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 thatall 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 explanatoryvariable 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 thatexplain 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 thisstatistic. Give the degrees of freedom and the P-value for this test. What do youconclude?(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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