothesis
B) 100% with 0% incorrect null hypothesis
C) 95% with 5% incorrect null hypothesis
D) 85% with 15% incorrect null hypothesis
83) What F-statistic has to combine t-statistics t1 and t2 using a specific formula?
a) The F-statistic with q = 2 restrictions
b) The F-statistic with q restrictions.
c) The F-statistic when q = 1.
d) The overall regression F-statistic
84) Which statement is not true about Interpreting the R2 and the Adjusted R2?
A) An increase in the R2 or adjusted R2 means that an added variable is statistically
significant.
B) A high R2 or adjusted R2 does not mean that the regressors are a true cause of the
dependent variable.
C) A high R2 or adjusted R2 does not mean that there is no omitted variable bias.
D) A high R2 or adjusted R2 does not necessarily mean that you have the most appropriate set
of regressors, nor does a low R2 or R2 necessarily mean that you have an inappropriate set of
regressors.
85) Which statement is incorrect regarding the interpretation of R2 and Adjusted R2 values?
A) A rise in R2 or adjusted R2 values indicates that the newly included variable is
statistically significant.
B) A high R2 or adjusted R2 value doesn't imply that the independent variables are
the true
causes of the dependent variable.
C) A high R2 or adjusted R2 value doesn't guarantee the absence of omitted variable bias.
D) High or low R2 or adjusted R2 values don't necessarily indicate the appropriateness or
inappropriateness of the chosen regressors.
86. What does the R^2 and Rbar^2 not tell you
a. included variable is not statistically significant b. regresses are a true cause of the independent variable
c. there is omitted variable bias
d. you have chosen the most appropriate set of regressors
87. Under the restriction model which two are we restricting…
A. Beta 1 and Beta 2
B. Ui and R^2
C. SE and STR
D. Beta 0 and Null Hypothesis
88. which one of the following is not an example of dynamic causal effect?
-The effect of consuming biotin gummies for hair growth in this month, in 6 months, and 1 year -
a. The effect of studying while playing music for 1 hour, 24 hours and 48 hours
b. The effect of increase in strawberries on strawberry milk in this year, next year and in 5 years
c. The effect of cats and dogs for the 12 years of cycle
d, because there isn't an effect on y of a change in x over time
89. Why do we use F statistics instead of t statistic in joint hypothesis? I) variables are not dependent on each other.
II) to reject the null hypothesis, at least one of the t’s needs to exceed 1.96.
III) the correlation between both the t’s become relevant.
IV) it is the joint significance of all the slope parameter estimates.
a) I only
b) I and not II
c) III and IV only d) All except I
90. Which nonlinear specification can be used to model the suspected difference in the effect on hours studied on test scores between students with high income and students with low income?
A) TestScore = β0 + β1 * Hours + β2 * Income + β3 * Hours * Income + ε
B) TestScore = β0 + β1 * ln(Hours) + β2 * ln(Income) + ε
C) TestScore = β0 + β1 * Hours + β2 * Income^2 + ε
D) TestScore = β0 + β1 * Hours^2 + β2 * Income + ε
91. What are some of the issues with implementing heteroskedasticity in OLS regressions?
A.
Biased estimates of regression dependent variables
A.
Inconsistent and biased estimates of regression coefficients
A.
Biased estimates of the independent variables
A.
Biased and inconsistent estimates of the intercept
92. We are given a dataset of income and expenditure and are told to estimate the relationship between them using a linear regression model. But, when plotted the data shows a non-linear relationship between the two variables, with the majority of the data points clustered at lower levels of income and expenditure, and a few data points scattered at higher levels. Which of the following statements below would be True about using a logarithmic transformation?
A) A logarithmic transformation is not useful when the data is clustered at lower levels.
B) A logarithmic transformation can only be used when both income and expenditure are negative.
C) A logarithmic transformation can only be used when the relationship between income and expenditure is already linear by nature.
D) A logarithmic transformation can be used to linearize the relationship between income and expenditure.
93. Which of these is not a possibility that occurs through the use of the interaction term Xi x Di, population regression line relating Yi, and the continuous variable Xi, and a slope depending on binary variable Di?
A.
Different intercepts, same slope / Yi =B0 +B1Xi +B2Di +ui;
A.
Different intercepts and slopes / Yi =B0 +B1Xi +B2Di +B3(Xi *Di)+ui; A.
Same intercept, different slopes / Yi =B0 +B1Xi +B2(Xi *Di)+ui.
A.
All of the above are all potential possibilities to occur
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
94. Of the five elements used in the general approach to modeling nonlinear regression functions taken in this chapter, which would apply the use of t-statistics and F-statistics to test the null hypothesis of the regression function being linear against the alternative hypothesis that it is linear?
A.
Identify a possible nonlinear relationship.
A.
Specify a nonlinear function, and estimate its parameters by OLS.
A.
Determine whether the nonlinear model improves upon a linear model.
A.
Plot the estimated nonlinear regression function.
A.
Estimate the effect on Y of a change in X.
95.
A research study conducted a joint test of three hypotheses related to the effectiveness of a new test. Which of the following
statements is correct?
a)
The null hypothesis was rejected, showing that all three hypotheses are supported by the data.
b)
The null hypothesis was accepted, showing that none of the hypotheses are supported by the data.
c)
The null hypothesis was rejected for two of the hypotheses, but not for the third.
d)
The
null
hypothesis
wasn’t
rejected,
showing
that
there
is
not
enough evidence to support the joint hypotheses.
96.
Which of the following statements is true regarding the interpretation of the intercept term in a linear-log population regression model?
A.
It
represents
the
value
of
the
dependent
variable
when
the
independent variable is zero
B.
It represents the slope of the regression line
C.
It represents the degree of the polynomial function
d.
It represents the coefficient of the highest power of the independent variable in the function
97.
If an error term is homoskedastic, then the resulting F-statistic is
a.
Homoskedastic
b.
Heteroskedastic
c.
Both a or b
d.
None of the above
98.
as the degrees of freedom go up what happens to the critical values for the
at any significance level?
a.
the critical value goes up as degrees of freedom increase
b)
the critical value will go up until it hits the maximum and then falls as degrees of freedom increase
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
c)
the critical value will go down until it hits the minimum and then increases as degrees of freedom increase
d)
the critical value will go down as degrees of freedom increase
99. In multiple regression, which of the following formulas may get the wrong F-statistic.?
1.
2.
3.
F = 4.
A. 1 and 2
B. 3 and 4
C. 2, 3 and 4
D.
1,
2,
3
and
4
Answer: D
100.
About tests of joint hypotheses, which of the following is correct?
A.
The more restrictions, the larger T-statistics will be.
B.
The more restrictions, the smaller T-statistics will be.
C.
The
more
restrictions,
the
higher
chance
to
reject.
D.
The more restrictions, the higher chance to accept.
101.
When conducting a joint hypothesis test in multiple regression, what is the null hypothesis typically testing? A) All coefficients in the model are equal to zero B) Two or more coefficients in the model are equal to each other
C) The intercept is equal to zero D) The error variance is equal to zero 102
. What is not included in a table of regression results?
A.
Estimated Regression Coefficients B.
Number of observations C.
Joint Hypothesis
D.
Measure of Fit 103. What is a factor of a table showing regression results? a) standard error
b) coefficient of a variable c) t-statistics d) scatter plot 104.
Which statistics should be used to test joint hypothesis?
A) f statistics b ) p statistic C) one at a time 105. Which of the following are solutions to address the fact that the size of a test is not always 5%, and depends on the correlation between two variables, and how are they implemented?
A. Using a different critical value in the procedure
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
B. Using a different test statistic designed to test both variables at once C. Both A and B D. None of the above 106. Which statement is NOT true?
a) A high R2 means that the included variables are statistically significant
b) A high R2 does not mean that you have eliminated omitted variable bias
c) A high R2 does not mean that you have unbiased estimator of a causal effect (β1)
d) A high R2 means that the regressors explain the variation
107. The size of the “common sense” test
a) It must be above 5%
b) It is 5%
c) It depends on the correlation between t
1 and t
2
d) None of the above
108. What are the two methods for testing single restrictions on multiple coefficients?
a) Rearrange the regression and perform the test directly
b) Disarrange the regression and perform the test directly
c) Arrange the regression and disperform the test
d) None of the above
109. What does the F-statistic test?
a) It test one part of the hypothesis
b) It tests an individual hypothesis
c) It tests all parts of a joint hypothesis at once
d) None of the above
110. What does a 95% confidence set do for coefficients?
a) Use a t-statistic
b) Contain the true population value of the coefficients in 95% of random samples
c) Generalize the coefficients of a confidence interval for one coefficient
d) None of the above
111. Base specification should contain
a) Estimates of interest change
b) Variables of primary interest
c) Control variables suggested by expert judgment and economic theory
d) Both b and c
112. A hypothesis that involves more than one restriction on the coefficients is called? 1.
a) A joint hypothesis
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
2.
b) A hypothesis test 3.
c) An F-Statistic 4.
d) A bonferroni test 113. How do we compute the P-value when using the F-statistic ?
a) When the q restrictions are tested with F-statistic at the null hypothesis
b) The P-Value of the F-statistic is computed using the larger sample sample Fq,∞ approximation to its distribution letting F to denote the value of F-
statistic being computed. c) When the F-statistic is at q=1 and then tested at a single regression and with a joint hypothesis d) For Homoscedasticity when it is computed with a simple formula of the sum squared residuals from two regressions which are restricted and unrestricted regressions 114. In which situation would the original formula for the joint hypothesis of β
1
= β
1,0 & β
2
= β
2,0 result in the below formula for P^t
1,
t
2 equaling zero? a) In small sample sizes, for both t
1 and t
2
. b) Both t
1 and t
2 are dependent c) Having a left/right skewed distribution d) In special cases under the null, t
1 and t
2 have independent standard normal distributions 115. What occurs when a omitted variable is both a determinant of Y and correlates with at least 1 included regressor ? a) OV bias arises in multiple regressions if the omitted variable satisfies conditions
b) Run a randomized controlled experiment to double check
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
c) Use panal data d) use the instrumental variable regression 116. How many methods can we use to test single restrictions on Multiple Coefficients? a)2 b)4 c)6 d)8 Let’s say, R^2
unrestricted
=0.6712 R^2
restricted
=0.4149 117. Restriction known as β0 and β3. The number of regressors in the unrestricted regression is 3, and the number of observations is 420, What is the homoscedastic-only F-statistic? A.162.14 B.138.07 C.6.35 D.27.5 118. Which of the following is true? A.
Omitted casual variables are the only variables used in measuring the omitted variable bias
b.
Decidingwhichvariablesareusedtoanalyzeadatasetha
sspecificorderand
guidelines that must be followed
c.
In order to test the restrictions of multiple coefficients the coefficients can be tested directly using STATA or by rearranging the regressors
d.
F-
statisticcanbemoreusefulforlargerdatasetsbecauseofi
tslargecritical values
119. Which statement is not true about f statistics? a. It is used to test a joint hypothesis about regression coefficients b.
Formulas for f statistic are integrated into modern regression software
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
c.
the joint null hypothesis has two restrictions which are b1=0 and b2=0 d.
The p-value of the f statistics can be computed using the small sample Fq,oo 120. Interpret the F-test for joint hypothesis testing ? = ( ?
2
?𝑛𝑟𝑒𝑠𝑡𝑟?𝑐𝑡𝑒? − ?
2
𝑟𝑒𝑠𝑡𝑟?𝑐𝑡𝑒?)/?
2
?𝑛𝑟𝑒𝑠𝑡𝑟?𝑐𝑡𝑒? * (𝑛 − ? − 1)/? Test score = ?
0 +
?
1STR + ?
2income +
?
3PctEL + ui Question : If the H0 are true, when restricting the regressors then X2 and X3 will have no impact. Also, how can we quantify this? Select all that is true. Consider a joint hypothesis with 2 restrictions: H0: ?
2=0and ?
3=0 Ha: ?
2≠0and ?
3≠0 A. WecanquantifythisbylookingattheR^2.Thisexplainsthefit. B. If F - statistic is small reject H0 C. When ?
1 and ?
3 has an effect on test scores we will reject H0 D. Yi=
?
0+
?
1X1+ui(Restricted model) Answer: A, C, D
121. In a study on the effect of physical exercise on stress levels researchers collected responses from a simple random sample of 200 individuals who completed a questionnaire. 50
of the questionnaires were misplaced and lost during a relocation of the research office. What is the impact of this event on the study's potential bias? A) The loss of questionnaires introduces significant bias, affecting the study's validity
B) The loss of questionnaires does not introduce any bias, as it is equivalent to having taken a simple random sample of 150 individuals
C) The loss of questionnaires introduces bias, but only if the sample size was initially below 150 D) The loss of questionnaires has no impact on the study, as the remaining sample size is still large enough to draw conclusions 122. Which of the following statements is true regarding confidence sets for multiple coefficients?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
A) Confidence sets for multiple coefficients are always wider than confidence intervals for single coefficients. B) Confidence sets for multiple coefficients are always narrower than confidence intervals for single coefficients. C) Confidence sets for multiple coefficients can be narrower or wider than confidence intervals for single coefficients depending on the size of the sample and the number of coefficients being estimated. D) Confidence sets for multiple coefficients are irrelevant in economics and are never used. 123. When joint testing for significance of β
1 and β
2, the null hypothesis is β
1= 0 and β
2=0. Which of these is not the alternate hypothesis? a) β
1
≠0, β
2=0 b) β
1= 0, β
2≠0 c) β
1≠0, β
2≠0 d Alternative hypothes is tests are done independently and separately. 124. Which of the following is one of the four pitfalls to guard against when
using the R2 or adjusted R2? a) The regressors are a true cause of the dependent variable b) It indicates that you have chosen the most appropriate set of regressors c) An increase in the R2 or adjusted R2 does not mean that an added variable is statistically significant d.
There necessarily is omitted variable bias 125. You have conducted an F-test to test the joint significance of two regression coefficients, B1 and B2. The null hypothesis is that both coefficients are equal to zero. The calculated F-statistic is 9.25, and the critical value at a significance level of 0.05 is 3.84. What can you conclude from this test?
A) Reject the null hypothesis and conclude that both coefficients are
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
significant at the 0.05 level. B) Fail to reject the null hypothesis and conclude that both coefficients are not significant at the 0.05 level. C) Reject the null hypothesis and conclude that at least one of the coefficients is significant at the 0.05 level.
D) Fail to reject the null hypothesis and conclude that at least one of the coefficients is significant at the 0.05 level. 126. Based on the below information, calculate the homoskedasticity-only F statistic and by using the homoskedasticity-only test define whether you accept or reject the hypothesis at 1% level R
2unrestricted= 0.5422 R
2restricted=0.5131 q=3
n=510 k=4 A) 8.05, reject B) 3.2, accept C) 10.7, reject D) 4.9, accept Explanation: The correct answer is C. Based on the calculation for homoskedasticity-only F statistic= [(0.5422-0.5131)/3] / (1-0.5422)/(510-4-
1) = 10.7. We will reject the hypothessis at the 1% level using the homoskedascity-only test because 10.7>4.61
. Therefore, 10.7 exceed the 1% critical value of 4.61 127. In a multiple regression model with two independent variables, X1 and X2, the null hypothesis is that both coefficients are equal to zero. If the calculated F-statistic is 6.58 and the critical value at a significance level of 0.10 is 2.11, what can you conclude from this test?
A) Reject the null hypothesis and conclude that both coefficients are significant at the 0.10 level B) Fail to reject the null hypothesis and conclude that both coefficients are not significant at the 0.10 level
C) Reject the null hypothesis and conclude that at least one of the coefficients is significant at the 0.10 level
D) Fail to reject the null hypothesis and conclude that at least one of the coefficients is significant at the 0.10 level 128.
Given the following equations for both unrestricted and restricted models, what is the number restrictions (q) in the restricted model and number of regressors (k) in the
unrestricted model? Unrestricted model (alternate hypothesis): B0 + B1STR + B2 Income + B3PctEL
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Restricted model (null hypothesis) : B0 + B2 Income + B3PctEL a)
Number of restrictions (q) : 3 , Number of regressors (k) 3 b)
Number of restrictions (q) : 2 , Number of regressors (k) 1 c)
Number of restrictions (q) : 1 , Number of regressors (k) 3 d)
Number of restrictions (q) : 1 , Number of regressors (k) 1 129.
The homoskedasticity-only F-statistic is given by the following formula [(SSR(restricted) - SSR(unrestricted)/q) / (SSR(unrestricted) / (n - k(unrestricted) - 1))],
Why F-statistic is always a non-negative value ? A.
SSR restricted >_ SSR unrestricted B. K-unrestricted is the number of regressors in the unrestricted regression C. R^(2)restricted are larger than the SSRrestricted numbers D. Q values are always positives
130.
Why is it required to use the f-statistic ? A) To test the joint null hypothesis B) To compute the p-value C) A and B D) None of above 131.
In the first regression, called the restricted regression, the null hypothesis is forced to be A)
False B)
True C)
Equal D)
0 132.
Fill in the blank: When referring to the F-statistic that has a sample distribution labeled as large, its distribution is the average of two __________ distributed squared normal variables that are random A) dependently B) independently C) chi-squared D) both b and c 133.
What is a 95% confidence interval for βi ? a.
The interval is the set of values for which a hypothesis test to the level of 5% cannot be rejected b.
The interval has a probability of 95% to contain the true value of βi. So in 95% of all samples that could be drawn, the confidence interval will cover the true value of βi. c.
Both A and B
d.
None of the Above 134. What is the recommended approach for deciding which variables belong in a regression model?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
a. Including all available variables to maximize the model's predictive power. b. Specifying a model based on prior reasoning and exploring alternative specifications. c. Only including variables that have a significant correlation with the dependent variable. d. Including variables based on the researcher's intuition.
135. How many coefficients restrictions does joint hypothesis imposes? a. Zero coefficient b. Two or more coefficients c. One coefficient d. None of the above
136. What is a “common sense” idea regarding the testing of joint hypotheses? a. Reject only if both t-statistics exceeds 1.96 b. Reject if either of the individual t-statistics exceeds 1.96 c. Reject only if both t-statistics exceeds 1.00 d. Reject if either of the individual t-statistics exceeds 1.00
137. Suppose we are testing a joint hypothesis in a multiple regression model where the restriction is that the coefficients on two variables are equal. Which of the following test statistics can be used to test this hypothesis? a. T-test b. F-test c. Chi-square test d. Z-test
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
138. The angry taxpayer hypothesizes that neither student-teacher ratio nor expenditure per pupil have an effect on student test scores. Please select the correct way of stating this hypotheses. a) H0: β1=0 and β2=0 vs. H1: β1≠0 and / or β2≠0. b) H0: β1=0 or β2=0 vs. H1: β1≠0 and / or β2≠0. c) H0: β1≠0 and β2≠0 vs. H1: β1=0 and / or β2=0. d) H0: β1>0 and β2>0 vs. H1: β1<=0 and / or β2<=0. 139. Given that R2unrestricted=0.3677, R2restricted=0.4561, number of restrictions q=2, the number of regressors in the unrestricted regression is k=3, and the number of observations is n=420, calculate the homoskedacity-only F-statstic. e.
-29.08
b) -58.16 c) -29.15 d) -18.39 Correct answer: a
Explaination: Given the formula F=((R2unrestricted−R2restricted)/q)/
((1−R2unrestricted)/(n−Kunrestricted−1)), -29.08 is the correct f-statstic. 140. Suppose we want to test H0: β1=0 and β2=0 against H1: β1≠0 and /or β2≠0 in the following regression: Yi=b0+b1x1i+b2x2i+b3x3i+b4x4i+b5x5i+ui. Please select what the correct unrestricted model and restricted model would be. a) Yi=b0+b1x1i+b2x2i+b3x3i+b4x4i+b5x5i+ui, Yi=b1x1i+b2x2i+b3x3i+b4x4i+b5x5i b) Yi=b0+b1x1i+b2x2i+b3x3i+b4x4i+b5x5i, Yi=b0+b2x2i+b3x3i+b4x4i c) Yi=b0+b1x1i+b2x2i+b3x3i+b4x4i+b5x5i+ui, Yi=b0+b3x3i+b4x4i+b5x5i+ui d) Yi=b0+b1x1i+b2x2i+b3x3i+b4x4i+b5x5i+ui, Yi=b3x3i+b4x4i+b5x5i+ui 141. Why is it ineffective and unreliable to test individual coefficients one at a time? a) The rejection probability under the null hypothesis does not equal the desired
significance level b) Each t-statistic has a variance equal to 1 and mean equal to zero c) The rejection rate will be very high and we will not reject the null hypothesis enough d) The rejection probability under the null hypothesis equals the desired significance level, but requires a lot of effort and is inefficient 142. How does F-statistics relate to R-squared in linear regression? a) F-statistics is not related at all to R-squared in linear regression
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
b) F-statistics test for a critical value depending on the significance level, similarly, R-squared tests for critical values c) F-statistics are computed to test the overall significance of a linear regression model, likewise, R-squared measures to what extent the variance in the dependent variable is explained by the independent variable. d) F-statistics are used to test the overall accuracy of a linear regression model, while R-squared is used to test the variance in the Y that is explained by the regressor e)
Both C and D 143. How can omitted variable bias be reduced in a regression model? a.
By introducing more meaningless variables. b.
By reducing the number of observations in the sample. c.
By removing meaningless variables from the model. d.
By increasing the sample size in the model. 144. What is regression not used for?
a. For predictions e.
To estimate casual effects f.
Summarize data g.
To find errors 145. Which of the following statements best describes omitted variable bias
in a regression model? a. It occurs when there is correlation between the dependent variable and one or more independent variables. b. It occurs when the independent variables in the regression model are not measured accurately. c. It occurs when a relevant independent variable is left out of the regression model. d. It occurs when the sample size used in the regression model is too small
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
146. How does the OLS estimator of the effect of interest, b1 is unbiased? a.
If it’s expected value matches the parameter of the population. b.
If the value is always equal to the parameter value. c.
If the value is always the different in repeated sampling of the sample
size. d.
If it’s expected value doesn’t matches the parameter of the population. 147. Which of the following is not one of the cases in the three log regression specifications ? a. Linear-log
b. Log-linear
c. Nonlinear-log d. Log-log 148. Models that are nonlinear in one or more parameters can be estimated by: a.
OLS but not by nonlinear least squares b.
Nonlinear least squares and by OLS c.
Nonlinear least squares but not by OLS d.
OLS and by nonlinear least squares 149. Which of the following is a common approach to model nonlinear relationships with a single independent variable in a multiple regression model? A) Polynomial transformations B) Exponential smoothing
C) Principal component analysis D) Factor analysis 150. Logarithmic Transformations are used in which terms? 1.
A) quadratics 2.
B) Percentages 3.
C) Cubics
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
4.
D) Regular Numbers Answer B) Percentages 151. Not always an error, imperfect multicollinearity is just a characteristic of what? A) OLS
B) Thedata
C) The question we’re answering
D) All of the above 152. Which is not true for a good control variable? A) Holdingconstantcontrolvariables,thevariableofinterestisrandomlyassigned. B) The control variable should be highly correlated with other factors affecting Y. C) f W is a control variable. If W is included in the regressor equation E( u|x, w)=0, but E(u|x) ≠ 0 D) They provide the researcher with control over the independent variable. 153. How can we avoid dummy variable traps that lead to high multicollinearity? A) add one less variable than the total number of categories (n-1) B) Includethey-interceptbeta0
C) add one more variable then the total number of categories (n+1) D) Use the actual total number of categories 154.
which is NOT a least squares 4 assumptions for causal inference in Multiple regression?
a.
b.
Are i.i.d.
c.
Large
outliers
are
common
but
part
of
the
distribution
d.
There is no perfect multicollinearity
155.
Which of the following statements best describes the Omitted Variable Bias?
a.
It occurs when a variable that is included in the model is not relevant to the outcome being
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
studied
b.
It
occurs
when
a
variable
that
is
not
included
in
the
model
is
correlated
with both the dependent variable and one or more of the independent variables
c.
It occurs when a variable that is included in the model is
correlated with both the dependent variable and one or
more of the independent variables
E.
It occurs when a variable that is not included in the model is not relevant to the
outcome being studied
156.
Which of the following is true about the OLS estimator in multiple regression:
a)
It
gives
the
exact
solution
to
the
problem
of
minimizing
the
sum
of
squared residuals.
b)
It always provides unbiased estimates of the population regression coefficients.
c)
It assumes that the errors are normally distributed.
d)
It can be expressed as a linear combination of the dependent variable and the independent variables.
157.
In a multiple regression model, the least squares estimator is derived
by
a.
minimizing the sum of squared prediction mistakes.
b.
setting the sum of squared errors equal to zero.
c.
minimizing the absolute difference of the residuals.
d.
forcing the smallest distance between the actual and fitted values.
158.
If W is an effective control variable in ? = ?
+ ? ? + ? ? + ?
, which of the following is
?
1
2
correct
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
A.
? = 0
B. 𝐸(? | ? ) = 0
?
?
C. 𝐸(? |? , ? ) = 0
?
?
?
D.
None
of
above
158
When more control variables are added to the regression:
a.
the adjusted R2 is raised and degrees of freedom are gained.
b.
the adjusted R2 is reduced and we degrees of freedom remain the same.
c.
the adjusted R2 is reduced and degrees of freedom are gained.
d.
the
adjusted
R2
is
raised
and
degrees
of
freedom
are
lost.
159
How can we determine what variables will have the most significant influence on a dependent variable in a multiple regression model?
a.
We can determine by looking at the p-values of the each variable
a.
We can determine by looking at the r-squared values
a.
We can determine by looking for the t-statistics of the variables
a.
We can determine by looking for the intercept of the variables
160 Assume a multiple linear regression model with two regressors. Each regressor is considered separate in a simple linear regression model, but both regressors are significantly related to the dependent variable. When both regressors are included in a multiple linear regression model, one of the regressors becomes insignificant. What could be a reason for this?
a) The two regressors are perfectly correlated, and including both in the multiple linear regression model creates multicollinearity.
b) The multiple linear regression model has a higher residual variance compared to the simple linear regression models.
c) The two regressors have a high degree of collinearity, causing one of the regressors to lose its significance when both are included in the model.
d) The two regressors are independent, and their combined effect cancels each other out.
161 What are the interchangeable statements about what makes for an effective control variable:
I.
An effective control variable is one which, when included in the regression, makes the error term uncorrelated with the variable of interest.
I.
Holding constant the control variable(s), the variable of interest is “as if ” randomly assigned.
I.
Among individuals (entities) with the same value of the control variable(s), the variable of interest is uncorrelated with the omitted determinants of Y 1.
1 and 2
2.
3 and 2
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
3.
1 and 3
4.
All of the above
5.
None of the above
162 Imagine you are a researcher studying the effects of income level and the level of happiness of the individual. You collect data on the income and their self-reported happiness level. However that is all you collect, you don't dive into gender or their potential support networks. What issue may your run into / might arise as you continue your research?
A.
Selection Bias
A.
Ommited variable bias
A.
Sampling Bias
A.
Measurement Bias
163 Which of the following is not a Least Squares Assumption for Causal Inference in Multiple Regression?
a. Large Outliers Are likely
b. Perfect Multicollinearity is ruled out
c. The Conditional Distribution of ui Given X1i , X2i , . . . , Xki Has a Mean of 0
d. (X1i , . . . , Xki, Yi), i = 1, n, are independently and identically distributed random variables
e. None of the above
164 What is the main difference we see between R-squared and adjusted R-squared?
a.
the adjusted r-squared considers the number of independent variables used for anticipating the target variable, while r-squared does not
a.
r-squared considers the number of independent variables used for anticipating the target variable, while adjusted r-squared does not
a.
r-squared is able to decrease with the addition of a new independent variable, while adjusted r-squared is unable to
a.
r-squared and adjusted r-squared are one and the same, and can be used interchangeably
165 The omitted variable bias occurs if which conditions are met:
I. The omitted variable is correlated with the included regressor
II. The omitted variable is a determinant of the dependent variable.
III. The omitted variable is present if ?
is greater than 1 2
a. I only
b. I and II
c. I, II, and III
d. I and III
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
166 The population of Pallet town consumes significantly more Coca-Cola than the rest of the
state. After conducting research on the phenomenon, you discover that Pallet town ranks 41st
out of 50 towns in the state regarding public nutritional education. You base
your regression
analysis on this fact and conclude that Pallet Town’s high rate of Coca-Cola consumption is
attributed to its low standards in public health education. Before publishing your research, you find that Pallet Town also contains a significantly large amount of 7-eleven convenience stores, CVS pharmacies, and Mcdonald's restaurants per capita compared to other towns within the state. This may prove to have a large effect on Coca-Cola consumption rates within the town, but you are running late on your deadline and decide to publish your findings anyway, without accounting for Pallet’s Town's unusual amount of Coca-Cola selling franchisees. Which of these terms would your findings most likely exhibit?
A) Omitted Variable Bias
B) Multiple Regression Analysis
C) Raider Foxtrot analysis
D) Sierra Demographic Examination
167 Continuing with the information presented in question 2, your findings are rejected from
publishing, and you decide to incorporate the new information regarding franchisee rates within
Pallet Town in your regression analysis. You calculate two estimated OLS regression lines: one
from your original estimate and another containing your new info. (RNK= Ranking of
Nutritional Education within state) (ConCC=Convenience of Coca Cola)
Which
Which conclusions can you draw when comparing your old OLS line of
regression to your new
OLS line of regression.
A) The difference between the coefficient of rank between the two estimators exists as
ConCC is held constant only in multiple-regressor regression model, decreasing the
coefficient of rank in the multiple regression model
B) The difference between the coefficient of rank between the two estimators exists as
ConCC is held constant only in singular-regressor regression model, decreasing the
coefficient of rank in the multiple regression model
C) From the perspective of casual interference, the original estimate is strongly subject to
Omitted Variable Bias
D) Both A and C
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
E) Both B and C
168 In a multiple regression equation with y as the dependent variable and x1 and x2 as the
independent variables, the following results were obtained:
Observed value of y=23
Predicted value of y=11
variance of residuals = 7.7
Compute the value of standardized residual for the given values.
Choose an answer
A)The value of standardized residual is 3.18.
B) The value of standardized residual is 17.26
C) The value of standardized residual is 4.33.
D) The value of standardized residual is 2.38
169 Regarding econometric models, perfect multicollinearity occurs when:
A) The model’s residuals are not normally distributed
B) There are insufficient observations in the model to reliably estimate the coefficients
C) Two or more independent variables are perfectly correlated with
each other
D) There is no linear relationship between the dependent variable and any of the independent
variables.
170 In terms of the population regression function, you wish to compare two
observations
containing a change within one of the X variables, holding another X variable as fixed. After
subtracting the model of your first observation from your second observation model. You intend
to isolate the coefficient (B1) of your changed X variable, holding the other X variable constant.
Which of the terms below best describes this practice.
A
) Measuring the partial effect on X1 holding X2 fixed
B) Locating Omitted Variable Bias on X1 holding X2 fixed
C) Calculating standardized residual on X1 holding X2 fixed
D) determinant of the dependent variable on X1 holding X2 fixed
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
171 Which of the following is NOT an assumption for Causal Inference in Multiple Regression? a) When the random variables of ?
1?
, ?
2?
,
.....
, ?
??
, ?
? are independently and identically
distributed. b) A perfect Multicollinearity. c) The conditional distribution of ?
? given ?
1?
, ?
2?
,
.....
, ?
?? has a mean of 0. d) Large Outliers are Unlikely. 172 What is Omitted Variable Bias and how do we use it in the first least square assumption ? . a) The multiple regression model extends the single variance regression model to include its additional variables to use for causal inference for the regressions themselves b) The population regression line that's in the equation for the relationship between Y and X^1 and X^2 that will hold the population and determine the average c) Omitted variable bias is when there are 2 conditions that are true in which there is a correlation that has an included regressor and it's also determinant of the dependent variable. Omitted variable bias is used in the first least square assumption by the first least squares assumption for causal inference that E1ui Xi2 = 0 then followed by ui in the linear regression with then a single regressor that represents all the factors of the error terms d) The coefficient of β
1 shows that there is a difference in predicted values of the Y regression in which there is a partial effect from Y to X^1 to the expected value of Yi 173 What makes an effective control variable?
a) Variables of interest act as if randomly assigned, because the controlled variables are held constant. b.
Within entities holding the same value of the control variables, the interest variable is uncorrelated with omitted determinants of Y. c) Variable that have regression included, makes error term uncorrelated with variable of interest.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
d) All the above 174 What does it mean when a relation between X and Y is nonlinear? a) linear regression is mis-specified. b) estimators of the effect on Y and X are biased. c) The solution is to estimate regression function that is nonlinear in X. d) A,B&C 175 What is not one of the three variables that are needed to meet the conditional mean independence regression model to work ? a) B1 has a causal interpretation b) B3 Biased c) B1 UnBiased d) B2 does not in general estimate a causal effect 176 In the multiple regression model which one is right ?
a. Y
i is i th observation on the dependent variable b. u
i is the error term c. β
1 is the slope coefficient on X
1 or the coefficient on X
1 d. β
0 is the dependent variable
177 What are good conditions for an adjusted R2? I. If W is an a control variable, and is included in the regression equation. II. holding constant control variables, the variable interest in case if randomly assigned. III. The control variable should not be correlated with the other factors affecting Y. A.I & III.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
B.II & I C. I, II, III D. II & III
178 What assumptions are true for causal inferences in multiple regression I) the conditional distribution of ui given x1i,…xki has a mean greater than 0 II) large outliers are unlikely III) there is no perfect multicollinearity a. I and II b. II and III c. I and III d. none of the above
179 In the equation, Test Score = B0 + B1STR+ B2PctEL + B3LchPct + ui, what happens to ui: A. ui increases if we increase STR B. we must find the t-statistic to determine ui C. nothing D. ui decreases as test score increases
180 What conditions are required for a good control variable: a
) the control variables should not be correlated with other factors affecting Y. b) Holding constant control variables, the variable of interest is Not randomly assigned. c) E (u/x) =\ not equal to 0.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
d) Add more variables and reduce the adjusted R^2.
181 Which of the following statements is true about nonlinear regression functions? A) Nonlinear regression functions always fit the data better than linear regression functions. B) Nonlinear regression functions are only useful for modeling complex relationships between variables. C) Nonlinear regression functions can be difficult to interpret and require specialized knowledge to use effectively. D) Nonlinear regression functions assume a linear relationship between the independent and dependent variables.
182 Which of the following statements about multicollinearity is true? A) Multicollinearity occurs when there is a strong positive or negative correlation between two or more predictor variables in a regression model. B) Multicollinearity always results in inaccurate coefficient estimates and should be avoided at all costs. C
) A common method for detecting multicollinearity is to calculate the variance inflation factor (VIF) for each predictor variable.
D) The only solution to multicollinearity is to remove one or more predictor variables from the regression model
183 Which of the following statements about the dummy variable trap is true? A. The dummy variable trap occurs when a regression model includes too many dummy variables. B. The dummy variable trap occurs when a regression model includes a constant term and at least one dummy variable that takes on the value of 1 for every observation in the sample. C. The dummy variable trap occurs when a regression model includes only continuous variables and no categorical variables. D. The dummy variable trap occurs when a regression model includes a constant term and at least one dummy variable that takes on the value of 0
for every observation in the sample.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
184 What are ideal randomized controlled variables most beneficial for? A. Trends/Patterns B. Casual Relationships C. Specific data about a company’s future projections D. Class results/averages of exam.
185 Which of the following statements is true about the least square assumption in economics? A. The least square assumption requires that the error term has a mean of zero. B. The least square assumption requires that the error term is normally distributed. C. The least square assumption requires that the error term has a constant variance (homoscedasticity). D. The least square assumption requires that the error term is always positive.
186 Why must we use an adjusted R2 when adding multiple regressors? (Olumide Martins) A. The original R2 continues to increase as you add more regressors B. The original R2 continues to decrease as you add more regressors C. The original R2 becomes biased and not consistent as you add more regressors D. The original R2 becomes biased and consistent as you add more regressors
187 Which of the following is a measure of fit for a multiple regression model?
A. R-squared B. Standard error of the estimate
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
C. Confidence interval D. F-statistic
188 What happens to the R^2 when another regressor is added? A) Always increases B) Always decreases C) Stays constant D) Resets to zero
189 Omitted variable bias is larger or smaller depends on the correlation between- ●
Regressor and the error term ●
Test score and student teacher ratio ●
Higher or lower test score ●
The error term and the variance
190 Which of the following statements is most likely true based on the given information? A) The effect of X on Y is constant regardless of the value of X. B) The effect of X on Y depends on the value of Y, not on the value of X. C) The effect of X on Y depends on the value of X, not on the value of Y. D) The effect of X on Y depends on the starting income level of individuals in a given population.
191 What happens to Adjusted R2 when adding a new variable? a) 4(n-k-1), 1(n-1/n-k-1), JRZ b) 4(n-k-1), k(n-1/n-k-1), IRZ c) 1(n-k-1), 1 (n-1/n-k-1), TRZ d) 1(n-k-1), 1(n-1/n-k-1), IRZ
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
192 Omitted variable bias occurs when a)The omitted variable is correlated with the included regressor b)The omitted variable is correlated with the included regressor and the omitted variable is a determinant of the dependent variable. c)The omitted variable is a determinant of the dependent variable. d)None of the above
193 An increase in the adjusted R-squared means? A. Adding a variable actually improves the fit of the model B. When a new variable is added to a model R-squared can increase or decrease C.Adjusted R-squared is lower than the value of R-squared. D. R-squared only can increase
194 When two or more of the regressors are highly correlated when it’s a linear function of the regressor that's highly correlated with another regressor. A) Imperfect multicollinearity B) Dummy Variable Trap C) Perfect multicollinearity D) None of above
195 A Dummy Variable is ? a) A variable that is coded 1 or 0 only b) Represent qualitative information through categorical variables c) Conditional mean of the outcome variables for each category d) All of the Above
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
196 When referring to an effective control variable, which one of the following is incorrect ? A) While in the regression, the variable of interest is not correlated with the error term B) The variables of interest can be labeled as ‘as if’ which are randomly assigned while there is a hold on control variables C) When the entries match the value of control variables, the variable of interest is uncorrelated with the omitted determinants D) None of the above are incorrect
197 How does the interpretation of the slope coefficient (B1) change? a) It remains the same across all cases of transformation.
b) It differs between the dependent and independent variables.
c) It differs depending on the specific case of transformation.
d) It differs between different levels of statistical significance 198 A researcher is conducting a multiple regression analysis to estimate the relationship between a dependent variable Y and several independent variables, X1, X2, and X3. Which of the following statements is true about the Ordinary Least Squares (OLS) method? A) OLS is a statistical technique used to estimate the parameters of a linear regression model.
B) OLS assumes that the residuals are normally distributed.
C) OLS can be used to estimate the relationship between Y and X1, while ignoring the effects of X2 and X3. D) OLS is used to estimate the intercept and slopes of a nonlinear regression model.
199 Which least squares assumption for causal inference can be applied to multiple regression, but not with linear regression with one variable? a.
The conditional distribution of u given X has mean zero, that is, E(u|X1i=x1..,Xki=xk)=0 b.
Large outliers are rare fourth and have finite moments c.
Independently and identically distributed data d.
There is no perfect multicollinearity 200 Which statement is NOT true about multicollinearity? 1.
Perfectmulticollinearityariseswhenoneoftheregressorsisaperfectlinearcombination
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
of the other regressors. 2.
Perfectmulticollinearityariseswhenamistakehasbeenmadeinspecifyingthe regression. 3.
Imperfectmulticollinearityariseswhenoneoftheregressorsisveryhighly correlated, and also perfectly correlated with other regressors. 4.
Perfectmulticollinearityariseswhenmultiplebinary,ordummy,variablesareusedas regressors. 201 Having the following information: Pink = D1 = {0,1} Red= D2 = {0,1} Green= D3 = {0,1} Yellow= D4 = {0,1} Yi= B1D1 +B2D2 + B3D3 + B4D4 + Ei Where, D1=0, D2=0, D3=0, D4=1 Calculate the Difference between Pink and Green: a) B4 -1 b) B3-B1 c) B1-B3 d) 1
202 What is the solution to perfect multicollinearity in a regression model? a. Dropping one of the correlated predictors. b. Transforming one or more of the correlated predictors. c. Combining two or more of the correlated predictors into a single predictor. d. None of the above.
203 Which of the following is true about the dummy variable trap?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
A. It occurs when all the dummy variables in a particular categorization are included in a regression model. B. It occurs when one of the dummy variables can be perfectly correlated by the other dummy variables included to specify the category. C. It occurs when the sample size is too large for the number of variables in the model. D. It occurs when the sample size is too small for the number of variables in
the model. 204 Which of the following statements is true about the presence of multicollinearity in a regression model? a) it increases the variance which reduces the accuracy of estimated values b) it decreases the variance which increases the accuracy of the estimated values c) it increases the variances which increases the accurate of the estimated values d) it decreases the variance which reduces the accuracy of the estimated values
205 Which of the following is true about using the adjusted R2? a) Is the fraction of the sample variance of Yi b) Increases whenever a regressor is added unless the estimated coefficient
is 0 c) Rapidly decreases when a new variable is adde
d) It quantifies the extent to which the regressors explain the variation in the dependent variable
206 Which of the following is not true about the adjusted R2 formula? a) As k increases, n-k-1 decreases b) As you limit the amount of regressors, n-k-1 overall increases
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
c) It is always less than or equal to the original R2 formula. d) It serves as an encouragement to include more independent variables in the R2 formula.
207 In the presence of omitted variables bias, suppose the school directors of California hire additional teachers to lower the STR by 2, and the test scores improve, albeit the improvement is less than expected, what could have possibly caused this? a) The estimated coefficient ?
1 is a large value, and the true coefficient must also have been large, thus it is simply coincidence. b) The estimated coeffcient ?
1 is a significant value, meaning the lower STR
should have an effect on student test scores, however, there were omitted variables, such as all the students were perfectly fluent in english, causing the true coefficient to be zero. c) The estimated coefficient ?
1 was a large value, however, it had failed to account for different omitted variables, meaning the true coefficient was low or near zero, hence the true effect of the lower STR was less significant than expected. d) The estimated coefficient ?
1 was a large value and the improvement was
lower than expected because there were several omitted variables that were not taking into account, causing the true coefficient to be negative.
208 Continuing with the preceding question, suppose the omitted variable that caused the lower-than-expected improvement was the presence of english-learners, meaning the class size was correlated with the fraction of english-learners. What would be the best solution to this problem? a) By evaluating each class, and ensure that all classes have zero english-
learners, the class size must now be the only independent variable that will affect the dependent variable, thus the problem does not exists anymore. b) By creating a subset of districts with the same fraction of english-learners, the class size will not be correlated with the amount of english-learners. Since the former omitted variable will now be held constant, the class size effect on test scores will be more accurate.
c) By creating a subset of districts with the same fraction of english-
learners, the class size will still be correlated with the amount of english-
learners, and the omitted variable will be held constant, thus estimated and
true coefficient should be closer in value. e)
None of the above
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
209 When a second regressor is added to a regression line, the estimated value (B1^), meaning the coefficient, of the first regressor might decrease in value, why might this occur? a) Due to the fact that B1^ must decrease in value as soon as a second regressor is introduced b) The second (added) regressor might explain some of the variation in the dependent variable c) The second (added) regressor will explain some of the variation in the dependent variable, automatically causing the estimated value of B1^ to decrease d) Because in the multiple regression, the second regressor is held constant, however, in the single-regressor regression, the second regressor is not held constant. Additionally, the single-regressor regression might be subject to omitted-variable bias.
210 Why is perfect multicollinearity normally a “bad thing”? a) In the case of perfect multicollinearity, one can not determine the marginal effect of one of the regressors (variables) by holding the other constant b) Perfect multicollinearity causes the multiple-regressor regression line to have zero prediction ability c) Both a and b d) Perfect multicollinearity, just like imperfect multicollinearity, means that two variables are slightly correlated
211 As more regressors are added to a regression model, what value will R-
squared approach? Assume all regressors have an estimated coefficient larger than 0 a) 0.99 b) 0 c) 1 d) Infinite Correct answer: c
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Related Documents
Recommended textbooks for you
Managerial Economics: Applications, Strategies an...
Economics
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Cengage Learning
Microeconomics: Private and Public Choice (MindTa...
Economics
ISBN:9781305506893
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:Cengage Learning
Economics: Private and Public Choice (MindTap Cou...
Economics
ISBN:9781305506725
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:Cengage Learning
Macroeconomics: Private and Public Choice (MindTa...
Economics
ISBN:9781305506756
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:Cengage Learning
Recommended textbooks for you
- Managerial Economics: Applications, Strategies an...EconomicsISBN:9781305506381Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. HarrisPublisher:Cengage LearningManagerial Economics: A Problem Solving ApproachEconomicsISBN:9781337106665Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike ShorPublisher:Cengage Learning
- Microeconomics: Private and Public Choice (MindTa...EconomicsISBN:9781305506893Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. MacphersonPublisher:Cengage LearningEconomics: Private and Public Choice (MindTap Cou...EconomicsISBN:9781305506725Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. MacphersonPublisher:Cengage LearningMacroeconomics: Private and Public Choice (MindTa...EconomicsISBN:9781305506756Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. MacphersonPublisher:Cengage Learning
Managerial Economics: Applications, Strategies an...
Economics
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Cengage Learning
Microeconomics: Private and Public Choice (MindTa...
Economics
ISBN:9781305506893
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:Cengage Learning
Economics: Private and Public Choice (MindTap Cou...
Economics
ISBN:9781305506725
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:Cengage Learning
Macroeconomics: Private and Public Choice (MindTa...
Economics
ISBN:9781305506756
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:Cengage Learning