It is important to note that late submissions will NOT be accepted.
1 Instructions
1. Please type your assignment by using a word processor. If you choose to write, then please
write clearly in ink.
2. It is also very important that you will hand in all your software outputs (e.g., tables and
gures, etc.)
3. Please nd the PHStat/Stata installation instructions on your course outline.
4. Students are encouraged to use Stata to do this assignment. To learn Stata basics, please
view the video clip on the course outline.
5. If you are not sure how to do regression using a software, please watch the videos posted in
the course outline and cuLearn.
6. Also please pay a close attention to academic plagiarism. If I nd two or more papers that
look very similar, there will be a heavy penalty (a maximum of 50 points will be deducted
from all the papers that look very similar.)
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2 Questions
1. The Stata le (equity.dta) contains data on the two nancial variables: S&P 500 price index
(Y) and dividend (X). The sample size is 91 observations.
(a) Use Stata to generate a graph of X on Y.
(b) Regress Y on X, then clearly explain all the regression outputs. Why do you think this
relationship is signi cant?
(c) Fit the data by using a semi-log model with the aid of Stata. Does this semi-log model
perform. better than the model in (b)? Why or why not?
(d) Given the estimated semi-log model, please calculate the slope and elasticity for X at
X = 2:5:
(e) Given the estimated semi-log model, please test for serial correlation in the residuals by
performing the Durbin-Watson test. Is there any heteroscedasticity problem? Please use
both graphical and statistical methods to address this concern.
2. The Excel le (amazon.xls) contains data on the two variables, sales (Y) and income (X) of
a sample of 10 observations from 1995 to 2004.
(a) Use Stata to generate descriptive statistics of X and Y. Explain the statistical results
that you have just obtained.
(b) Construct a scatter diagram.
(c) Find the least-squares regression line of Y on X by using Stata.
(d) Find the least-squares regression line of X on Y by using Stata.
(e) Test the null hypothesis at the 0.05 signi cance level that the regression coe cient of
the population regression is 0.0 versus the alternative hypothesis that the regression
coe cient exceeds 0.0. Perform. the test without the aid of the computer software as well
as with the aid of the computer software.
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(f) Find the 95% con dence interval for the regression coe cient without the aid of the
computer software as well as with the aid of the computer software.
(g) Construct the prediction interval for the conditional mean of Y for a given X = Xp = 5
with the aid of the software.
(h) Conduct diagnostic checks for the residuals by using the Durbin-Watson test, the Breusch-
Pagan test, and the Jarque-Bera test. Please clearly explain your conclusions.
3. The Excel le (prices.xls) contains data on three variables, gas price (Y), natural gas (X),
and electricity (Z) of a sample of 10 observations from 1996 to 2005.
(a) Find the least-squares regression equation of Y on X and Z with the aid of Stata. [Hint:
the regression equation is Y = 0 + 1X + 2Z + .]
(b) Find the coe cient of determination, R2, with the aid of the computer software. What
does the number in R2 imply?
(c) Find the value of the F test. What does the F test say about the overall signi cance of
this model?
(d) Test the null hypothesis at the 0.05 signi cance level that the regression coe cient of
the population regression, 1, is 0.0 versus the alternative hypothesis that the regression
coe cient exceeds 0.0.
(e) Test the null hypothesis at the 0.05 signi cance level that the regression coe cient of
the population regression, 2, is 0.0 versus the alternative hypothesis that the regression
coe cient exceeds 0.0.
(f) Based on the estimated equation bY = b0 +b1X +b2Z, determine the estimated value of
Y from the given values of X and Z.
(g) Estimate the gas price at the natural gas of 9 and the electricity of 8.
(h) Calculate the VIF for each independent variable. Is there any multi-collinearity problem
in this regression? Please explain.
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(i) You can also build a regression model with one independent variable, say either X or
Z: Use the four important speci cation criteria given in Chap. 6 to work out the best
regression model. Please explain your answer in detail.
4. The Stata data le (elemapi.dta) contains data on 21 school-related variables in 400 U.S.
schools. Please refer to the text le (elemapi description.txt) for a description of these vari-
ables.
(a) Regress api00 on meals, acs k3, avg ed, and full with the aid of Stata. [Hint: the
regression equation is Y = 0 + 1X1 + 2X2 + 3X3 + 4X4 + .]
(b) Find the coe cient of determination, R2, with the aid of the computer software. What
does the number in R2 imply?
(c) Find the value of the F test. What does the F test say about the overall signi cance of
this model?
(d) Test the null hypothesis at the 0.05 signi cance level that the regression coe cient of
the population regression, 1, is 0.0 versus the alternative hypothesis that this regression
coe cient is not 0.0.
(e) Test the null hypothesis at the 0.05 signi cance level that the regression coe cient of
the population regression, 2, is 0.0 versus the alternative hypothesis that this regression
coe cient is not 0.0.
(f) Test the null hypothesis at the 0.05 signi cance level that the regression coe cient of
the population regression, 3, is 0.0 versus the alternative hypothesis that this regression
coe cient is not 0.0.
(g) Test the null hypothesis at the 0.05 signi cance level that the regression coe cient of
the population regression, 4, is 0.0 versus the alternative hypothesis that this regression
coe cient is not 0.0.
(h) Use Variance In ation Factor (VIF) to detect potential multi-collinearity.
(i) Regress api00 on meals, acs k3, and full with the aid of Stata. [Hint: the regression
equation is Y = 0 + 1X1 + 2X2 + 3X3 + .] Use all your knowledge about multi-
ple regression, compare this regression model with the model used in part (a). Which
regression model perform. better? Why?