Question 2 (50 marks) Suppose that we wish to study the effect of income, age and gender on an individual's expenditure on pizza. Using a sample of 40 individuals aged 18 and older, the following results are obtained from 3 alternative models, estimated using OLS in Eviews, where: PIZZA Individual's annual expenditure on pizza (in dollars) AGE=Individual's age (in years) INCOME Individual's annual income (in dollars) = FEMALE = 1 when an individual is female and 0 when an individual is male C = a constant term Model 1: Dependent Variable: PIZZA Method: Least Squares Included observations: 40 Variable Coefficient Std. Error t-Statistic Prob. INCOME 128.9803 34.59125 3.728698 0.0006 1.121270 0.459527 2.440053 0.0195 R-squared 0.135457 Mean dependent var 191.5500 Adjusted R-squared 0.112706 S.D. dependent var 155.8806 S.E. of regression 146.8338 Akaike info criterion 12.86519 Sum squared resid 819285.8 Schwarz criterion 12.94963 Log likelihood -255.3037 Hannan-Quinn criter. 12.89572 5.953856 Durbin-Watson stat 1.494713 0.019461 F-statistic Prob(F-statistic) Model 2: Dependent Variable: PIZZA Method: Least Squares Included observations: 40 Variable Coefficient Std. Error t-Statistic Prob. 342.8848 72.34342 4.739682 0.0000 AGE -7.575556 2.316988 0.0023 INCOME 1.832479 0.464301 0.0003 R-squared 0.329251 Mean dependent var 191.5500 Adjusted R-squared 0.292994 S.D. dependent var 155.8806 S.E. of regression 131.0701 Akaike info criterion 12.66138 Sum squared resid 635636.7 Schwarz criterion 12.78805 Log likelihood F-statistic Prob(F-statistic) -250.2276 Hannan-Quinn criter. 12.70718 9.081100 Durbin-Watson stat 0.900938 0.000619 Model 3: Dependent Variable: PIZZA Method: Least Squares Included observations: 40 Variable Coefficient Std. Error t-Statistic Prob. C INCOME 461.8640 1.854548 51.34408 0.310124 AGE -8.182830 1.550055 5.980027 -5.279059 0.0000 8.995468 0.0000 0.0000 FEMALE -190.2518 27.76806 -6.851463 0.0000 R-squared 0.708871 Mean dependent var 191.5500 Adjusted R-squared 0.684610 S.D. dependent var 155.8806 S.E. of regression 87.54187 Sum squared resid 275888.8 Akaike info criterion Schwarz criterion 11.87675 12.04564 Log likelihood -233.5350 Hannan-Quinn criter. 11.93782 F-statistic 29.21886 Durbin-Watson stat 1.847621 Prob(F-statistic) 0.000000 Please turn over The specification of the models is as follows: Model 1: PIZZA = B + BINCOME + e Model 2: PIZZA = B + BINCOME + B3AGE + e Model 3: PIZZA = B + BINCOME + 3AGE + 4FEMALE + e The following questions refer to Model 2: a) Provide an interpretation of the coefficient estimates (including the constant term). Do the results of the estimation make economic sense? (5 marks) b) Fill out the missing values of the t-statistics and write down the null and the alternative hypotheses of the tests they are computed for. (5 marks) c) Which of the coefficients of the model are statistically significant at the 5% level and why? (3 marks) of it. d) Compute the 95% confidence interval (interval estimate) for 3 and provide an interpretation (5 marks) e) What would the inclusion of an interaction effect (INCOME AGE) in the model attempt to capture? (6 marks) f) Can we expect heteroscedasticity of errors to be a feature of this model and why? What would be an informal way to detect it? (5 marks) g) What are the consequences of heteroscedasticity when estimating a model using OLS and what can be done to address them? The following questions relate to Model 3: (8 marks) h) The results related to Model 3 above incorporate the variable FEMALE in the regression estimation. Interpret the coefficient on the variable FEMALE and its significance. i) What evidence is there to suggest that Model 3 is preferred to Model 2? (2 marks) (6 marks) j) What restrictions on the coefficients of Model 3 yield Model 1. Conduct an F test to test these restrictions (use a 5% level of significance). What question would you be trying to answer by performing this test? (5 marks)