Exam 3: Residual Statistics

Given: (6 pts. each) Dependent Variable: LNWAGES Method: Least Squares Date: 12/05/08 Time: 10:01 Sample: 1534 Included observations: 534 Variable Coefficient Std. Error t-Statistic Prob. C 1.165162 0.106127 10.97895 0.0000 ED 0.076850 0.007867 9.768470 0.0000 FEM -0.232071 0.041253 -5.625564 0.0000 R-squared 0.192822 Mean dependent var 2.059181 Adjusted R-squared 0.189782 S.D. dependent var 0.527733 S.E. of regression 0.475024 Akaike info criterion 1.354700 Sum squared resid 119.8191 Schwarz criterion 1.378747 Log likelihood -358.7049 F-statistic 63.42366 Durbin-Watson stat 1.903586 Prob(F-statistic) 0.000000 Where: LNWAGES = the natural log of pay per hour of work ED = years of education FEM = 1 if female, 0 otherwise A) Interpret the value of the constant term. B) Interpret the value of the coefficient on ED. C) Interpret the value of the coefficient on FEM. D) According to this model, what are the expected wages of a female with 16 years of education?

Given: (7 pts. each) Dependent Variable: WAGES Method: Least Squares Date: 12/08/08 Time: 10:39 Sample: 1534 Included observations: 534 Variable Coefficient Std. Error t-Statistic Prob. C 8.622140 0.505267 17.06451 0.0000 EXPER 0.080909 0.024238 3.338126 0.0009 FEM -0.765100 0.764604 -1.000648 0.3175 EXFER*FEM -0.079757 0.035061 -2.274768 0.0233 R-squared 0.061907 Mean dependent var 9.023947 Adjusted R-squared 0.056597 S.D. dependent var 5.138874 S.E. of regression 4.991333 Akaike info criterion 6.060745 Sum squared resid 13204.10 Schwarz criterion 6.092808 Log likelihood -1614.219 F-statistic 11.65871 Durbin-Watson stat 1.765220 Prob(F-statistic) 0.000000 Where:WAGES = pay per hour of work EXPER = years of experience FEM = 1 if female, 0 otherwise CHICK_t-2 + e_t " A) Interpret the coefficient on EXPER. B) Interpret the coefficient on EXPER*FEM. C) Draw a diagram reflecting the regression results with WAGES on the vertical axis and EXPER on the horizontal axis. Label all intercepts and slopes. D) What would be the new values of the structural parameters if the dummy was flip-flopped? E) Which regression fits better, the one from question 1 or the one from question 2? Explain.

Given: (7 pts. each) Dependent Variable: $\mathrm { B } \mathbb { I N G E }$ Method: Least Squares Sample(adjusted): 1695 Included observations: 695 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. C 0.818558 0.125126 6.541884 0.0000 GPA -0.125652 0.033407 -3.761217 0.0002 MALE 0.135596 0.036207 3.745041 0.0002 WHITE 0.200085 0.056133 3.564477 0.0004 R-squared 0.056816 Mean dependent var 0.628777 Adjusted R-squared 0.052721 S.D. dependent var 0.483480 S.E. of regression 0.470563 Akaike info criterion 1.335963 Sum squared resid 153.0075 Schwarz criterion 1.362115 Log likelihood -460.2471 F-statistic 13.87497 Durbin-Watson stat 2.015544 Prob(F-statistic) 0.000000 Where: BINGE = 1 if student is a binge drinker, 0 otherwise GPA = grade point average MALE = 1 if male, 0 otherwise WHITE = 1 if white, 0 otherwise A) Interpret the constant term. B) Interpret the coefficient on GPA. C) Interpret the coefficient on MALE. D) According to this model, what is the probability that a white female with a 2.8 GPA is a binge drinker?

Given: (4 pts.) Dependent Variable: $\mathrm { B } \mathbb { I N G E }$ Method: ML - Birary Logit (Quadratic hill climbing) Sample(adjusted): 1695 Included observations: 695 after adjusting endpoints Convergence achieved after 4 iterations Covariance matrix computed using second derivatives Variable Coefficient Std. Error z-Statistic Prob. C 2.174010 0.565780 3.842498 0.0001 GPA -0.552753 0.159758 -3.459934 0.0005 MALE 0.581107 0.163816 3.547312 0.0004 What is the probability that a male with a GPA = 2.8 is a binge drinker? Show your calculations.

Suppose you are estimating an equation to predict daily changes in the Dow Jones Industrial Average over the past 5 years (so you have 1250 observations.) In addition to a bunch of other explanatory variables, you decided to include a dummy variable (ODDDAY = 1 on an odd numbered day (i.e. the 25^th of the month, as opposed to the 26^th); zero otherwise) to capture whether or not the day was odd numbered. Your hypothesis is that people psychologically prefer even numbers, so the DJIA should move higher on even number days and lower on odd number days. Your results look like this $\hat { Y }$ = -12.87 + ……. - 7.92 ODDDAY (-4.65) (-2.1) (where …… represents results on all the rest of the X variables and t-statistics are in parentheses) A) The results shown can be taken to mean that you were right: the negative feelings about odd days cause people to react negatively in the stock market, and those negative odd-day feelings cause the DJIA fall. True, false, or uncertain? Explain. B) What would be a good guess for the value of the p-value on the coefficient attached to ODDDAY? Explain. C) When you drop ODDDAY from the model R² decreases a small amount; adjusted R² decreases a small amount; and the Akaike Information Criterion falls a small amount. Explain what these three changes imply about whether ODDDAY belongs in the model or not. D) A classmate says your model must be bad because the estimated intercept coefficient of -12.87 makes no sense-the DJIA cannot be negative. How do you respond?