Deck 6: Multiple Linear Regression Analysis

Question 1

Omitted variable bias occurs when

A)always occurs when performing multiple linear regression analysis.
B)always occurs when performing simple linear regression analysis.
C)independent variables that should be included in the analysis are not included and those independent variables are related to the variables in the regression model.
D)independent variables that should not be included in the analysis are included in the analysis.

Answer 1

C

Question 2

Figure:
Suppose you regress the self-reported number of cigarettes smoked per day on Age,Family Size,and Years of Education and that you get the results in Figure 6.2.
Based on the estimates in Figure 6.2,you should conclude that,holding all other independent variables constant,each additional year of age is estimated to be associated with

A)a statistically significant increase of 1.56 percent in cigarettes smoked per day.
B)a statistically insignificant increase of 1.56 percent in cigarettes smoked per day.
C)a statistically significant increase of 0.0156 cigarettes smoked per day.
D)a statistically insignificant increase of 0.0156 cigarettes smoked per day.

Answer 2

D

Question 3

Omitted variable bias is a problem because

A)it causes perfect multicollinearity.
B)it causes the model to no longer be linear in the parameters.
C)it prevents the model from being able to be estimated by ordinary least squares.
D)it prevents correctly estimating marginal effects.

Answer 3

D

Question 4

The "holding all other independent variables constant" condition is important

A)to ensure that we are correctly estimating marginal effects.
B)because it comes at the end of every definition in economics.
C)because economists want to know how a change in the dependent variable affects the independent variable.
D)to ensure that the error term is correlated with the independent variables.

Question 5

The numerator of the appropriate test statistic for testing for the joint significance of a subset of independent variables is

A)
B)
C)
D)

Question 6

Suppose you wish to know whether Age and Family Size are jointly significant in the model $\text { Cigarettes Per Day } = \beta _ { 0 } + \beta _ { 1 } \text { Age } + \beta _ { 2 } \text { Family Size } + \beta _ { 3 } \text { Years of Education } + \varepsilon \text {. }$
The Restricted Model for testing the joint significance of the two variables?

A) $\text { Cigarettes Per Day } = \beta _ { 0 } + \beta _ { 1 } \text { Age } + \beta _ { 2 } \text { Family Size } + \varepsilon ^ { * } \text {. }$

B) $\text { Cigarettes Per Day } = \beta _ { 0 } + \beta _ { 1 } \text { Age } + \beta _ { 2 } \text { Years of Education } + \varepsilon ^ { * }$

C) $\text { Cigarettes Per Day } = \beta _ { 0 } + \beta _ { 1 } \text { Years of Education } + \varepsilon ^ { * } \text {. }$

D)None of the above.

Question 7

Figure:
Suppose you regress the number of medals won by countries in the 1996,2000,2004,and 2008 Olympics on GDP Per Capita (Thousands),Population (Millions),and Olympic Year and that you get the results in Figure 6.1.
Based on the estimates in Figure 6.1,you should conclude that,holding all other independent variables constant,a $1,000 increase in GDP Per Capita is estimated to

A)increase Total Medals Won by a statistically significant 0.2865 because 0 is not included in the 95% confidence interval.
B)increase Total Medals Won by a statistically insignificant 0.2865 because 0 is included in the 95% confidence interval.
C)increase Total Medals Won by a statistically insignificant 0.2865 because 0.2865 is included in the 95% confidence interval.
D)increase Total Medals Won by a statistically significant 0.2865 because 0.2865 is included in the 95% confidence interval.

Question 8

In multiple linear regression analysis,the number of independent variables should be

A)more than 5.
B)guided by economic theory.
C)enough to guarantee that statistical significance is achieved.
D)as large as possible.

Question 9

Figure
Suppose that in the course of testing whether Age and Family Size are jointly significant,you estimate the results in Figure 6.3.
When testing for the joint significance of Age and Family Size (Figure 6.3),the
Is

A)22,548.428.
B)23.294.
C)22,436.942.
D)23.227.

Question 10

Figure:
Suppose you regress the self-reported number of cigarettes smoked per day on Age,Family Size,and Years of Education and that you get the results in Figure 6.2.
Based on the estimates in Figure 6.2,you should conclude that,holding all other independent variables constant,each additional family member is estimated to be associated with

A)a statistically significant decrease of 0.093 cigarettes smoked per day.
B)a statistically insignificant decrease of 0.093 cigarettes smoked per day.
C)a statistically significant increase of 0.093 cigarettes smoked per day.
D)a statistically insignificant increase of 0.093 cigarettes smoked per day.

Question 11

Suppose you wish to know whether Age and Family Size are jointly significant in the model
The appropriate null hypothesis for this test is

A)H₀: β₀ = β₁ = β₂ = β₃ = 0.
B)H₀: β₁ = β₂ = 0.
C)H₀: β₁ = 0.
D)H₀: β₂ = 0.

Question 12

Multiple linear regression analysis determines the

A)true value of the population slope coefficient.
B)linear relationship between the dependent variable and exactly one independent variable.
C)linear relationship between the dependent variable and many independent variables.
D)true value of the population intercept.

Question 13

Tests of joint significance are based on comparing

A)the explained sum of squares from the unrestricted regression to the explained sum of squares from the restricted regression.
B)the explained sum of squares from the unrestricted regression to the unexplained sum of squares from the unrestricted regression.
C)the unexplained sum of squares from the restricted regression to the explained sum of squares from the restricted regression.
D)the unexplained sum of squares from the unrestricted regression to the unexplained sum of squares from the restricted regression.

Question 14

The intuition behind a test of joint significance is that if a subset of variables is jointly significant,then

A)the unexplained sum of squares should be much larger in the restricted regression than in the unrestricted regression.
B)the unexplained sum of squares should be much smaller in the restricted regression than in the unrestricted regression.
C)the explained sum of squares should be much smaller in the restricted regression than in the unrestricted regression.
D)the total sum of squares should be much larger in the restricted regression than in the unrestricted regression.

Question 15

Tests of joint significance are used to determine whether

A)the multiple linear regression achieves individual significance of each independent variable.
B)we can reject that specific coefficients are different from 0.
C)the estimated coefficients differ for two different subsets of the data.
D)we can reject that a subset of estimated coefficients are jointly equal to 0.

Question 16

The denominator of the appropriate test statistic for testing for the joint significance of a subset of independent variables is

A)
B)
C)
D)

Question 17

Figure:
Suppose you regress the number of medals won by countries in the 1996,2000,2004,and 2008 Olympics on GDP Per Capita (Thousands),Population (Millions),and Olympic Year and that you get the results in Figure 6.1.
Based on the estimates in Figure 6.1,you should conclude that,holding all other independent variables constant,Olympic Year is estimated to have

A)a statistically significant positive effect on Total Medals Won because -1.128 < .05.
B)a statistically insignificant positive effect on Total Medals Won because |-1.128| > .05.
C)a statistically significant positive effect on Total Medals Won because |-1.128| < 1.96.
D)a statistically insignificant positive effect on Total Medals Won because |-1.128| < 1.96.

Question 18

Figure:
Suppose you regress the number of medals won by countries in the 1996,2000,2004,and 2008 Olympics on GDP Per Capita (Thousands),Population (Millions),and Olympic Year and that you get the results in Figure 6.1.
Based on the estimates in Figure 6.1,you should conclude that a 1 million increase in population is estimated to be associated with

A)a statistically significant .042 increase in population.
B)a statistically significant .042 increase in the total number of medals won,holding all other independent variables constant.
C)a statistically insignificant .042 increase in the total number of medals won.
D)a statistically insignificant .042 increase in the total number of medals won,holding all other independent variables constant.

Question 19

Figure:
Suppose you regress the number of medals won by countries in the 1996,2000,2004,and 2008 Olympics on GDP Per Capita (Thousands),Population (Millions),and Olympic Year and that you get the results in Figure 6.1.
Based on the estimates in Figure 6.1,you should conclude that

A)the regression function is overall statistically significant because 3.6997E - 22 < .05.
B)the regression function is overall statistically insignificant because 3.6997E - 22 < .05.
C)the regression function is overall statistically insignificant because .4739 > .05.
D)the regression function is overall statistically significant because 2.4135E - 09 < 0.05.

Question 20

Figure
Suppose that in the course of testing whether Age and Family Size are jointly significant,you estimate the results in Figure 6.3.
When testing for the joint significance of Age and Family Size (Figure 6.3),the
Is

A)22,548.428.
B)23.294.
C)22,436.942.
D)23.227.

Question 21

Figure
Suppose that in the course of testing whether Age and Family Size are jointly significant,you estimate the results in Figure 6.3.
Chow tests are based on comparing the

A)sum of the unexplained sums of squares added together from separate regressions to the unexplained sum of squares for the pooled regression.
B)unexplained sums of squares from separate regressions to each other.
C)sum of the explained sums of squares from separate regressions to the explained sum of squares for the pooled regression.
D)explained sums of squares from separate regressions to each other.

Question 22

What is the coefficient of determination? What information does it provide? Explain.

Question 23

Suppose you are estimating salary as a function of age,education,hours of work and the number of young children and you are concerned that the salary functions differ for men and women.You could test this possibility by performing a

A)t-test for individual significance.
B)t-test for joint significance.
C)Chow test.
D)subset test.

Question 24

Figure:
Suppose that in the course of testing whether salary functions differ for males and females,you estimate the pooled and male and female results in Figure 6.4.
The appropriate critical value for the Chow test in Figure 6.4 is

A)1.927.
B)2.032.
C)2.463.
D)2.978.

Question 25

What are the multiple linear regression assumptions required for OLS to be BLUE? Explain why each one is important.

Question 26

How do you perform a test of the overall significance of the regression function? What are the null and alternative hypothesis for this test? What is the rejection rule? What is the intuition for why the test works? Explain.

Question 27

Figure:
Suppose that in the course of testing whether salary functions differ for males and females,you estimate the pooled and male and female results in Figure 6.4.
Based on the results in Figure 6.4,you should

A)reject the null hypothesis.
B)fail to reject the null hypothesis.
C)reject the alternative hypothesis.
D)fail to reject the alternative hypothesis.

Question 28

How does the Adjusted R-squared differ from the R-squared? Why would the Adjusted R-squared be preferred to the R-squared?

Question 29

Figure:
Suppose that in the course of testing whether salary functions differ for males and females,you estimate the pooled and male and female results in Figure 6.4.
Based on the results of you the Chow test in Figure 6.4 you should

A)focus on the pooled sample results.
B)focus on the male and female subsample results.
C)collect more data that does not fail the Chow test.
D)focus on the male results only.

Question 30

Figure
Suppose that in the course of testing whether Age and Family Size are jointly significant,you estimate the results in Figure 6.3.
When testing for the joint significance of Age and Family Size (Figure 6.3),the appropriate test statistic is

A)37.162.
B)0.115.
C)23.227.
D)1.600.

Question 31

Write out the estimated sample regression function of y on x₁ and x₂.Explain what each of the estimated values means.

Question 32

How do you perform a test of the joint significance of a subset of slope coefficients? What are the null and alternative hypothesis for this test? What is the rejection rule? What is the intuition for why the test works? Explain.

Question 33

Figure
Suppose that in the course of testing whether Age and Family Size are jointly significant,you estimate the results in Figure 6.3.
When testing for the joint significance of Age and Family Size (Figure 6.3),you should

A)reject the null hypothesis because 1.600 < 2.61.
B)fail to reject the null hypothesis because 1.600 < 2.61.
C)reject the null hypothesis because 1.600 < 8.53.
D)fail to reject the null hypothesis because 1.600 < 8.53.

Question 34

Why is multiple linear regression analysis such a valuable tool? Explain.

Question 35

Figure
Suppose that in the course of testing whether Age and Family Size are jointly significant,you estimate the results in Figure 6.3.
Chow tests are used to determine whether

A)an estimated slope coefficient is different for different subsamples of the data.
B)a subset of independent variables is jointly significant.
C)estimated sample regression functions are different for two different subsamples of the data.
D)a subset of estimated slope coefficients is jointly significant for two different subsamples of the data.

Question 36

How do you perform a test of the individual significance of a slope coefficient? What are the null and alternative hypothesis for this test? What is the rejection rule? What is the intuition for why the test works? Explain.

Question 37

Figure
Suppose that in the course of testing whether Age and Family Size are jointly significant,you estimate the results in Figure 6.3.
When testing for the joint significance of Age and Family Size (Figure 6.3),you should

A)reject the null hypothesis and conclude that β₂ = β₃ = 0.
B)fail to reject the null hypothesis because and conclude that β₂ = β₃ = 0.
C)reject the null hypothesis and conclude that at least one of β₂ or β₃ is not equal to 0.
D)fail to reject the null hypothesis and conclude that at least one of β₂ or β₃ is not equal to 0.

Question 38

The test statistic for this Chow test is

A)
B)
C)
D)

Question 39

Figure:
Suppose that in the course of testing whether salary functions differ for males and females,you estimate the pooled and male and female results in Figure 6.4.
The tests statistic for the Chow test in Figure 6.4 is

A)0.0436.
B)9.327.
C)18.654.
D)37.307.

Question 40

Why is the "all other independent variables constant" condition important? Explain.

Question 41

A researcher is interested in estimating how the test scores of elementary schools is related to average class size,parents education level (in years),and percent of English learners at the school.The researcher obtains a sample of 200 California public schools and obtains the following results with standard errors are in parentheses
a)The F-statistic for this regression is 48.32.Test the overall significance of the regression model at the 5% level.What are the hypothesis,critical value,rejection rule and decision.
b)Perform a t-test of for the individual significance for the slopes.
c)Comment on the economic significance of the coefficient estimates.
d)If you are interested in sending your child to a school with high test scores what would factors would you look for?

Question 42

A researcher is interested in estimating how the test scores of elementary schools is related to average class size,parents education level (in years),and percent of English learners at the school.The researcher obtains a sample of 200 California public schools and obtains the following results
a)Interpret the coefficient estimates.Are these results consistent with what you expected?
b)Are there any omitted variables in this regression? If so,list them.
c)Interpret the R-squared.Is the value of the R-squared high as you expected?
d)Calculate the Adjusted R-squared and comment on what it means.
e)Predict the test score for a school with average class sizes of 28,an education level of 14 years,and 3% English learners.
f)Design an experiment to determine how class size affects test scores.How would the results from that experiment differ from the results presented above?

Question 43

How do you perform a Chow test for structural differences between two subsets of the data? What is the rejection rule? What is the intuition for why the test works? Explain.

Question 44

Suppose you are interested in determining the factors that determine the number of crimes committed on campus.To this end,you collect data from 75 colleges on number of crimes per students enrolled,number of police officers per students,unemployment rate,tuition,and the percentage of male students.You run a regression and obtain the following results
a)Which of the coefficient estimates are statistically significant at the 5% level?
b)You run an additional regression in order to jointly test if two coefficients are equal to 0.State the hypothesis,calculate the test statistic,state the regression rule,and state your decision.