Interested in the possible relationship between the size of his tip versus the size of the check and the number of diners in the party, a food server has recorded the following for a sample of 8 checks:

a. Determine the multiple regression equation and interpret the partial regression coefficients.
b. What is the estimated tip amount for 3 diners who have a $40 check?
c. Determine the 95% prediction interval for the tip left by a dining party like the one in part (b).
d. Determine the 95% confidence interval for the mean tip left by all dining parties like the one in part (b).
e. Determine the 95% confidence interval for the partial regression coefficients, β1 and β2.
f. Interpret the significance tests in the computer printout.
g. Analyze the residuals. Does the analysis support the applicability of the multiple regression model to these data?

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Observation Number y Tipx,-Check x2-Diners $7.5 0.5 2.0 3.5 9.5 2.5 3.5 1.0 $40 15 30 25 50 20 35 10 4 4 4