Question: Inference basics. You run a multiple regression with 65 cases and 4 explanatory variables. (a) What are the degrees of freedom for the F statistic

Inference basics. You run a multiple regression with 65 cases and 4 explanatory variables.

(a) What are the degrees of freedom for the F statistic for testing the null hypothesis that all four of the regression coefficients for the explanatory variables are zero?

(b) Software output gives MSE = 42. What is the estimate of the standard deviation σ of the model?

(c) The output gives the estimate of the regression coefficient for the first explanatory variable as 10.3 with a standard error of 3.1. Find a 95% confidence interval for the true value of this coefficient.

(d) Test the null hypothesis that the regression coefficient for the first explanatory variable is zero. Give the test statistic, the degrees of freedom, the P-value, and your conclusion.

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