Thread: Determine When Coefficent of X1 should be zero

Which of the following would not tell you that the coefficient for x1 should be zero and hence x1 should not be in the model?
A. The 95% confidence interval for B1 contains zero, so x1 gives no additional contribution to explaining the variation of y above and beyond what x2 and x3 do.
B. The pvalue associated with the x1 is 25.6%, so at the 5% level, we would not reject the null hypothesis that B1 = 0, given x2 and x3
C. The overall f-test tells us that all of the coefficients for all of the x’s should be zero
D. The residual standard error is too low (at 1.661) for B1 to be anything other than zero
E. All of the above are evidence that x1 should not be in the model.

Anyone? I'm really stumped here.

I'm not sure about D, especially what you mean by residual st error of $\displaystyle \beta_1$
I assume you mean the estimate of $\displaystyle \beta_1$'s st deviation, well that should be compared to the
square root of our MSE, and that can be small as well.
That would make the test stat large, making $\displaystyle \beta_1$ non-zero based on the data.