A soft drink bottling company wants to develop a regression model to predict delivery time (in minutes) based on the number of cases delivered. A sample of 16 deliveries was selected.  The Excel output for this regression model is given below.   (a) State the regression equation. (b) Interpret the meaning of b0 and b1 in this problem. (c) What is the predicted delivery time when the number of cases is 30 , assuming 30 is within the range of number of cases delivered for this problem? (d) At the 0.05 level of significance, is there evidence of a linear relationship between the number of cases delivered and the delivery time? (e) Construct a 95% confidence interval estimate of the population slope β1. Interpret the confidence interval estimate. (f) How useful do you think this regression model is for predicting the delivery times?

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A soft drink bottling company wants to develop a regression model to predict delivery time (in minutes) based on the number of cases delivered. A sample of 16 deliveries was selected.  The Excel output for this regression model is given below.

 

(a) State the regression equation.

(b) Interpret the meaning of b0 and b1 in this problem.

(c) What is the predicted delivery time when the number of cases is 30 , assuming 30 is within the range of number of cases delivered for this problem?

(d) At the 0.05 level of significance, is there evidence of a linear relationship between the number of cases delivered and the delivery time?

(e) Construct a 95% confidence interval estimate of the population slope β1. Interpret the confidence interval estimate.

(f) How useful do you think this regression model is for predicting the delivery times?

SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
ANOVA
Regression
Residual
Total
0.902485095
0.814479346
0.801227871
2.929785508
df
16
1
14
15
$5
MS
F Significance F
527.5789963 527.579 61.4633 1.73154E-06
120.1710037 8.583643
647.75
Coefficients Standard Error t Stat
Intercept
11.81040892
Number of Cases 3.234200743
P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
2.116119099 5.581165 6.77E-05 7.271784847 16.349033 7.271784847 16.349033
0.412533338 7.839853 1.73E-06 2.349404733 4.11899675 2.349404733 4.118996754
Transcribed Image Text:SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total 0.902485095 0.814479346 0.801227871 2.929785508 df 16 1 14 15 $5 MS F Significance F 527.5789963 527.579 61.4633 1.73154E-06 120.1710037 8.583643 647.75 Coefficients Standard Error t Stat Intercept 11.81040892 Number of Cases 3.234200743 P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 2.116119099 5.581165 6.77E-05 7.271784847 16.349033 7.271784847 16.349033 0.412533338 7.839853 1.73E-06 2.349404733 4.11899675 2.349404733 4.118996754
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(d) At the 0.05 level of significance, is there evidence of a linear relationship between the number of cases delivered and the delivery time?

(e) Construct a 95% confidence interval estimate of the population slope β1. Interpret the confidence interval estimate.

(f) How useful do you think this regression model is for predicting the delivery times?

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