Question 1 A researcher estimates an equation for the valuation of homes and tow

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Question 1 A researcher estimates an equation for the valuation of homes and towns surrounding Boston using a sample of 506 homes. The estimation equation is given by VALUE, A + ?,ROOMS, + ?,CRIME,+ ?,DIST+ e, where, VALUE- median value of owner-occupied homes in thousands of dollars ROOMS average number of rooms per dwelling CRIME per capita crime rate DIST weighted distances to five Boston employment centers a. Obtaining the residuals from the above model, the researcher estimated the following least squares regression. The relevant output is shown in the table below. sQ Dependent Variable: EHAT_SQ Included observations: 506 Coefficient 1007.037 305.311 23.822 2.285 -0.039 4.419 ESS 5,038,458 Std. Errort-value 4.92 4.84 4.92 1.84 -2.04 P-value 0.000 0.000 0.000 0.067 0.042 0.074 Variable 204.522 ROOMS ROOMS CRIME CRIME DIST R2-0.08467 63.088 4.844 1.242 0.019 2.466 TSS -5,504,525 where EHAT SQ denotes the squares of the estimated least squares residuals. Using the above results, perform the White's test for heteroskedasticity. Remember to construct the White's test statistic and compare it with the relevant critical value. Clearly state your conclusion as to whether there is formal evidence of heteroskedasticity in the model. Use a 5% significance level. b. If you take a closer look, it is clear that this researcher has estimated a model that does not exactly follow the theory behind the White's test for heteroskedasticity. What would you do differently and why? Briefly explain.

Explanation / Answer

a. Test Statistic : nR2 = 506* 0.08467 = 42.84302

critical point: 1.145476

Here the null hypothesis is homoskedasticity . Since test statistic > critical point , we reject the null hypothesis and can say that there exists some evidence for heteroskedasticity

b. I would reduce the variables keep only the significant variables so that my R2 will change affecting white test

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