Dependent Variable: PRICE Method: Least Squares Date: 10/13/21 Time: 12:26 Sample: 1 900 Included observations: 900...

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Dependent Variable: PRICE Method: Least Squares Date: 10/13/21 Time: 12:26 Sample: 1 900 Included observations: 900 Variable Coefficient Std. Error t-Statistic Prob. C SQFT AGE BATHS -62.46140 9.182401 7.916557 0.348160 -0.577210 0.138497 23.13072 5.660916 -6.802295 0.0000 22.73831 0.0000 -4.167680 0.0000 4.086038 0.0000 R-squared Adjusted R-squared S.E. of regression 0.629735 Mean dependent var 0.628495 S.D. dependent var 67.92448 Akaike info criterion Sum squared resid 4133906. Schwarz criterion Log likelihood -5071.597 Hannan-Quinn criter. 151.2452 111.4407 11.27910 11.30045 11.28726 F-statistic 507.9623 Durbin-Watson stat 1.979329 Prob(F-statistic) 0.000000 (a) (2 marks) You suspect that the change in price associated with an extra square feet of house size depends on how old the house is. Extend the model in question 1(a) to allow for this (write the new model down). Estimate this model and include your Eviews output. (b) (2 marks) Comment on the significance of all the coefficients in the extended model you just estimate for question 3(a) using the p-value appraoch. (Don't forget to state the significance level at which the coefficients are significant, e.g. 1, 5 or 10 percent) (c) (3 marks) Using this extended model, write down the expressions for the marginal effect E(price X) where X denote all observations on sqft and age. Interpret this expression for a house with age equal to a particular level, say age. Note, there is no need to put in any numbers here and you can use bk to denote estimate for k- sqft (d) (8 marks) Find point estimates AND 95% interval estimates for the marginal effect of an extra hundred square feet of total living area on house price for houses that are (i) 2 years old, and (ii) 45 years old. How do these estimates change as age increases? [You can use Eviews to find the appropriate standard errors]. Dependent Variable: PRICE Method: Least Squares Date: 10/13/21 Time: 12:26 Sample: 1 900 Included observations: 900 Variable Coefficient Std. Error t-Statistic Prob. C SQFT AGE BATHS -62.46140 9.182401 7.916557 0.348160 -0.577210 0.138497 23.13072 5.660916 -6.802295 0.0000 22.73831 0.0000 -4.167680 0.0000 4.086038 0.0000 R-squared Adjusted R-squared S.E. of regression 0.629735 Mean dependent var 0.628495 S.D. dependent var 67.92448 Akaike info criterion Sum squared resid 4133906. Schwarz criterion Log likelihood -5071.597 Hannan-Quinn criter. 151.2452 111.4407 11.27910 11.30045 11.28726 F-statistic 507.9623 Durbin-Watson stat 1.979329 Prob(F-statistic) 0.000000 (a) (2 marks) You suspect that the change in price associated with an extra square feet of house size depends on how old the house is. Extend the model in question 1(a) to allow for this (write the new model down). Estimate this model and include your Eviews output. (b) (2 marks) Comment on the significance of all the coefficients in the extended model you just estimate for question 3(a) using the p-value appraoch. (Don't forget to state the significance level at which the coefficients are significant, e.g. 1, 5 or 10 percent) (c) (3 marks) Using this extended model, write down the expressions for the marginal effect E(price X) where X denote all observations on sqft and age. Interpret this expression for a house with age equal to a particular level, say age. Note, there is no need to put in any numbers here and you can use bk to denote estimate for k- sqft (d) (8 marks) Find point estimates AND 95% interval estimates for the marginal effect of an extra hundred square feet of total living area on house price for houses that are (i) 2 years old, and (ii) 45 years old. How do these estimates change as age increases? [You can use Eviews to find the appropriate standard errors].