Assume that the following regression has been computed for your department's monthly overhead expense from data observed in the past 12 months.

{Required:}
(1) Assess the probability that the "true" coefficient of \(\mathrm{X}_{2}\) is between 15 and 25.
(2) Test whether the presence of each independent variable contributes significantly toward explanation of the changes in the dependent variable (at \(99 \%\) confidence level).

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Y 1,000+ 10X, +20X+ 30X, (200) (2) (5) (8) r = 92% S-400 The numbers in parentheses are the standard errors of the regression coefficients.