1. Use the data in MLB1 for this exercise.
(i) Run the following model:
log(ð‘ ð‘Žð‘™ð‘Žð‘Ÿð‘¦)= ð›½0 + ð›½1 ð‘¦ð‘’ð‘Žð‘Ÿð‘ + ð›½2 ð‘”ð‘Žð‘šð‘’ð‘ ð‘¦ð‘Ÿ+ ð›½3 ð‘ð‘Žð‘£ð‘”+ ð›½4 hð‘Ÿð‘¢ð‘›ð‘ ð‘¦ð‘Ÿ+ð›½5 ð‘Ÿð‘ð‘–ð‘ ð‘¦ð‘Ÿ+ð‘¢ 012345
Report your estimation results in the usual form.
(ii) Now drop the variable ð‘Ÿð‘ð‘–ð‘ ð‘¦ð‘Ÿ. What happens to the statistical significance of hð‘Ÿð‘¢ð‘›ð‘ ð‘¦ð‘Ÿ? What about
the size of the coefficient on hð‘Ÿð‘¢ð‘›ð‘ ð‘¦ð‘Ÿ?
(iii) Add the variables ð‘Ÿð‘¢ð‘›ð‘ ð‘¦ð‘Ÿ (runs per year), ð‘“ð‘™ð‘‘ð‘ð‘’ð‘Ÿð‘ (fielding percentage), and ð‘ ð‘ð‘Žð‘ ð‘’ð‘ ð‘¦ð‘Ÿ (stolen
bases per year) to the model from part (ii). Which of these factors are individually significant? (iv) In the model from part (iii), test the joint significance of ð‘ð‘Žð‘£ð‘”, ð‘“ð‘™ð‘‘ð‘ð‘’ð‘Ÿð‘, and ð‘ ð‘ð‘Žð‘ ð‘’ð‘ ð‘¦ð‘Ÿ.
2. Use the data in HTV to answer this question.
(i) Estimate the regression model
ð‘’ð‘‘ð‘¢ð‘ = ð›½0 + ð›½1 ð‘šð‘œð‘¡hð‘’ð‘‘ð‘¢ð‘ + ð›½2 ð‘“ð‘Žð‘¡hð‘’ð‘‘ð‘¢ð‘ + ð›½3 ð‘Žð‘ð‘–ð‘™ + ð›½4 ð‘Žð‘ð‘–ð‘™^2 + ð‘¢ 01234
by OLS and report the results in the usual form. Test the null hypothesis that ð‘’ð‘‘ð‘¢ð‘ is linearly related to ð‘Žð‘ð‘–ð‘™ against the alternative that the relationship is quadratic.
(ii) Using the equation in part (i), test ð»0: ð›½1 = ð›½2 against a two-sided alternative. What is the ð‘-value of the test?
(iii) Add the two college tuition variables to the regression from part (i) and determine whether they are jointly statistically significant.
3. Use the data in GPA2 for this exercise.
(i) Estimate the model
ð‘ ð‘Žð‘¡ = ð›½0 + ð›½1 hð‘ ð‘–ð‘§ð‘’ + ð›½3 hð‘ ð‘–ð‘§ð‘’^2 + ð‘¢
where hð‘ ð‘–ð‘§ð‘’ is the size of the graduating class (in hundreds), and write the results in the usual form. Is the quadratic term statistically significant?
(ii) Using the estimated equation from part (i), what is the “optimal†high school size? Justify your answer.
(iii) Is this analysis representative of the academic performance of all high school seniors? Explain.
(iv) Find the estimated optimal high school size, using ð‘™ð‘œð‘”(ð‘ ð‘Žð‘¡) as the dependent variable. Is it much different from what you obtained in part (ii)?
4. Use the housing price data in HPRICE1 for this exercise.
(i) Estimate the model
log(ð‘ð‘Ÿð‘–ð‘ð‘’) = ð›½0 + ð›½1 log (ð‘™ð‘œð‘¡ð‘ ð‘–ð‘§ð‘’) + ð›½2 log (ð‘ ð‘žð‘Ÿð‘“ð‘¡) + ð›½3ð‘ð‘‘ð‘Ÿð‘šð‘ + ð‘¢
and report the results in the usual OLS format.
(ii) Find the predicted value of ð‘™ð‘œð‘”(ð‘ð‘Ÿð‘–ð‘ð‘’), when ð‘™ð‘œð‘¡ð‘ ð‘–ð‘§ð‘’ = 20,000, ð‘ ð‘žð‘Ÿð‘“ð‘¡ = 2,500, and ð‘ð‘‘ð‘Ÿð‘šð‘ = 4.
(iii) For explaining variation in price, decide whether you prefer the model from part (i) or the model described below:
ð‘ð‘Ÿð‘–ð‘ð‘’ = ð›½0 + ð›½1 ð‘™ð‘œð‘¡ð‘ ð‘–ð‘§ð‘’ + ð›½2 ð‘ ð‘žð‘Ÿð‘“ð‘¡ + ð›½3ð‘ð‘‘ð‘Ÿð‘šð‘ + ð‘¢
Jermaine Byrant
Nicole Johnson
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