PART III: SHORT ANSWER QUESTIONS (100 POINTS) Roman Roy, a real estate analyst, is analyzing the assessed value of all houses in Silver Spring, Maryland. The goal of his analysis is to predict the assessed value (in $1,000's) based on the house size and whether the house has a fireplace (0 =no, 1 = yes). To do so, he develops a regression model and estimates it using data from a random sample of houses. 1) Write down the regression population model that Roman wants to estimate. What are some of the factors that could be captured in the error term? [10 points] 2) Write down the sample regression model that Roman will estimate with his sample. [5 points] 3) Consider the following results of the regression analysis. R Square Regression Statistics Adjusted R Square Observations ANOVA Regression Residual 0.3323 0.2829 28 SS MS F Significance F 2 5146.396 25731.198 6.7201 0.0043 25 103382.712 3828.9893 Total 27 154845.108 Coefficients Standard Error tStat P-value Intercept Size 269.419 33.570 8.026 0.000 0.049 0.014 3.525 0.002 Fireplace 12.162 27.035 0.450 0.656 Write down the prediction model (or regression equation) (5 points) 4) Interpret the coefficient associated with household size [10 points] 5) What is the predicted value of a 1,200 square feet house with fireplace? (show your work) [10 points] 6) What is the R2 of the model? Interpret it. [10 points] 7) Kendall, Roman's colleague, points out that the value of the coefficient associated with fireplace is many times larger than the value of the coefficient associated with household size. Thus, he claims that "having a fireplace adds a statistically significant boost to the predicted value of the house." Is his claim correct? Why? Show ALL your work [25 points] Which assumptions are required for the test results in 7) to be accurate? [10 points] 9) Suppose that the errors of the model are not normal. a) Provide a figure of the residuals that reflects this assumption violation [10 points] b) In light of the central limit theorem, what is a potential fix to this assumption violation? [5 points]