Please help with these questions
a) (5 points) Suppose that all of the wines in the sample came from France and USA. What problem, if any, would this cause for estimating regression (1) using OLS? You estimate regression (1) and obtain the following estimates. The standard errors are shown in parenthesis below the estimate. A price 2 5 + 0.1 Score + 1.2 France 0.5 Australia (0.10) (0.045) (0.70) (0.30) b) (5 points) Precisely interpret the estimate on the intercept, and the slope estimates on the dummy variables France and Australia. 0) (4 points) Using an Ftest, test the null hypothesis that the effect of score on wine prices is zero against the alternative that it is not at the 5% signicance level. (1) (4 points) Construct a 95% condence interval for the effect of a 10-point increase in scores on wine prices. e) (5 points) Jointly test the null hypothesis that Austmim = 0 and Bprance = 0, at a 5% signicance level. Assume the t-statistics for testing each restriction individually have a correlation of 0.5. f) (5 points) Suppose you instead wanted to use France as the reference category. Write down the new regression model and nd the estimates for the intercept and all slope coeicients. g) (4 points) Suppose you decide that oak ageing matters for determining the price of a wine, so you add it to the regression model to get price 2 g + scoreScore + pmmeFrance + AuStmh-aAustralia + aakoak + u (2) where oak represents the number of years of oak ageing. Would the R2 and the adjusted R2 in regression (2) be higher or lower than the one without oak (i.e., regression (1))? Explain. h) (4 points) Suppose you wanted to extend regression (1) to let the effect of scores on wine price to depend on the level of score. Write down the regression model that accounts for this effect. Question 4 - 36 points Suppose you are given the following sample regression function: price 2 )80 + scomScore + pmmeFrance + AustmlmAustralia + u (1) where price is the wine price measured in dollars, score is the score given by a wine expert (scale 1 to 100 points), Europe and Australia are dummy variables indicating the wine's country of origin. The reference category is United States (USA). The sample size is 50. a) (5 points) Suppose that all of the wines in the sample came from France and USA. What problem, if any, would this cause for estimating regression (1) using OLS? You estimate regression (1) and obtain the following estimates. The standard errors are shown in parenthesis below the estimate. A price 2 5 + 0.1 Score + 1.2 France 0.5 Australia (0.10) (0.045) (0.70) (0.30)
