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# Inference basics. You run a multiple regression with 66 cases and 5 explanatory variables.

1. Inference basics.
You run a multiple regression with 66 cases and 5 explanatory variables.
(a) What are the degrees of freedom for the F statistic for testing the null hypothesis that
all five of the regression coefficients for the explanatory variables are zero?
(b) Software output gives MSE = 36. What is the estimate of the standard deviation Sigma of the model?
(c) The output gives the estimate of the regression coefficient for the first explanatory
variable as 12.5 with a standard error of 2.4. Find a 95% confidence interval for the true value of this coefficient.
2. Bank auto loans.
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.
(a) The F statistic reported is 71.34. State the null and alternative hypotheses for this
statistic. Give the degrees of freedom and the P-value for this test. What do you
conclude?
(b) The value of R2 is 0.297. What percent of the variation in interest rates is explained by the 13 explanatory variables?

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