1. When estimating the parameters of a linear regression model, the OLS estimator is ascalar value and the OLS estimate is a random variable.2. For a linear regression model including only an intercept, the OLS estimator of thatintercept is equal to the sample mean of the independent variable.3. If the error term in a linear regression model is normally distributed, then the distributionof the OLS estimator, conditional on explanatory variables, is also normal.4. The value of the coefficient of determination, R2 of Model 1:In yi = a + Bx; + E;(M1)is different from the value of R2 of the Model 2:Yi = a+ Bx; + Ei.(M2)5. Consider an earnings function In wage = 0.6 + 0.16 · educ estimated on a sample ofn = 1000 individuals. The standard error of the estimated slope coefficient equals 0.11.This allows us to interpret the estimated slope coefficient as: ceteris paribus expectedreturns to schooling are 16%.

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Answered: When estimating the parameters of a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A linear regression model is fitted to determine if a relationship exists between consumer rating of cereal(response) and the number of grams of sugar contained in each serving, grams of fat per serving and grams of dietary fibre per serving as predictors. The sample used was of size 77. (a) The regression sum of squares of fitted model was 13002.226 and error sum of squares was 1994.574. Test for significance of fit. (1) the test statistic for the significance of the model fit(round off answer to two decimal points)
A recent Gallup survey of a random sample of Americans (18 and older) found that the average number of alcoholic drinks consumed per week (drinks) by males was 4.2 and by females was 1.4.[¹] Suppose we use the underlying survey data to estimate a least-squares regression of the average number of drinks a person reports consuming per week (Drinks;) on a dummy variable equal to 1 if i is female and 0 otherwise (Female;). (Assume all respondents identify as either male or female.) The estimated regression line equation can be written as: Drinks = a +bFemale Alcohol Consumption by Gender What is the numerical value of b?
The null hypothesis being tested in the least-squares regression output for B is B1 = B1,0=1. True False
There may be an association between a country's birthrate and the life expectancy of its inhabitants. A report this past year, coming from a random sample of 20 countries, contained the following information: the least-squares regression equation relating the two variables number of births per one thousand people (denoted by x) and female life expectancy (denoted by y and measured in years) is y = 82.28 – 0.51 x, and the standard error of the slope of this least-squares regression line is approximately 0.35. Based on this information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population slope B,. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.10 level of significance, and perform a two-tailed test. Then complete the parts below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the…
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Suppose that I want to estimate the effect of x₁ on y. Consider the univariate regression line: how to calculate a and b₁ using OLS? y = a + b₁x₁
A local University conducted a survey of over 2,000 MBA alumni to explore the issue of work-life balance. Each participant received a score ranging from 0 to 100, with lower scores indicating a higher imbalance between work and life. A sample of the data is available below. Let x = average number of hours worked per week and y=work-life balance scale score for each MBA alumnus. Investigate the link between these two variables by conducting a complete simple linear regression analysis of the data. Summarize your findings. E Click the icon to view the data. The least squares regression equation is y =+ (Ox. (Round to two decimal places as needed.) Revenue and Message Rate for Recent Movies Check the usefulness of the hypothesized model. What are the hypotheses to test? O A. H Bo =0 against H: Bo #0 Hours WLB Score 50 75.22 B. H: B, #0 against H: B, =0 45 78.45 OC. H B, = 0 against H B, 0 50 49.68 55 40.11 OD. H Bo#0 against H: Bo =0 50 70.41 60 55.91 Determine the estimate of the…
Suppose x1 and x2 are predictor variables for a response variable y. a. The distribution of all possible values of the response variable corresponding to particular values of the two predictor variables is called a distribution of the response variable. b. State the four assumptions for multiple linear regression inferences.
Assume a multiple linear regression y = Bo + B1 a1+ B2x2 + e. Which statement(s) is(are) true about the variance inflation factors (VIFS) of the coefficient estimates b1 and b2 ? I. The VIF of b, is the same as the VIF of b2. II. VIF will likely be large if X2 is highly positively correlated with X1 II. VIF will likely be large if X2 is highly negatively correlated with X1 IV. VIF will likely be close to 1 if X1 and X2 are independent O l and IV 1, II, III and IV Il and III OIV only I only
The accompanying scatterplot shows the relationship between the age of an internet user and the amount of time spent browsing the internet per week (in minutes). The accompanying residual plot is also shown along with the QQ plot of the residuals. Choose the statement that best describes whether the condition for Normality of errors does or does not hold for the linear regression model. Choose the statement that best describes whether the condition for Normality of errors does or does not hold for the linear regression model. A.The residual plot displays a fan shape; therefore the Normality condition is not satisfied.B.The QQ plot mostly follows a straight line; therefore the Normality condition is satisfied.C.The scatterplot shows a negative trend; therefore the Normality condition is satisfied.D.The residual plot shows no trend; therefore the Normality condition is not satisfied.
A group of Maternal and Child Health public health practitioners are interested in the relationship between depression and a number of health outcomes. Suppose the research team gathers information on a group of participants, and constructs a multiple linear regression model looking at the relationship between depression and household income dichotomized as above and below the federal poverty line controlling for a number of potential confounders. The following is a computerized output displaying the results of their analysis. Parameter Estimate Standard Error t Value Pr > |t| Intercept 0.2617346843 0.09209917 2.84 0.0046 Income (1/0) -.1962038300 0.04574793 -4.29 <.0001 Race (W or AA) -.0320329506 0.03900447 -0.82 0.4118 bmicontinuous 0.0051185980 0.00216986 2.36 0.0186 Alcohol (Y/N) -.0088735044 0.03090631 -0.29 0.7741 A) What are the independent and dependent variables? B) Which potential…
IS the following statment true or false, please explain why For each x term in the multiple regression equation, the corresponding β is referred to as a partial regression coefficient.

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