1. Estimate Model 1 and summarise your estimation results. Interpret the estimates of β2, β3 and β5. (Note: a summary regression report should contain regression equation followed by standard errors, test statistics, the number of observations, goodness of fit statistic and the F value. See the example below)
?? = 5.6 - 0.06??1 + 0.43??2 ???? . . ? . . . . ? . . . . ? . . ?? . . ? . . . . ? . . (. . ? . . ) ?? = ? ??! = ? ?? = ? 2.
2. Plot the squared residuals on Y axis of model 1 vs. Size and Beds on X axis (separate plots) and comment on the assumption of homoscedasticity in the variance of the error term. (To save squared residuals in Gretl, in the model window select →save→ squared residuals →and type a name "usq1" in the "Name of variable" and type "squared residual from model 1" under the "Description" and click →ok. In the main window highlight usq1, Size and Beds and choose → View → Multiple graphs → XY Scatter → and push "usq1" into the →Y-axis variable and the Size and Beds in to the → X-axis variables then click ok.
3. Test the individual significance of the slope coefficients and comment on your results. Use a two sided alternative and a 1% significance level.
4. Consider two houses that have the same size, same baths, same stories and same number of garages but one is two beds and the other is five beds. How much difference in the prices should an investor expect between the two houses according to model 1? Construct a 95% confidence interval for this difference in the prices and interpret your result.
5. Test that the variance of the error term in model 1 is homoscedastic against it is heteroscedastic using the Koenker test. Use a 1% significance level. (You must provide the null and alternative hypotheses, test statistic, the distribution of the test statistic under the null and the degrees of freedom, critical value(s), decision rule and your conclusion)
6. Re-estimate Model 1 using the robust standard errors and summarise your estimation results. Comment on your results in relation to your estimation results in question 1.0