A regression equation for two independent variables and one department variable has the following form:

{Required:}
(1) Explain the meaning of the numbers 20, 4, and 2 in the regression equation.
(2) Assuming normality, estimate the probability that the cost of the activity will lie between 41 and 56 if \(\mathrm{X}_{1}=4\) and \(\mathrm{X}_{2}=5\).
(3) Calculate the standard error of the regression coefficient for \(\mathrm{X}_{1}\) and \(\mathrm{X}_{2}\).
(4) If the total variance of weekly cost for the activity is 1,000 , calculate the coefficient of correlation, \(\mathrm{r}\).

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C = 20 + 4X, +2X, Where C = weekly cost X, direct labor hours per week = X = number of orders processed per week S-5 standard deviation of weekly direct labor hours = (. - .) = 0.8 = .8944 10-1 standard deviation of weekly number of orders processed = (X-X) = 0.5 = .7071 10-1