Step 1: Banks charge different interest rates for different loans. A random samp

Question

Step 1: Banks charge different interest rates for different loans. A random sample of 2229 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. Table 11.4 gives the coefficients for the fitted model and the individual t statistic for each explanatory variable in the study. The t values are given without the sign, assuming that all tests are two-sided. TABLE 11.4 Regression coefficients and t statistics for Exercise 11.5 Variable Intercept 5.47 Loan size n dollars 0,0015 0,30 Length of loan (in months) 0,906 4,20 Percent down payment 0,522 8.35 Cosigner (0 no, l yes) 0,009 3.02 Unsecured loan (0 no I yes 0.034 Total payments (borrower's monthly installment debt 0.100 1.37 Total income (borrowers total monthly income) -0,170 2.37 Bad credit report (0 no. l *yes) 0,012 199 Young borrower (0 older than 25. I 25 or younger) 0.027 2.85 Male borrower (0 female, 1 m male) 0.00 0.89 Married (0 3no, 1 yes) Own home (0 no, 1 yes) -0.011 2.73 Years at current address 0,124 4.2 State the null and alternative hypotheses tested by an individual t statistic. o Ho: A B. A, -0 vs. H.: At least one B is not 0.

Explanation / Answer

Step 1:
Ho : j = 0 vs Ha: j 0
It is two sided test and is trying to determine if the coefficient has any significance on the response variable

Step 2:
Degrees of freedom, df = n - k - 1 = 2229 - 13 - 1 = 2215
n is the sample size, k is the number of predictor variables and the extra 1 is for the intercept.

Step 3:
|t| > 1.9610, for a two tailed test, the critical value is 1.9610. Since all t values are represented positive, the absolute sign is used.

Step 4:
All variables except for total payments, male borrower and married

Check which of the t values are greater than the t critical value 1.961 for significance

Step 5:
The corresponding explanatory variable does not contribute significantly to the prediction of the response variable, when the other explanatory variables are available.

Step 6:
1. False
2. True
3. True
4. True

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