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Multiple Regression

Consider the following model, which was estimated on 133 observations
 
\begin{tabular}{rllll}
$y_i=$~&~$~2.23+$~&~$~0.63x_{1i}+$~~&~$~0.17x_{2i}+$~&~$\hat{\epsilon_i}$~\\
&~$(1.11)$~&~$(0.16)$~&~$(0.06)$~&~\\
\end{tabular}
where ~R^2=0.224 and standard errors are in parentheses. Test the joint significance of the regression.

Consider the following model, which was estimated on 133 observations
 
\begin{tabular}{rllll}
$y_i=$~&~$~2.23+$~&~$~0.63x_{1i}+$~~&~$~0.17x_{2i}+$~&~$\hat{\epsilon_i}$~\\
&~$(1.11)$~&~$(0.16)$~&~$(0.06)$~&~\\
\end{tabular}
Standard errors are in parentheses. Assuming ~cov(x_{1i},~x_{2i})=0~. Test the joint significance of the regression.

Consider the following model, which was estimated on 133 observations
 
y_i=1.13+0.44x_{i}-~0.03x^2_{i}+\hat{\epsilon_i}
Find the value of ~x_i~ at which the function is maximised.

Consider the following model, which was estimated on 133 observations
 
y_i=1.13+0.44x_{i}-~~0.03ln(x_{i})+\hat{\epsilon_i}
Find the value of ~x_i~ at which the function is minimised.

Consider the following model:
 
y_i=1.13+0.44x_{i}-~0.03x^2_{i}+\hat{\epsilon_i}
Find ~\delta{y}/\delta{ln(x)}~.

Consider the following model, which was estimated on 133 observations
 
y_i=1.13-0.36x_{1i}+~0.07x^2_{1i}+\hat{\epsilon_i}
where the variance-covariance matrix is written
 
\left~[
\begin{tabular}{lll}
1.01~&~0.11~&~0.04~\\
0.11~&~0.29~&~-0.03~\\
0.04~&~-0.03~&~0.10~\\
\end{tabular}
\right~]
Test the hypothesis that the marginal effect of ~y~ w.r.t ~x_{1i}~ is zero when ~x_{1i}=2~.

Consider the following model, which was estimated on 133 observations
 
y_i=1.13-0.36x_{1i}-~0.07(1/x_{1i})+\hat{\epsilon_i}
where the variance-covariance matrix is written  
\left~[
\begin{tabular}{lll}
1.01~&~0.11~&~0.04~\\
0.11~&~0.29~&~-0.03~\\
0.04~&~-0.03~&~0.10~\\
\end{tabular}
\right~]
Test the hypothesis the marginal effect of ~y~ w.r.t ~x_{1i}~ is zero when ~x_{1i}=1~.

Consider the following model estimated on a sample of 81 observations:
 
\begin{tabular}{rlllll}
$y_i=$~&~$~1.16+$~&~$~1.43x_{1i}+$~~&~$~0.77x_{2i}+$~~~&~$~0.23x_{3i}+$~&~$\hat{\epsilon_i}$~\\
&~$(0.35)$~&~$(0.26)$~&~$(0.21)$~&~$(0.11)$~&~\\
\end{tabular}
where standard errors are in parentheses and RSS=7.36. Calculate the RSS of a model which imposes the hypothesis that the coefficient in ~x_{1i}~ is unity.

Consider the following model estimated on a sample of 81 observations:
 
\begin{tabular}{rlllll}
$y_i=$~&~$~1.16+$~&~$~1.43x_{1i}+$~~&~$~0.77x_{2i}+$~~~&~$~0.23x_{3i}+$~&~$\hat{\epsilon_i}$~\\
&~$(0.26)$~&~$(0.44)$~&~$(0.26)$~&~$(0.11)$~&~\\
\end{tabular}
where standard errors are in parentheses and RSS=7.36. Imposing the hypothesis that the coefficient on ~x_{1i}~ is unity and ~x_{2i}~ is zero yielded a RSS of 7.95. Calculate the value of the test for the hypothesis.

Consider the following a random sample of 2714 individual young workers in the U.S. [National Longitudinal Survey of Youth 1979 (NLSY79)], who were aged between 14 and 21 in 1979. The following output is based on a model to explain earnings:
 
\begin{tabular}{lllll}
$learnings$~&~$Coef$~&~$Std~Err$~&~$t$~&~$P>|t|$~\\
$tenure$~&~.0338157~&~.0049998~&6.76~&~0.000~\\
$tenure2$~&~-.0007474~&~.0002304~&~-3.24~&~0.001~~~~\\
$age$~&~-.0072442~&~.0043806~&~-1.65~&~0.098~~~~\\
$female$~&~-.2888998~&~.0189968~&~-15.21~&~~0.000~\\
$ethnic2$~&~.0139359~&~$x_1$~&~0.34~&~0.735~\\
$ethnic3$~&~-.0786273~&~~.029267~&~-2.69~&~$x_2$~\\
$school$~&~.0818975~~&~.0050734~&~$x_3$~&~0.000~\\
$asvabc$~&~.0115505~&~.0013143~&~8.79~&~0.000~~~~~\\
$cons$~&~1.34236~~&~.1830481~&~7.33~&~0.000~~~~~\\
\end{tabular}
where: learnings=ln(earnings), female=1 if female and 0 if male, tenure is a measure of work experience, tenure2=tenure*tenure, school is a measure of years of schooling, asvabc=a measure of arithmetic and reading ability, ethnic2=1 if hispanic, 0 otherwise, ethnic3=1 if black, 0 otherwise (ethnic1 taken as the default dummy variable). Construct a 95% CI for the coefficient on school:




Using the result given the earlier question regarding earnings equation for the sample of 2714 individual young workers in the U.S. [National Longitudinal Survey of Youth 1979 (NLSY79)], which of the following is the best interpretation of the coefficient on the variable ~female~.

Using the result given the earlier question regarding earnings equation for the sample of 2714 individual young workers in the U.S. [National Longitudinal Survey of Youth 1979 (NLSY79)], if the variable ~female~ is replaced by the variable ~male~. Which of the following statements would be correct interpretation of the coefficient on ~male~.

Using the result given the earlier question regarding earnings equation for the sample of 2714 individual young workers in the U.S. [National Longitudinal Survey of Youth 1979 (NLSY79)], which of the following is the best interpretation of the coefficient on the variable ~school~.

Using the result given the earlier question regarding earnings equation for the sample of 2714 individual young workers in the U.S. [National Longitudinal Survey of Youth 1979 (NLSY79)], suppose you drop the variable ethnic3 and instead include the variable ethnic1. What would be the coefficient estimates on the variables ethnic1 and ethnic2.



  • Unrestricted R^2
  • DoF unrestricted model
  • Unrestricted RSS
  • Number of restrictions
  • Unrestricted error variance
  • DoF restricted model
  • Restricted RSS
  • Restricted R^2
  • Restricted error variance
  • F-test
  • Critical Value
  • 0.650
  • 15.41
  • 0.497
  • 0.685
  • 0.504
  • 17.12
  • 3
  • 1.153
  • 34
  • 2.911
  • 31

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