Question: A regression study was performed to examine the relationship between the selling price (y) and annual local, county, and school taxes (x). The data were collected for 24 houses and shown in the following table.

a. (15) Perform a complete regression analysis (following and indicating the 8 steps in regression modeling) using the data. Interpret your output, stating hypotheses and conclusions. Test the normality assumption using the appropriate statistical test, and test the constant variance and uncorrelated errors assumptions using graphical methods.

b. (5) Suppose you are considering buying a house in the region, and you found one. If the selling price of the house is $300,000 and the annual taxes are $5500, would you buy the house? Explain your reasoning.

c. (10) Suppose a friend of yours claimed that your regression model doesn’t reflect the problem because the intercept was not zero. He argued that if the annual taxes are zero, it means that the house did not exist, and the selling price would be zero. Moreover, he solved the problem by modeling it as a no-intercept model, and showed you the results. Assume the significance level, ?=5%.

The regression equation is

Sale = 5.29Taxes

Predictor Coef SE Coef T P

Noconstant

Taxes 5.2892 0.1336 39.58 0.000

S = 4.31430

Analysis of Variance

Source DF SS MS F P

Regression 1 29154 29154 1566.29 0.000

Residual Error 23 428 19

Total 24 29582

Anderson-Darling normality test results: A-D = 0.266 and p-value = 0.659.

What would be your response? In particular, is the independent variable, Taxes, statistically significant? Is it a valid model (consider the error assumptions)? Which one, simple linear model or no-intercept model, is a better model? Why?