(a) An econometrician estimates the following models: Y, = BotB,X,+B,X, +u, and Y, =B,+B,X,+ B,X2+ B,X; +v, where u, and v, are independent and identically distributed (iid) disturbances and X", is an irrelevant variable. Given this information, what can you conclude about the value of; (i) R and (ii) Adjusted R?? Will it be higher in the second model than in the first model? (4) (b) Using a hypothetical scatterplot of data for a regression model with R2=0.94 and one for a regression equation with R2=0.48. (4) (c) Explain what the meaning of the sampling distribution of B (4) (d) Describe the three types of data sets commonly used in econometrics. (3){a} Explain the meaning of each of these terms: i. Population regression function {PRF} ii. Sample regression function [SRF] iii. Stochastic error term iv. Residual term (4} {b} Ordinary Least Squares estimates have several desirable properties known as BLUE. What does this acronym stand for? Discuss the properties of OILS estimators. {5) {c} Decide whether you would expect the relationships between the following pairs of dependent and independent variables to be positive, negative, or ambiguous. Explain your reasoning i. Aggregate net investment in South Africa in a given year and GDP in that year. ii. The number of acres of maize planted in a season and the price of maize at the beginning of that season. iii. The quantity of canned sh demanded and the retail price of a can of sh. {6] You decide to model ice-cream sales at the ice-cream store nearest to your university. You estimate the following regression equation (standard errors in parenthesis): Y = 131.6 + 4.17, - 35.62P, + 122.4A; (0.68) (18.0) (104.2) N=29 R2 = 0.82 Where Yt = the total number of ice-creams sold during the th two-week time period It = average temperature (in degrees C) during the period t P: = the price of ice-cream (in Rand) at the store in period t At = a dummy variable equal to 1 if the owner places an advert in the university newsletter during the period t, 0 otherwise (a) Is there any evidence that this equation violates any of the Classical assumptions? (5) (b) Why is hypothesis testing important in any regression exercise? (2) (c) Test for the significance of coefficients obtained in this model at the 5% level of significance. (6) (d) Interpret the meaning of the coefficients of Tt, Pt and At. Be specific. (4) (e) What additional variables would you add to this equation? (3)