We specify the following linear regression model log(price) = β0 + β1sqrmt + β2room + u to study the determinants of house prices: sqrmt is the square meters of the house, room is the number of bedrooms, and price is the price in thousands of euros. The estimates obtained using OLS with a sample of n = 103 observations are log\(price) = 8 (0.01) + 0.01 (0.01) sqrmt + 0.08 (0.01) rooms, R2 = 0.5, X 103 i=1 uˆ 2 i = 157 (standard errors in parentheses) (a) (0.25 points) For the rst house in the sample, log(price1) = 12, sqrmt1 = 80, room1 = 2. Explain how to nd uˆ1 (write the formula replacing all the available values but no need of doing the calculations). (b) (0.25 points) What is the predicted dierence in the price of two houses A and B, both with the same number of square meters, but A with 2 bedrooms more than B? The answer has to include the magnitude and the measurement units. (c) (0.5 points) Interpret R2 = 0.5 and explain how to nd P103 i=1(log(pricei)−log(price))2 (no need of doing the calculations). (d) (0.5 points) Write the formula used to obtain se(βˆ 1) = 0.01. (e) (0.5 points) Construct a 95% condence interval for β1 (the critical value is 1.97). (f) (0.5 points) If the p − value of a test is p − value = 0.04, can you reject the null at 5%? And at 1%? Why? (g) (0.5 points) Test (two-tailed) at 5% the null hypothesis that one more bedroom is predicted to increase the price by 10% (the critical value is 1.97). The answer has to include (i) the null hypothesis, (ii) the alternative hypothesis, (iii) the formula and the value of the test statistic, (iv) the rejection rule and (v) the conclusion of the test. (h) (1 point) We now want to assess how the correlation between room and sqrmt aects the estimation of β1. Knowing that in the regressions sqrmt = α0 + α1rooms + u, the determination coecient is R2 = 0.5, compute the variance ination factor associated to β1. (i) (1 point) Suppose we now omit the relevant variable room and estimate the wrong model log(price) = β0 +β1sqrmt+u. The correlation between room and sqrmt is 0.7 and suppose β2 > 0. Is the estimator of β1 obtained in this model unbiased? If not, discuss the sign of the bias. (j) (1 point) Extend the model by adding a new regressor which makes the eect of room on price dependent on sqrmt. (k) (1 point) We now add two more regressors: crime (the number of crimes committed in the area where the house is located) and age (the age of the house). The model is now log(price) = β0 + β1sqrmt + β2rooms + β3crime + β4age + u with R2 = 0.7. Test the null H0 : β3 = β4 = 0. The answer has to include (i) the restricted model, (ii) the test statistic (write the formula, replace all the available values but no need of computing the value) , (iii) the rejection rule. Use 3 as critical value.