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 OUTPUTRegression StatisticsMultiple RR SquareAdjusted R SquareStandard ErrorObservationsANOVARegressionResidualTotal0.9024850950.8144793460.8012278712.929785508df1611415$5MSF Significance F527.5789963 527.579 61.4633 1.73154E-06120.1710037 8.583643647.75Coefficients Standard Error t StatIntercept11.81040892Number of Cases 3.234200743P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%2.116119099 5.581165 6.77E-05 7.271784847 16.349033 7.271784847 16.3490330.412533338 7.839853 1.73E-06 2.349404733 4.11899675 2.349404733 4.118996754

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Answered: A soft drink bottling company wants to…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Question

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

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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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