# A plot the selling price versus the number of square

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functions in MS Excel. a) Plot the selling price versus the number of square feet. Describe the pattern. b) Estimate the true regression equation for predicting Price from Size . Draw the regression line on the plot in part (a). c) We should expect a positive relationship between the sizes of houses and their selling prices. Test whether Size has statistically significant predictive power. Assume α = 0.05. State hypotheses, give a test statistic and P-value, and state your conclusion. d) Construct a 95% confidence interval for the marginal price of an additional square foot. e) Suppose that you have a friend who is thinking about purchasing a home that is 1600 square feet in size. The asking price is \$180,000. What advice would you give your friend? f) Among the houses just two have floor areas close to 1800 square feet. Give a 90% confidence interval for the mean selling price of houses with floor areas of 1800 square feet. g) Suppose now that your family is selling a house whose size is equal to the mean of our sample. Give an interval that predicts the price your family will receive with 95% confidence.

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Question 2 – Bank Auto Loans Banks charge different interest rates for different loans. A random sample of 2,229 loans made by banks for the purchase of new automobiles was studied to identify variables that explain the interest rate charged. A multiple regression was run with interest rate as the response variable and 13 explanatory variables. a) The F statistic reported was 71.34. State the null and alternative hypotheses for this test statistic. Give the degrees of freedom and P-value for this test. What do you conclude? b) The R 2 was 0.297. What does this value tell you? Explain in one sentence. The table below gives the coefficients for the fitted model and the individual t statistics for each explanatory variable in the study. The t -values are given without the sign, assuming that all tests are two-sided.

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