Question

PLEASE BE VERY SPECIFIC WITH EACH STEP

A soft drink bottler is analyzing the vending machine service routes in his distribution system. He is interested in predicting the amount of time required by the route driver to service the vending machines in an outlet. The industrial engineer responsible for the study has suggested that the two most important variables affecting the delivery time (Y) are the number of cases of product stocked (X₁) and the distance walked by the route driver (X₂). The engineer has collected 24 observations on the delivery times, which are shown on the Excel file.

Delivery Time, Y	Number of Cases, X1	Distance, X2 (ft)
16.68	7	560
	…
10.75	4	150

a) Fit the model Y=Beta0 + Beta1X1 + Beta2X2 + E to the delivery time data, and give the least squares function.

b) Find the value of SSE that is minimized by the least squares method.

c) Estimate s, the standard deviation of the model.

d)   Conduct the ANOVA F-test for model usefulness at the a = 0.05 significance level (be sure to specify the null and alternative hypotheses).

e)   Conduct the individual t-tests for b₁ and b₂ at the a = 0.05 significance level (be sure to specify the null and alternative hypotheses).

f)    Find and interpret the coefficient of determination R², and the adjusted coefficient of determination R_a².

g)   Which model do you think would be best: a simple linear regression with X₁ as the predictor variable, a simple linear regression with X₂ as the predictor variable, or the first-order multiple regression model with both X₁ and X₂?

h)   Using the chosen model from part g), predict the delivery time when 10 cases need to be stocked, and the distance to be walked is 500 ft. Give a 95% prediction interval for this estimate.

Answer 1

Solution:-

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.974013
R Square	0.948701
Adjusted R Square	0.943815
Standard Error	2.429995
Observations	24
ANOVA
	df	SS	MS	F	Significance F
Regression	2	2293.244	1146.621801	194.1821959	2.85856E-14
Residual	21	124.0024	5.904876068
Total	23	2417.246
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	4.447238	0.952469	4.66916828	0.00013136	2.466470152	6.428005	2.46647	6.428005
X Variable 1	1.497691	0.130207	11.50242877	1.58356E-10	1.226911987	1.768471	1.226912	1.768471
X Variable 2	0.010324	0.002854	3.617924066	0.001613583	0.004389701	0.016258	0.00439	0.016258