Assume that the following regression equation has been computed for your department's monthly overhead expense from the data observed in the past 10 months.

{Required:}
(1) Calculate the standard error of the regression coefficient for \(\mathrm{X}_{1}\) and \(\mathrm{X}_{2}\).
(2) Assess the probability that the true coefficient of \(\mathrm{X}_{1}\) is between 20 and 31 .
(3) If the total variance of monthly overhead expense over the past ten months is \(\$ 100,000\), calculate the coefficient of correlation, r.
(4) Estimate the probability that the overhead expense will be between \(\$ 304\) and \(\$ 484\) for a month where \(\mathrm{X}_{1}=4\) and \(\mathrm{X}_{2}=5\). Assume that the distribution of the overhead expense is normal.

(5) 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=120+ 23.5X, +42X2 where X, direct labor hours per month X = number of orders processed per month standard error of estimate (S) = 60 standard deviation of monthly direct labor hours. (X-X) = 8 n-1 standard deviation of monthly number of orders processed (. - .) M-1 5