4. ( 20pts) For this question let price denote sale price for a house, sqft square footage, and age denote its age. Below we present the output of two regression: The left panel contains the output from regressing price on a sqft and age. The right panel contains the output from regressing price on sqft. (a) By relying on the formula for R2, explain how the R2 increases when we add age. (b) Suppose you know the sqft of a house and you want to predict its price. Based on the R2 of both regressions: Do you think also knowing age would be very helpful in improving your prediction? Justify your answer. (c) Suppose that the total number of observations is 4682 and consider the model price =1+2 sqft +3 age +. Use the output from both regressions to compute F statistic for the null hypothesis that 3=0 against the alternative that 3=0. (Hint: Recall problem 3 ). (d) Explain how you can compute the F statistic you obtained in part (c) by using only the output in the left hand panel. (Note: There will be a small difference in the answers due to rounding errors in the output). 4. ( 20pts) For this question let price denote sale price for a house, sqft square footage, and age denote its age. Below we present the output of two regression: The left panel contains the output from regressing price on a sqft and age. The right panel contains the output from regressing price on sqft. (a) By relying on the formula for R2, explain how the R2 increases when we add age. (b) Suppose you know the sqft of a house and you want to predict its price. Based on the R2 of both regressions: Do you think also knowing age would be very helpful in improving your prediction? Justify your answer. (c) Suppose that the total number of observations is 4682 and consider the model price =1+2 sqft +3 age +. Use the output from both regressions to compute F statistic for the null hypothesis that 3=0 against the alternative that 3=0. (Hint: Recall problem 3 ). (d) Explain how you can compute the F statistic you obtained in part (c) by using only the output in the left hand panel. (Note: There will be a small difference in the answers due to rounding errors in the output)