Question 1

Multiple linear regression analysis determines the

Accepted Answer

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. 
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. C

Question 2

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

Accepted Answer

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. 
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. A

Question 3

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.

Accepted Answer

You perform a test of the overall significance of the regression function by comparing the p-value for the overall regression (the significance F)to the chosen significance level.The null and alternative hypothesis for the test are

H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \ldots = \beta _ { k } = 0

H _ { A } :

at least one of

\beta _ { 0 } , \beta _ { 1 } , \beta _ { 2 } , \ldots , \beta _ { k } \neq 0

The rejection rule for the 5 percent significance level is:

\text { Reject } H _ { 0 } \text { if <i>significance </i> } F < .05

This test works for the following reason.By definition,the significance F is the probability of observing the estimated sample regression function that we actually observed if the true value of all of the population coefficients are 0.A very small value therefore indicates that it is very unlikely to observe the results that we actually observed if H₀ were actually true.Hence,if we observe a very small,the fact that we observed the results that we did observe provides statistical evidence that H₀ is likely not true.

Question 4

Omitted variable bias occurs when

Accepted Answer

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. 
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.

Question 5

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. $\text { Pooled }$

$\begin{array}{l}
\text { ANOVA }\
\begin{array}{lccccc}
\hline & d f & S S & M S & F & \text { Significance } F \
\hline \text { Regression } & 4 & 2.30931 \mathrm{E}+12 & 5.77328 \mathrm{E}+11 & 282.1787278 & 1.2198 \mathrm{E}-215 \
\text { Residual } & 4286 & 8.76901 \mathrm{E}+12 & 2045965635 & & \
\text { Total } & 4290 & 1.10783 \mathrm{E}+13 & & & \
\hline
\end{array}
\end{array}$

$\text { Male }$

$\begin{array}{l}
\text { ANOVA }\
\begin{array}{lccccc}
\hline & d f & S S & M S & F & \text { Significance } F \
\hline \text { Regression } & 4 & 1.54309 \mathrm{E}+12 & 3.85772 \mathrm{E}+11 & 131.8489492 & 9.4649 \mathrm{E}-101 \
\text { Residual } & 2136 & 6.24964 \mathrm{E}+12 & 2925860190 & & \
\text { Total } & 2140 & 7.79272 \mathrm{E}+12 & & & \
\hline
\end{array}
\end{array}$

$\text { Female }$

$\begin{array}{lccccc} 
\text { ANOVA }\
\hline& \text { of } & S S & M S & F & \text { Significance } F \
\hline \text { Regression } & 4 & 6.15055 \mathrm{E}+11 & 1.53764 \mathrm{E}+11 & 153.1758618 & 2.2255 \mathrm{E}-115 \
\text { Residual } & 2145 & 2.15323 \mathrm{E}+12 & 1003838471 & & \
\text { Total } & 2149 & 2.76829 \mathrm{E}+12 & & &\
\hline
\end{array}$
Figure 6.4
-Based on the results in Figure 6.4,you should

Accepted Answer

A) reject the null hypothesis. 
B) fail to reject the null hypothesis. 
C) reject the alternative hypothesis. 
D) fail to reject the alternative hypothesis. 
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 6

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.

$\begin{array}{lc}

\text { SUMMARY OUTPUT }\
\
\
\hline \text { Regression Statisties } & \
\hline \text { Multiple R } & 0.473932054 \
\text { R Square } & 0.224611592 \
\text { Adyasted R Square } & 0.218853757 \
\text { Standerd Error } & 14.85665558 \
\text { Observations } & 408 \
\hline
\end{array}$

$\begin{array}{lccccc}
 \text { ANOVA }\
\hline & \text { ff } & S S & M S & F & \text { Sigejficance F } \
\hline \text { Regressice } & 3 & 25830.70959 & 8610.236529 & 39.00973242 & 3.69997 E-22 \
\text { Residual } & 404 & 89170.96688 & 220.7202151 & \
\text { Total } & 407 & 115001.6765 & & \
\hline
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coefficients } & \text { Standand Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & 385.4384477 & 338.9966744 & 1.136997725 & 0.25621316 & -280.9792491 & 1051.856144 \
\text { GDP Per Capita (Thousands) } & 0.28651666 & 0.046941033 & 6.103756974 & 2.4315 \mathrm{E}-09 & 0.194237479 & 0.37879584 \
\text { Popplasion (Milions) } & 0.041979674 & 0.00443387 & 9.467954334 & 2.42102 \mathrm{E}-19 & 0.033263338 & 0.050696011 \
\text { Year } & -0.191084928 & 0.169402339 & -1.127994491 & 0.259991678 & -0.524105098 & 0.141935242 \
\hline
\end{array}$

$\text { Figure } 6.1$
-Based on the estimates in Figure 6.1,you should conclude that

Accepted Answer

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

Question 7

Figure
Suppose that in the course of testing whether Age and Family Size are jointly significant,you estimate the results in Figure 6.3. $\begin{array}{lc}
\text { SUMMARY OUTPUT }\
\
\
\hline\text { Regrestion Starittict } & \
\hline \text { Muftiple R. } & 0.070494476 \
\text { R Sequrt } & 0.004969471 \
\text { Adigated R. Square } & 0.001879314 \
\text { Standard Esror } & 4.819403326 \
\text { Observations } & 970 \
\hline
\end{array}$

$\begin{array}{l}
\text { ANOVA }\
\begin{array}{lccccc}
\hline & d f & S 5 & M S & F & \text { Signifieance } F \
\hline \text { Regranion } & 3 & 112.0566012 & 37.3522004 & 1.608161442 & 0.185858614 \
\text { Reaidual } & 966 & 22436.94237 & 23.22664841 & & \
\text { Total } & 969 & 22548.99897 & & & \
\hline
\end{array}
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coeffeientt } & \text { Srandard Error } & \text { t Stat } & \text { P-value } & \text { Lower } 9596 & \text { Upper } 9596 \
\hline \text { Intercept } & 4.049920982 & 1.042107341 & 3.886280064 & 0.000108739 & 2.004865844 & 6.094976119 \
\text { Age } & 0.015626984 & 0.010365497 & 1.507396119 & 0.131984878 & -0.004714504 & 0.035968471 \
\text { Family Size } & -0.093093463 & 0.084602383 & -1.100364552 & 0.271447442 & -0.259119103 & 0.072932177 \
\text { Years of Education } & 0.005642075 & 0.06474525 & 0.087142685 & 0.930576157 & -0.121415476 & 0.132699626 \
\hline
\end{array}$

$\text { SUMALARY OUTPUT }$

$\begin{array}{lc}
\hline \text { Regrestion Staritticz } & \
\hline \text { Multiple R. } & 0.005034034 \
\text { R Square } & 2.53415 \mathrm{E}-05 \
\text { Adjuted R. Square } & -0.00100769 \
\text { Standard Error } & 4.826368211 \
\text { Observations } & 970 \
\hline
\end{array}$$0.115170636$

$\begin{array}{l}
\text { ANOVA }\
\begin{array}{lccccc}
\hline & d f & S S & M S & F & \text { Signffeance } F \
\hline \text { Regresion } & 1 & 0.571425385 & 0.571425385 & 0.024531191 & 0.875573561 \
\text { Reiidual } & 968 & 22548.42754 & 23.29383011 & & \
\text { Total } & 969 & 22548.99897 & & & \
\hline
\end{array}
\end{array}$

$\begin{array}{l}
\begin{array}{lcccccc}
\hline & \text { Coefficienty } & \text { Standard Emor } & \text { t Star } & \text { P-value } & \text { Lower } 9596 & \text { Upper } 9596 \
\hline \text { Intercept } & 4.288825645 & 0.732966216 & 5.851327866 & 6.66867 E-09 & 2.850439806 & 5.727211483 \
\text { Years of Education } & 0.009850586 & 0.062893064 & 0.156624361 & 0.875573561 & -0.113571873 & 0.133273045 \
\hline
\end{array}\
\text { Figure } 6.3
\end{array}$
-Chow tests are used to determine whether

Accepted Answer

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. 
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 8

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

Accepted Answer

Multiple linear regression analysis is a

Question 9

Tests of joint significance are used to determine whether

Accepted Answer

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. 
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 10

Omitted variable bias is a problem because

Accepted Answer

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. 
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.

Question 11

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

Accepted Answer

A)  $\left( U S S _ { \text {restricted } } - U _ { \text {SS } } S _ { \text {unrestricted } } \right) / q .$ 
B)  $\left( U S S _ { \text {unrestricted } } - U S S _ { \text {restricted } } \right) / q .$ 
C)  $\text { USS } S _ { \text {unrestricted } } / ( n - k - 1 )$ 
D)  $U _ { S S _ { \text {restricted } } / ( n - k - 1 ) }$ 
A)  $\left( U S S _ { \text {restricted } } - U _ { \text {SS } } S _ { \text {unrestricted } } \right) / q .$ 
B)  $\left( U S S _ { \text {unrestricted } } - U S S _ { \text {restricted } } \right) / q .$ 
C)  $\text { USS } S _ { \text {unrestricted } } / ( n - k - 1 )$ 
D)  $U _ { S S _ { \text {restricted } } / ( n - k - 1 ) }$

Question 12

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.

Accepted Answer

You perform a test of the individual sig

Question 13

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.

$\begin{array}{lc}

\text { SUMMARY OUTPUT }\
\
\
\hline \text { Regression Statisties } & \
\hline \text { Multiple R } & 0.473932054 \
\text { R Square } & 0.224611592 \
\text { Adyasted R Square } & 0.218853757 \
\text { Standerd Error } & 14.85665558 \
\text { Observations } & 408 \
\hline
\end{array}$

$\begin{array}{lccccc}
 \text { ANOVA }\
\hline & \text { ff } & S S & M S & F & \text { Sigejficance F } \
\hline \text { Regressice } & 3 & 25830.70959 & 8610.236529 & 39.00973242 & 3.69997 E-22 \
\text { Residual } & 404 & 89170.96688 & 220.7202151 & \
\text { Total } & 407 & 115001.6765 & & \
\hline
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coefficients } & \text { Standand Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & 385.4384477 & 338.9966744 & 1.136997725 & 0.25621316 & -280.9792491 & 1051.856144 \
\text { GDP Per Capita (Thousands) } & 0.28651666 & 0.046941033 & 6.103756974 & 2.4315 \mathrm{E}-09 & 0.194237479 & 0.37879584 \
\text { Popplasion (Milions) } & 0.041979674 & 0.00443387 & 9.467954334 & 2.42102 \mathrm{E}-19 & 0.033263338 & 0.050696011 \
\text { Year } & -0.191084928 & 0.169402339 & -1.127994491 & 0.259991678 & -0.524105098 & 0.141935242 \
\hline
\end{array}$

$\text { Figure } 6.1$
-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

Accepted Answer

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. 
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 14

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?

Accepted Answer

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. 
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 15

Figure
Suppose that in the course of testing whether Age and Family Size are jointly significant,you estimate the results in Figure 6.3. $\begin{array}{lc}
\text { SUMMARY OUTPUT }\
\
\
\hline\text { Regrestion Starittict } & \
\hline \text { Muftiple R. } & 0.070494476 \
\text { R Sequrt } & 0.004969471 \
\text { Adigated R. Square } & 0.001879314 \
\text { Standard Esror } & 4.819403326 \
\text { Observations } & 970 \
\hline
\end{array}$

$\begin{array}{l}
\text { ANOVA }\
\begin{array}{lccccc}
\hline & d f & S 5 & M S & F & \text { Signifieance } F \
\hline \text { Regranion } & 3 & 112.0566012 & 37.3522004 & 1.608161442 & 0.185858614 \
\text { Reaidual } & 966 & 22436.94237 & 23.22664841 & & \
\text { Total } & 969 & 22548.99897 & & & \
\hline
\end{array}
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coeffeientt } & \text { Srandard Error } & \text { t Stat } & \text { P-value } & \text { Lower } 9596 & \text { Upper } 9596 \
\hline \text { Intercept } & 4.049920982 & 1.042107341 & 3.886280064 & 0.000108739 & 2.004865844 & 6.094976119 \
\text { Age } & 0.015626984 & 0.010365497 & 1.507396119 & 0.131984878 & -0.004714504 & 0.035968471 \
\text { Family Size } & -0.093093463 & 0.084602383 & -1.100364552 & 0.271447442 & -0.259119103 & 0.072932177 \
\text { Years of Education } & 0.005642075 & 0.06474525 & 0.087142685 & 0.930576157 & -0.121415476 & 0.132699626 \
\hline
\end{array}$

$\text { SUMALARY OUTPUT }$

$\begin{array}{lc}
\hline \text { Regrestion Staritticz } & \
\hline \text { Multiple R. } & 0.005034034 \
\text { R Square } & 2.53415 \mathrm{E}-05 \
\text { Adjuted R. Square } & -0.00100769 \
\text { Standard Error } & 4.826368211 \
\text { Observations } & 970 \
\hline
\end{array}$$0.115170636$

$\begin{array}{l}
\text { ANOVA }\
\begin{array}{lccccc}
\hline & d f & S S & M S & F & \text { Signffeance } F \
\hline \text { Regresion } & 1 & 0.571425385 & 0.571425385 & 0.024531191 & 0.875573561 \
\text { Reiidual } & 968 & 22548.42754 & 23.29383011 & & \
\text { Total } & 969 & 22548.99897 & & & \
\hline
\end{array}
\end{array}$

$\begin{array}{l}
\begin{array}{lcccccc}
\hline & \text { Coefficienty } & \text { Standard Emor } & \text { t Star } & \text { P-value } & \text { Lower } 9596 & \text { Upper } 9596 \
\hline \text { Intercept } & 4.288825645 & 0.732966216 & 5.851327866 & 6.66867 E-09 & 2.850439806 & 5.727211483 \
\text { Years of Education } & 0.009850586 & 0.062893064 & 0.156624361 & 0.875573561 & -0.113571873 & 0.133273045 \
\hline
\end{array}\
\text { Figure } 6.3
\end{array}$
-When testing for the joint significance of Age and Family Size (Figure 6.3),the $\text { USS unrestricted }$
Is

Accepted Answer

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

Question 16

Suppose you wish to know whether Age and Family Size are jointly significant in the model $$\text { Cigarettes Per Day } = \beta _ { 0 } + \beta _ { 1 } \text { Age } + \beta _ { 2 } \text { Family Size } + \beta _ { 3 } \text { Years of Education. }$$
The appropriate null hypothesis for this test is

Accepted Answer

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

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.

$\begin{array}{lc}

\text { SUMMARY OUTPUT }\
\
\
\hline \text { Regression Statisties } & \
\hline \text { Multiple R } & 0.473932054 \
\text { R Square } & 0.224611592 \
\text { Adyasted R Square } & 0.218853757 \
\text { Standerd Error } & 14.85665558 \
\text { Observations } & 408 \
\hline
\end{array}$

$\begin{array}{lccccc}
 \text { ANOVA }\
\hline & \text { ff } & S S & M S & F & \text { Sigejficance F } \
\hline \text { Regressice } & 3 & 25830.70959 & 8610.236529 & 39.00973242 & 3.69997 E-22 \
\text { Residual } & 404 & 89170.96688 & 220.7202151 & \
\text { Total } & 407 & 115001.6765 & & \
\hline
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coefficients } & \text { Standand Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & 385.4384477 & 338.9966744 & 1.136997725 & 0.25621316 & -280.9792491 & 1051.856144 \
\text { GDP Per Capita (Thousands) } & 0.28651666 & 0.046941033 & 6.103756974 & 2.4315 \mathrm{E}-09 & 0.194237479 & 0.37879584 \
\text { Popplasion (Milions) } & 0.041979674 & 0.00443387 & 9.467954334 & 2.42102 \mathrm{E}-19 & 0.033263338 & 0.050696011 \
\text { Year } & -0.191084928 & 0.169402339 & -1.127994491 & 0.259991678 & -0.524105098 & 0.141935242 \
\hline
\end{array}$

$\text { Figure } 6.1$
-Based on the estimates in Figure 6.1,you should conclude that,holding all other independent variables constant,Olympic Year is estimated to have

Accepted Answer

A) a statistically significant 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. 
A) a statistically significant 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 that in the course of testing whether Age and Family Size are jointly significant,you estimate the results in Figure 6.3. $\begin{array}{lc}
\text { SUMMARY OUTPUT }\
\
\
\hline\text { Regrestion Starittict } & \
\hline \text { Muftiple R. } & 0.070494476 \
\text { R Sequrt } & 0.004969471 \
\text { Adigated R. Square } & 0.001879314 \
\text { Standard Esror } & 4.819403326 \
\text { Observations } & 970 \
\hline
\end{array}$

$\begin{array}{l}
\text { ANOVA }\
\begin{array}{lccccc}
\hline & d f & S 5 & M S & F & \text { Signifieance } F \
\hline \text { Regranion } & 3 & 112.0566012 & 37.3522004 & 1.608161442 & 0.185858614 \
\text { Reaidual } & 966 & 22436.94237 & 23.22664841 & & \
\text { Total } & 969 & 22548.99897 & & & \
\hline
\end{array}
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coeffeientt } & \text { Srandard Error } & \text { t Stat } & \text { P-value } & \text { Lower } 9596 & \text { Upper } 9596 \
\hline \text { Intercept } & 4.049920982 & 1.042107341 & 3.886280064 & 0.000108739 & 2.004865844 & 6.094976119 \
\text { Age } & 0.015626984 & 0.010365497 & 1.507396119 & 0.131984878 & -0.004714504 & 0.035968471 \
\text { Family Size } & -0.093093463 & 0.084602383 & -1.100364552 & 0.271447442 & -0.259119103 & 0.072932177 \
\text { Years of Education } & 0.005642075 & 0.06474525 & 0.087142685 & 0.930576157 & -0.121415476 & 0.132699626 \
\hline
\end{array}$

$\text { SUMALARY OUTPUT }$

$\begin{array}{lc}
\hline \text { Regrestion Staritticz } & \
\hline \text { Multiple R. } & 0.005034034 \
\text { R Square } & 2.53415 \mathrm{E}-05 \
\text { Adjuted R. Square } & -0.00100769 \
\text { Standard Error } & 4.826368211 \
\text { Observations } & 970 \
\hline
\end{array}$$0.115170636$

$\begin{array}{l}
\text { ANOVA }\
\begin{array}{lccccc}
\hline & d f & S S & M S & F & \text { Signffeance } F \
\hline \text { Regresion } & 1 & 0.571425385 & 0.571425385 & 0.024531191 & 0.875573561 \
\text { Reiidual } & 968 & 22548.42754 & 23.29383011 & & \
\text { Total } & 969 & 22548.99897 & & & \
\hline
\end{array}
\end{array}$

$\begin{array}{l}
\begin{array}{lcccccc}
\hline & \text { Coefficienty } & \text { Standard Emor } & \text { t Star } & \text { P-value } & \text { Lower } 9596 & \text { Upper } 9596 \
\hline \text { Intercept } & 4.288825645 & 0.732966216 & 5.851327866 & 6.66867 E-09 & 2.850439806 & 5.727211483 \
\text { Years of Education } & 0.009850586 & 0.062893064 & 0.156624361 & 0.875573561 & -0.113571873 & 0.133273045 \
\hline
\end{array}\
\text { Figure } 6.3
\end{array}$
-Chow tests are based on comparing the

Accepted Answer

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. 
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 19

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.
 $\begin{array}{lc}
\text { SUMMARY OUTPUT }\
\
\
\hline \text { Regression Statistier } & \
\hline \text { Multiple R } & 0.070494476 \
\text { R Square } & 0.004969471 \
\text { Adpasted R Square } & 0.001879314 \
\text { Standard Error } & 4.819403326 \
\text { Observations } & 970 \
\hline
\end{array}$

$\begin{array}{lccccc}
 \text { ANOVA }\
\hline & \text { df } & \text { SS } & \text { MS } & F & \text { Significance } F \
\hline \text { Regression } & 3 & 112.0566012 & 37.3522004 & 1.608161442 & 0.185858614 \
\text { Residual } & 966 & 22436.94237 & 23.22664841 & & \
\text { Total } & 969 & 22548.99897 & & & \
\hline
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & \text { P-value } & \text { Lower } 9396 & \text { Upper } 95 \% \
\hline \text { Intercept } & 4.049920982 & 1.042107341 & 3.886280064 & 0.000108739 & 2.004865844 & 6.094976119 \
\text { Age } & 0.015626984 & 0.010365497 & 1.507596119 & 0.131984878 & -0.004714504 & 0.035968471 \
\text { Family Sire } & -0.093093463 & 0.084602383 & -1.100364552 & 0.271447442 & -0.259119103 & 0.072932177 \
\text { Years of Education } & 0.005642075 & 0.06474525 & 0.087142685 & 0.930576157 & -0.121415476 & 0.132699626 \
\hline
\end{array}$

$\text { Figure } 6.2$
-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

Accepted Answer

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. 
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.

Question 20

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

Accepted Answer

A)  $\left( U S S _ { \text {restricted } } - U S S _ { \text {unrestricted } } \right) / q$ 
B)  $\left( U S S _ { \text {unrestricted } } - U S S _ { \text {restricted } } \right) / q .$ 
C)  $U _ { S S _ { \text {unrestricted } } } / ( n - k - 1 ) \text {. }$ 
D)  $U _ { S S _ { \text {restricted } } / ( n - k - 1 ) . }$ 
A)  $\left( U S S _ { \text {restricted } } - U S S _ { \text {unrestricted } } \right) / q$ 
B)  $\left( U S S _ { \text {unrestricted } } - U S S _ { \text {restricted } } \right) / q .$ 
C)  $U _ { S S _ { \text {unrestricted } } } / ( n - k - 1 ) \text {. }$ 
D)  $U _ { S S _ { \text {restricted } } / ( n - k - 1 ) . }$

Multiple linear regression analysis determines the

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

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.

Omitted variable bias occurs when

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

Tests of joint significance are used to determine whether

Omitted variable bias is a problem because

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

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.

Suppose you wish to know whether Age and Family Size are jointly significant in the model $\text { Cigarettes Per Day } = \beta _ { 0 } + \beta _ { 1 } \text { Age } + \beta _ { 2 } \text { Family Size } + \beta _ { 3 } \text { Years of Education. }$ The appropriate null hypothesis for this test is

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

An Introduction to Econometrics and Statistical Inference

Collection and Management of Data

Summary Statistics

Simple Linear Regression

Hypothesis Testing in Linear Regression Analysis

Qualitative Variables and Non-Linearities in Multiple Linear Regression Analysis

Model Selection in Multiple Linear Regression Analysis

Heteroskedasticity

Time Series Analysis

Auto-Correlation

Limited Dependent Variables

Panel Data

Instrumental Variables for Simultaneous Equations, Endogenous Independent Variables, and Measurement Error

Quantile Regression, Count Data, Sample Selection Bias, and Quasi-Experimental Methods

Filters

Exam 6: Multiple Linear Regression Analysis

Multiple linear regression analysis determines the

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

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.

Omitted variable bias occurs when

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

Tests of joint significance are used to determine whether

Omitted variable bias is a problem because

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

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.

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

An Introduction to Econometrics and Statistical Inference

Collection and Management of Data

Summary Statistics

Simple Linear Regression

Hypothesis Testing in Linear Regression Analysis

Qualitative Variables and Non-Linearities in Multiple Linear Regression Analysis

Model Selection in Multiple Linear Regression Analysis

Heteroskedasticity

Time Series Analysis

Auto-Correlation

Limited Dependent Variables

Panel Data

Instrumental Variables for Simultaneous Equations, Endogenous Independent Variables, and Measurement Error

Quantile Regression, Count Data, Sample Selection Bias, and Quasi-Experimental Methods

Filters