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Jomo Kenyatta University of Agriculture and Technology *
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HPS 2112
Subject
Statistics
Date
Nov 24, 2024
Type
docx
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Uploaded by erickuria55
1
Research and Analysis
Student’s Name
Institutional Affiliation
Course
Instructor
Due Date
2
Research and Analysis
M9-1
Dependent Variable
Scales Sold
Independent Variable
Months employed
Observations
14+1 =15
Intercept coefficient
113.7453874
Independent variable
coefficient
2.367463621
Regression Model
Scales sold= 113.74 + 2.37 X months employed
R-square
0.790138792
Adjusted R-square
0.773995622
Intercept P-value
0.000108415
Independent variable
P-value
9.39543 x
10
−
6
Your Interpretations
and Analyses
1.
The figure for P. Value of independent variable is less
than 0.05. Therefore, the regression coefficient is
deductively significant
2.
Considering the F. statistic is considerably large, the
model is viewed as having fitted well.
3.
A unit change in the “Months employed” will result in
a change in “scales sold” by 2.37
M9-2
Dependent Variable
Sales
Independent Variable
1
Price
Independent Variable
2
Advertising expenditure
Independent Variable
3
No data provided
Observations
24+1 = 25
Intercept coefficient
275.83333
Coefficient of
Independent variable
1
175
Coefficient of
Independent variable
2
19.68
3
Coefficient of
Independent variable
3
No data is provided
Regression Model
Sales= 275.83 +175 x price + 19.68 x Advertising expenditure
R-square
0.978108766
Adjusted R-square
0.974825081
Intercept P-value
0.023898351
P-value of
Independent variable
1
0.0008316
P-value of
Independent variable
2
1.1263 x
10
−
11
P-value of
Independent variable
3
Data is inexistent
Your Interpretations
and Analyses
1.
The value for p-value of all independent variables is
less than 0.05. as such, the regression coefficient is
perceivably significant.
2.
The f-statistic is sufficiently large. This data suggests
that the model if fitted well.
M9-3
Dependent Variable
Credit card charges
Independent Variable
1
Annual income
Independent Variable
2
Household size
Independent Variable
3
Years of post high-school education
Observations
2,999+1 = 3000
Intercept coefficient
2119.600282
Coefficient of
Independent variable
1
121.3384676
Coefficient of
Independent variable
2
528.0996852
Coefficient of
Independent variable
3
535.3593516
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4
Regression Model
Credit card charges= 2119.60 + 121.34 x annual income +
528.1 x household size + (-535.36) x years of post high-school
education
R-square
0.363202867
Adjusted R-square
0.362565219
Intercept P-value
2.27497 x
10
−
10
P-value of
Independent variable
1
5.4905 x
10
−
262
P-value of
Independent variable
2
4.29401 x
10
−
34
P-value of
Independent variable
3
1.15792 x
10
19
Your Interpretations
and Analyses
1.
The value for p-value of all independent variables is
less than 0.05. as such, the regression coefficient is
perceivably significant.
2.
The f-statistic is sufficiently large. This data suggests
that the model if fitted well.
Related Documents
Related Questions
I have no idea how to fill in the blank in this regression output... please help
arrow_forward
Interpreting Simple Linear Regression
1. Linear correlation coefficient r = 0.794556
2. Coefficient of Determination ( r square) 0.631319
3. Standard Error of the estimate = 12.9668
4. SSR (Explained variation) = 5182.41
5. SSE ( Unexplained variation) = 3026.49
6. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523
7. Level of Significance = 0.1
8. Critical Value= 0.378419
Question : Based on the linear correlation coefficient (r) in Line 1, the variables(X,Y) are positively correlated
True
False
arrow_forward
Interpreting Simple Linear Regression
1. Linear correlation coefficient r = 0.794556
2. Coefficient of Determination ( r square) 0.631319
3. Standard Error of the estimate = 12.9668
4. SSR (Explained variation) = 5182.41
5. SSE ( Unexplained variation) = 3026.49
6. SST = 8208.90
7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523
8. Level of Significance = 0.1
9. Critical Value= 0.378419
10. t test = 0.794556
Question
What is meant by a hypothesis? State the hypothesis in this example?
A hypothesis is a claim about the correlation between the Y and X variables in the population under study:
There are two hypothesis (claims)
Null Hypothesis is that (rho) = 0
Alternative Hypothesis is (rho) is not equal to 0
A hypothesis is a claim about the correlation between the Y and X variables in the population under study:
There is only one hypothesis (claim) as follows:
Null Hypothesis is that (rho) = 0
A…
arrow_forward
Interpreting Simple Linear Regression
1. Linear correlation coefficient r = 0.794556
2. Coefficient of Determination ( r square) 0.631319
3. Standard Error of the estimate = 12.9668
4. SSR (Explained variation) = 5182.41
5. SSE ( Unexplained variation) = 3026.49
6. SST = 8208.90
7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523
8. Level of Significance = 0.1
9. Critical Value= 0.378419
Question
What is the meant by the standard error of the estimate? Which number measures the scatter of points about the regression line?
arrow_forward
Interpreting Simple Linear Regression 1. Linear correlation coefficient r = 0.794556 2. Coefficient of Determination ( r square) 0.631319 3. Standard Error of the estimate = 12.9668 4. SSR (Explained variation) = 5182.41 5. SSE ( Unexplained variation) = 3026.49 6. SST = 8208.90 7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523 8. Level of Significance = 0.1 9. Critical Value= 0.378419 10. t test = 0.794556 Question What is meant by a hypothesis? State the hypothesis in this example? A hypothesis is a claim about the correlation between the Y and X variables in the population
arrow_forward
Interpreting Simple Linear Regression
1. Linear correlation coefficient r = 0.794556
2. Coefficient of Determination ( r square) 0.631319
3. Standard Error of the estimate = 12.9668
4. SSR (Explained variation) = 5182.41
5. SSE ( Unexplained variation) = 3026.49
6. SST = 8208.90
7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523
8. Level of Significance = 0.1
9. Critical Value= 0.378419
Question
What is meant by SSR? Which number measures the variation explained by the regression line?
Sum of the Squares Regression (SSR); amount of variation in Y explained by the variation in X explanatory variable
Sum of the Squares Regression (SSR); amount of variation in X explained by the variation in Y
SSR is the percent variation in total variation SST that is explained by the variation in X or SSR/SST = 5182.41/8208.90 = 0.631319 or 63%
Both A and C
arrow_forward
Why is the equation of the regression line for this scatter plot ?
arrow_forward
The regression equation is Health Index= y + a Age + ß Blood sugar + 8 Blood Pressure
SE
20986
339.28
Age
Blood sugar
209.2
Blood pressure 207.2
S = 962.233 R-Sq = 86.6% R-Sq (adj) = 76.5%
Coef
Constant
Analysis of Variance
Source
DF
Regression
3
Residual Error. 4
Total
7
SS
Coef
2912
71.95
179.3
225.4
23863180
3703570
27566750
T
7.21
4.72
*
0.92
MS
7954393
925892
F
***
P
0.002
0.009
0.308
**
P
0.032
a) What is dependent and independent variables?
b) Fully write out the regression equation.
c) Fill in the missing values **, ****, and *****.
d) Hence test whether & is significant. Give reasons for your answer.
e) Perform the F Test making sure to state the null and alternative hypothesis.
arrow_forward
What is a numerical prediction from the regression line equation shown in the photo?
arrow_forward
5) Can i get help with this question please
arrow_forward
A researcher’s results are shown below using Femlab (labor force participation rate among females) to try to predict Cancer (death rate per 100,000 population due to cancer) in the 50 U.S. states.
Regression Statistics
Multiple R
0.313422848
R Square
0.098233882
Adjusted R Square
0.079447088
Standard Error
32.07003698
Observations
50
Variable
Coefficients
Standard Error
t Stat
Intercept
343.619889
61.0823514
5.62552
Femlab
–2.2833659
0.99855319
–2.28667
Which statement is valid regarding the relationship between Femlab and Cancer?
Multiple Choice
At the .05 level of significance, there isn’t enough evidence to say the two variables are related.
This model explains about 10 percent of the variation in state cancer rates.
If your sister starts working, the cancer rate in your state will decline.
A rise in female labor participation rate will cause the cancer rate to decrease within a state.
arrow_forward
A student collected concentration versus absorbance data for a series of standards
and produced a standard curve. Which value of 2 would reflect the linear
regression curve the student produced?
Absorbance
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
² = 0.10
² = 0.76
² = 0.98
2 = 0.45
1
Absorbance vs. Concentration
2
3
Concentration (ppm)
4
5
6
arrow_forward
To investigate the relationship between the milage and sales price for a popular car model the pictured scatterplot was used.
a) Based on the excel output that's pictured, what is the estimated regression equation that could be used to predict the price given the miles?
b) Does the model fit the data? (ie whether the regression relationship is statistically significant) Did the estimated regression equation provide a good fit? (ie use the coefficient of determination to explain variability independent variable)
c) Suppose you are considering purchasing a car of this model with 60000 miles. Using the estimated regression equation, predict the price.
arrow_forward
Q2 Part b
arrow_forward
Multiple regression analysis was used to study the relationship between a dependent variable, y, and four independent variables; x1, x2, x3, and x4. The following is a partial result of the regression analysis involving 31 observations.
Coefficients
Standard Error
Intercept
18.00
6.00
x1
12.00
8.00
x2
24.00
48.00
x3
-36.00
36.00
x4
16.00
2.00
ANOVA
df
SS
MS
F
Regression
125
Error
Total
760
Compute the multiple coefficient of determination.
Perform a t test and determine whether or not β1 is significantly different from zero (α = .05).
Perform a t test and determine whether or not β4 is significantly different from zero (α = .05).
At α = .05, perform an F test and determine whether or not the regression model is significant.
arrow_forward
A) Which point from the data has the largest residual?
B) Explain what the residual means in context. Is this point an outlier? An influential point?
The residual means that when the swim time is______, the observed heart rate is about _____ beats less than the predicted rate. When this point is removed, it has an effect on the regression line, so it is influential. The point is not an outlier, because the residual is less than twice the standard deviation.
arrow_forward
What variables do Teczar find have the most significant controlled associations with women in national parliaments?
arrow_forward
/was/ui/v2/assessment-player/index.html?launchid=831489a9-d255-4984-8d47-074c80bc17d6#/question
Problems
Question 2 of 8
Two variables are defined, a regression equation is given, and one data point is given.
Weight
Training =
Weight
=
=
maximum weight capable of bench pressing (pounds)
number of hours spent lifting weights a week
The data point is an individual who trains 5 hours a week and can bench 150 pounds.
99 + 11.7(Training)
(a) Find the predicted value for the data point and compute the residual.
Enter the exact answers.
Residual = i
II
Predicted value =
eTextbook and Media
3'
"
lbs
lbs
C
D
6
O
W
arrow_forward
None
arrow_forward
There is a dataset of size n = 51 and is for the 50 states and the District of Columbia in the United States. The dependent variable is year 2002 birth rate per 1000 females 18 to 19 years old and independent variable is the violent crime rate (per 1000 population). A simple linear regression model is run with the results given below.
What is the Pearson correlation coefficient between x and y variables?
The R squared of the model?
What kind of relationship there is?
arrow_forward
sample of trucks and their "static weight" and "weight in motion"
weights are in thousands of pounds.
What percent of the variability in static weight can be explained by the linear model rounded to the nearest 10th?
arrow_forward
Dep. Variable:
Model:
Method:
Date:
Time:
No. Observations:
Df Residuals:
Df Model:
Covariance Type:
Intercept
educ
IQ
KWW
exper
black
feduc
meduc
Least Squares
Wed, 23 Nov 2022
08:57:40
coef
-503.0058
40.5455
3.1654
7.2094
16.2338
-59.2987
10.8278
5.0471
std err
nonrobust
138.947
8.660
1.199
wage
OLS
2.120
3.740
52.143
5.353
6.106
722
714
7
R-squared:
Adj. R-squared:
Prob (F-statistic):
F-statistic:
Log-Likelihood:
AIC:
BIC:
-3.620
4.682
2.640
3.400
4.340
-1.137
2.023
0.827
P> [t]
0.000 -775.800
0.000
0.008
0.001
0.000
0.256
0.043
0.409
0.189
0.181
23.83
23.543
0.812
3.047
8.891
-161.671
0.318
-6.941
3.310-29
-5288.5
(0.025 0.9751
1.0590+04
1.063e+04
-230.212
57.548
5.519
11.372
23.577
43.074
21.338
17.035
Above is a regression of men's monthly earnings in dollars as a function of their years of education, their IQ score in "points", their Knowledge of the World of Work (KWW)
score in points (a measure of their knowledge of how occupations work), their years of work experience…
arrow_forward
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Related Questions
- I have no idea how to fill in the blank in this regression output... please helparrow_forwardInterpreting Simple Linear Regression 1. Linear correlation coefficient r = 0.794556 2. Coefficient of Determination ( r square) 0.631319 3. Standard Error of the estimate = 12.9668 4. SSR (Explained variation) = 5182.41 5. SSE ( Unexplained variation) = 3026.49 6. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523 7. Level of Significance = 0.1 8. Critical Value= 0.378419 Question : Based on the linear correlation coefficient (r) in Line 1, the variables(X,Y) are positively correlated True Falsearrow_forwardInterpreting Simple Linear Regression 1. Linear correlation coefficient r = 0.794556 2. Coefficient of Determination ( r square) 0.631319 3. Standard Error of the estimate = 12.9668 4. SSR (Explained variation) = 5182.41 5. SSE ( Unexplained variation) = 3026.49 6. SST = 8208.90 7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523 8. Level of Significance = 0.1 9. Critical Value= 0.378419 10. t test = 0.794556 Question What is meant by a hypothesis? State the hypothesis in this example? A hypothesis is a claim about the correlation between the Y and X variables in the population under study: There are two hypothesis (claims) Null Hypothesis is that (rho) = 0 Alternative Hypothesis is (rho) is not equal to 0 A hypothesis is a claim about the correlation between the Y and X variables in the population under study: There is only one hypothesis (claim) as follows: Null Hypothesis is that (rho) = 0 A…arrow_forward
- Interpreting Simple Linear Regression 1. Linear correlation coefficient r = 0.794556 2. Coefficient of Determination ( r square) 0.631319 3. Standard Error of the estimate = 12.9668 4. SSR (Explained variation) = 5182.41 5. SSE ( Unexplained variation) = 3026.49 6. SST = 8208.90 7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523 8. Level of Significance = 0.1 9. Critical Value= 0.378419 Question What is the meant by the standard error of the estimate? Which number measures the scatter of points about the regression line?arrow_forwardInterpreting Simple Linear Regression 1. Linear correlation coefficient r = 0.794556 2. Coefficient of Determination ( r square) 0.631319 3. Standard Error of the estimate = 12.9668 4. SSR (Explained variation) = 5182.41 5. SSE ( Unexplained variation) = 3026.49 6. SST = 8208.90 7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523 8. Level of Significance = 0.1 9. Critical Value= 0.378419 10. t test = 0.794556 Question What is meant by a hypothesis? State the hypothesis in this example? A hypothesis is a claim about the correlation between the Y and X variables in the populationarrow_forwardInterpreting Simple Linear Regression 1. Linear correlation coefficient r = 0.794556 2. Coefficient of Determination ( r square) 0.631319 3. Standard Error of the estimate = 12.9668 4. SSR (Explained variation) = 5182.41 5. SSE ( Unexplained variation) = 3026.49 6. SST = 8208.90 7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523 8. Level of Significance = 0.1 9. Critical Value= 0.378419 Question What is meant by SSR? Which number measures the variation explained by the regression line? Sum of the Squares Regression (SSR); amount of variation in Y explained by the variation in X explanatory variable Sum of the Squares Regression (SSR); amount of variation in X explained by the variation in Y SSR is the percent variation in total variation SST that is explained by the variation in X or SSR/SST = 5182.41/8208.90 = 0.631319 or 63% Both A and Carrow_forward
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