3. The regression outputs below (based on different methods) were estimated using data from 1080 houses...

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3. The regression outputs below (based on different methods) were estimated using data from 1080 houses sold in Baton Rouge, Louisiana during mid-2005. We will be concerned with the selling price (PRICE, measured in dollars), the size of the house in square feet (SQFT), and the age of the house in years (AGE). We define a new variable that measures house size in terms of hundreds of square feet, SQFT100 = SQ FT/100. The proposed model is given by: log(PRICE) = 1 + 2SQFT100 + 3AGE h by 11.120 0.03876 (0.027) (0.00087) (i) Least Squares (ii) with HC standard errors Call: lm (formula = res2 sqft100) Residuals: Min 11.120 (0.033) ~ Coefficients: Test for heteroskedasticity using a Breusch-Pagan test and the variable SQFT100. Is there evidence of heteroskedasticity at a 1% level of significance? Assume the variance of the resid- uals follows the model var(e) = ha + aSQFT100). Below is the respective regression output. 0.03876 -0.01756 (0.00123) (0.00175) 1Q Median -0.08709 -0.07543 -0.05488 -0.01223 4AGE + e. b -0.01756 (0.00136) 3Q b 0.0001734 (0.0000227) Max 1.56199 = 0.0001734 (0.0000372) Estimate Std. Error t value Pr (> [t|) (Intercept) 0.0772423 0.0140495 5.498 4.8e-08 *** sqft100 0.0001417 0.0005543 0.256 0.798 Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 Residual standard error: 0.1835 on 1078 degrees of freedom Multiple R-squared: 6.061e-05, Adjusted R-squared: -0.000867 F-statistic: 0.06535 on 1 and 1078 DF, p-value: 0.7983 = (a) Ho a2 = 0. Since x: 0.065 < Xerit 6.63, we fail reject Ho at the 1% level of significance, and conclude that heteroskedasticity is not present. (b) Ho : a2 = 0. Since x = 0.065 < Xerit 6.63, we reject Ho at the 1% level of significance, and conclude that heteroskedasticity is present. (c) Ho a2 = 0. Since x: = 6.63 > Xerit 0.065, we fail reject Ho at the 1% level of significance, and conclude that heteroskedasticity is not present. 3. The regression outputs below (based on different methods) were estimated using data from 1080 houses sold in Baton Rouge, Louisiana during mid-2005. We will be concerned with the selling price (PRICE, measured in dollars), the size of the house in square feet (SQFT), and the age of the house in years (AGE). We define a new variable that measures house size in terms of hundreds of square feet, SQFT100 = SQ FT/100. The proposed model is given by: log(PRICE) = 1 + 2SQFT100 + 3AGE h by 11.120 0.03876 (0.027) (0.00087) (i) Least Squares (ii) with HC standard errors Call: lm (formula = res2 sqft100) Residuals: Min 11.120 (0.033) ~ Coefficients: Test for heteroskedasticity using a Breusch-Pagan test and the variable SQFT100. Is there evidence of heteroskedasticity at a 1% level of significance? Assume the variance of the resid- uals follows the model var(e) = ha + aSQFT100). Below is the respective regression output. 0.03876 -0.01756 (0.00123) (0.00175) 1Q Median -0.08709 -0.07543 -0.05488 -0.01223 4AGE + e. b -0.01756 (0.00136) 3Q b 0.0001734 (0.0000227) Max 1.56199 = 0.0001734 (0.0000372) Estimate Std. Error t value Pr (> [t|) (Intercept) 0.0772423 0.0140495 5.498 4.8e-08 *** sqft100 0.0001417 0.0005543 0.256 0.798 Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 Residual standard error: 0.1835 on 1078 degrees of freedom Multiple R-squared: 6.061e-05, Adjusted R-squared: -0.000867 F-statistic: 0.06535 on 1 and 1078 DF, p-value: 0.7983 = (a) Ho a2 = 0. Since x: 0.065 < Xerit 6.63, we fail reject Ho at the 1% level of significance, and conclude that heteroskedasticity is not present. (b) Ho : a2 = 0. Since x = 0.065 < Xerit 6.63, we reject Ho at the 1% level of significance, and conclude that heteroskedasticity is present. (c) Ho a2 = 0. Since x: = 6.63 > Xerit 0.065, we fail reject Ho at the 1% level of significance, and conclude that heteroskedasticity is not present.

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Based on the BreuschPagan test results there is evidence of heteroskedasticity at a 1 level of signi... View the full answer