Question

2. Use the data in hpricel.wfl uploaded on Moodle for this exercise. We assume that all assump- tions of the Classical Linear Model are satisfied for the model used in this question. (a) Estimate the model and report the results in the usual form, including the standard error of the regression. Obtain the predicted price when we plug in lotsize - 10, 000, sqrft - 2,300, and bdrms- 4; round this price to the nearest dollar. (b) Run a regression that allows you to compute the 95% confidence interval of E (price | lotsize:= 10000, aqrft-2300, bdrms= 4) Note that your prediction may differ somewhat due to rounding error. Compute this confidence interval. If you were going to an auction of a house with lotsize 10,000, sgrft 2,300, and bdrms -4, based on this data, would you be 95% confident that the price will be in this interval? (c) Compute a 95% prediction interval for the price of house with lotsize 10,000, sort 2, 300, and bdrms -4. If you were going to an auction of a house with lotsize 10,000, 8qrft = 2,300, and bdrms = 4, based on this data, would you be 95% confident that the price will be in this prediction interval? Notes: . In order to get the standard error for predicted value of price given lot size, square footage and number of bedrooms, we use the property that OLS results do not change qualitatively when we add or subtract a constant from an explanatory variable. Only the interpretation of the constant term changes. So, if you rerun the regression with lotsize- 10000, sqrft 2300, and bdrms -4 as explanatory variables, then the constant term will be the predicted price of a house with lotsize 10,000, sqrft 2, 300, and bdrms-4. The calculation of the prediction is not a big deal, but getting its standard error would have required using the estimated variance and covariances of the estimated intercept and slope parameters and using the formula for the variance of a linear combination of these to compute the variance of the prediction. With this reparameterisation trick, you get the standard error of price directly. This is a very useful trick. . It is important to note the distinction between the confidence interval for Ε (price l lotsize-, 10000, sgr/t-2300, bdrms-4)-Ao + 1000081 + 230092 + 4ß3 and the prediction interval for price conditional on lotsize = 10000, sgrft = 2300, bdrms = 4. Our estimate of the mean of price given house characteristics varies in different samples because the estimates of the intercept and slope parameters vary, that is, it only varies because of "estimation uncertainty". The price itself, however, includes u, a source of uncertainty that we cannot explain with the three observed characteristics, so the prediction interval for pbe is much wider, because it allows for the variation in u in addition to the variation in the estimated coefficients. In fact, the variation in u dominates and as we get larger and larger samples, the estimation uncertainty becomes smaller and smaller while the variation due to u does not change. Equation: UNTITLED Workfile: HPRICE 1::Hprice1 View Proc Object Print Name Freeze Estimate Forecast Stats Resids Dependent Variable: PRICE Method: Least Squares Date: 04/29/19 Time: 16:10 Sample: 188 Included observations: 88 Variable Coefficient Std. Error t-Statistic Prob LOTSIZE SQRFT BDRMS 0.002068 0.000642 3.220096 0.0018 0.122778 0.013237 9.275093 0.0000 13.85252 9.010145 1.537436 0.1279 21.77031 29.47504 -0.738601 0.4622 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 293.5460 102.7134 11.06540 11.17800 11.11076 2.109796 0.672362 Mean dependent var 0.660661 S.D. dependent var 59.83348 Akaike info criterion 300723.8 Schwarz criterion -482.8775 Hannan-Quinn criter 57.46023 Durbin-Watson stat 0.000000

Answer 1

tu The padlesed pace 's 318.09717-318 (ANS)

230, bd 나 Recoleat 85 calc tulutons canu be done Size data μ๘n24 Resmoỉ once Jou have 2500 딘30a) defined eanDkn. dctc elnet.