Problems [PDF]

Zitiervorschau

Problem 1 (7 points): In order to explain the US defense budget, you are using the data from 1962 to 1981 with the following variables (all measured in billions USD) and estimate the corresponding model (Model 1):(Use α=0.05 for references) Yt: X2t: X3t: X4t: D1t:

Defense budget outlay for year t GNP for year t US military sales in year t Aerospace industry sales in year t Dummy variable presenting the military conflict involving more than 100,000 troops; D1t=1 if more than 100,000 troops are involved and equal to 0 if fewer than 100,000 troops are involved.

Dependent Variable: Y Method: Least Squares Variable Coefficient C 21.40251 D1 -48.21987 X2 0.013879 X3 0.073146 X4 1.389753 X4*D1 1.540792 X2*D1 0.022406 R-squared 0.996366 Adjusted R-squared 0.994688 S.E. of regression 2.111972 Sum squared resid 57.98554 Log likelihood -39.02338 Durbin-Watson stat 2.233771

Sample: 1962 1981 Included observations: 20 Std. Error t-Statistic Prob. 1.496947 14.29744 0.0000 6.871544 -7.017328 0.0000 0.003207 4.328062 0.0008 0.203805 0.358902 0.7254 0.130197 10.67423 0.0000 0.325005 4.740818 0.0004 0.005781 3.876038 0.0019 Mean dependent var 83.86000 S.D. dependent var 28.97771 Akaike info criterion 4.602338 Schwarz criterion 4.950845 F-statistic 593.9815 Prob(F-statistic) 0.000000

1. Explain the meaning of each estimated coefficient and R2 in the above model. 2. Test for significance of each independent variable and test for overall significance of the model. 3. Conduct the test of autocorrelation in the model using the information above. State clearly the conditions to apply this test? If those conditions are not met, name other tests you can use instead. 4. When GNP increases by 1 bil USD (other variables unchanged), what is the confidence interval of the difference in the changing levels of defense budget between the cases of there are more than 100,000 or fewer than 100,000 troops involved in the military conflict?

5. For the case when there are fewer than 100,000 troops involving in the conflict (this condition indicates that we are concerning on the coefficients of X2 and X4 only), if we simultaneously increase X2 and X4 by 1 billions USD, test the proposition that the defense budget will increase 1.4 billions USD. What is the confidence interval for the increase in the level of defense budget in this case? (The covariance between two estimated coefficients of 2 variables X2 and X4 is -0.00036). 6. Do you think that the military budget does not depend on the number of troops involving in the conflict given that if you regress Y on X2, X3 and X4 (with intercept), you get R2=0.971 and RSS=461.28? 7. What would happen if the model included dummies for both cases of there are more than 100,000 and fewer than 100,000 troops involved in the military conflict, (two dummy variables)? What is this problem called? What are the consequences of this problem? How to correct this problem if it exists? 8. The information below is the F statistic and p-value in the test for one of the problems in the model. What type of problem, name of test, null and alternative hypothesis and conclusion about the problem. Ramsey RESET Test: F-statistic 2.110154 Probability Log likelihood ratio 7.432899 Probability

0.119102 0.059308

Problem 2 (2 points): Given the output below for the logistic regression in which GRADE is 1 if students get A, 0 if not A. GPA is the grade point average before entering the Uni, PSI=1 if study in the new system, 0 if not. Answer the following questions: Logistic regression

Number of obs LR chi2(2) Prob > chi2 Pseudo R2

Log likelihood = -11.498832

1. 2. 3. 4.

GRADE

Coef.

GPA PSI _cons

3.427025 2.694516 -12.54891

Std. Err. 1.239022 1.133268 4.200189

z 2.77 2.38 -2.99

P>|z| 0.006 0.017 0.003

= = = =

32 20.23 0.0000 0.4680

[95% Conf. Interval] .9985864 .4733511 -20.78113

5.855463 4.915682 -4.316689

Write the estimated logistic model and logit model Test for significance of Independent variables. Explain the meaning of each coefficient (using log odd form). What is the probability of getting Grade A when a student studying in the new system and having GPA of 3. 5. At the level in question 4, if PSI is fixed, how the probability of getting A changes if GPA increases 1 point?