12.90 The manager of a catering business conducted a study on the amount of preparation time (in hours)

needed based on the number of dishes to be prepared and the number of servings. She uses 10 previous catering records to determine the following regression model:

Y = b0 + b1X1 + b2X2 + e where Y = preparation time X1 = number of dishes to be prepared X2 = number of servings The following is part of the EXCEL computer output from the estimate regression.

R@Square = 0.9713 Coefficients Standard Error t Stat Intercept 3.0841 0.0271 113.8044 X1 2.9306 0.1855 5.0167 X2 1.1375 0.3026 3.7591

a. Interpret the estimated regression coefficients.

b. Interpret the coefficient of determination.

c. Test, at the 1% significance level, the null hypothesis that, taken together, the two independent variables do not linearly influence the response rate.

d. Find and interpret a 90% confidence interval for b1.

e. Test the null hypothesis H0 : b2 = 0 against the alternative H1 : b2 7 0 and interpret your findings.