# Variable b t intercept 1547 loan size in dollars

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Variable b t Intercept 15.47 Loan size (in dollars) -0.0015 10.30 Length of loan (in months) -0.906 4.20 Percent down payment -0.522 8.35 Co-signer (0 = no, 1 = yes) -0.009 3.02 Unsecured loan (0 = no, 1 = yes) 0.034 2.19 Total payments (borrower’s monthly installment debt) 0.100 1.37 Total income (borrower’s total monthly income) -0.170 2.37 Bad credit report (0 = no, 1 = yes) 0.012 1.99 Young borrower (0 = older than 25, 1 = 25 or younger) 0.027 2.85 Male borrower (0 = female, 1 = male) -0.001 0.89 Married (0 = no, 1 = yes) -0.023 1.91 Own home (0 = no, 1 = yes) -0.011 2.73 Years at current address -0.124 4.21 c) State the null and alternative hypotheses tested by an individual t statistic. What are the degrees of freedom for these t statistics? What values of t will lead to rejection of the null hypothesis at the 5% level? d) Which explanatory variables are significantly different from zero in this model? Explain carefully what you conclude when an individual t statistic is not significant. e) Examine the sign of each of the statistically significant coefficients and give a short explanation of what they tell us. Use one short sentence for each. f) How would you proceed in order to find a more parsimonious model that still provides an adequate fit to the data? Explain in one or two sentences.

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Question 3 – Office Rents An economist wanted to investigate the relationship between office rents and vacancy rates. He took a random sample of monthly office rents ( Rent ), the percentage of vacant office space ( Vacancy )and the city’s unemployment rate ( Unemployment ) in 30 different cities. The data are in the worksheet OfficeRents in the Excel spreadsheet. a) Fit a regression model to predict Rent from Vacancy and Unemployment . b) Compute and interpret the value of R-squared. c) What would your conclusion be if you test the hypothesis that the coefficients for Vacancy and Unemployment are both zero? Explain in one sentence. Include the test-statistic, the degrees of freedom and the P-value in your answer. d) What would your conclusion be from a hypothesis test for the coefficient for Vacancy ?

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