Question

In: Statistics and Probability

A regional express delivery service company recently conducted a study to investigate the relationship between the...

A regional express delivery service company recently conducted a study to investigate the relationship between the cost of shipping a package ($), the package weight (in pound) and the distance shipped (in miles). Twenty packages were randomly selected from among the large number received for shipment, and a detailed analysis of the shipping cost was conducted for each package.

Cost_of_Shipment Package_Weight Distance_Shipped
$3.30 4.10 95
$2.00 0.30 160
$11.00 5.10 240
$2.60 5.90 47
$1.90 4.50 53
$8.00 3.50 250
$15.50 7.00 260
$5.00 2.40 209
$1.00 0.60 100
$4.40 0.75 280
$6.00 6.20 115
$1.70 1.10 90
$14.50 6.50 240
$14.00 7.50 190
$9.20 6.60 160
$1.10 2.70 45
$12.10 8.10 160
$1.50 0.70 80
$8.00 4.40 202
$3.90 3.20 145
$4.40 0.75 280
$16.50 7.20 280
$15.50 7.00 250
$14.00 7.50 190
$3.30 4.10 95
$2.20 1.50 160
$11.00 5.10 240
$1 0.6 100
$4 0.75 280
$2 0.7 80
$8 4.4 202
$2 4.5 52
$8.00 3.2 240
$15.50 7.6 270
$5.00 2.5 211
$1.00 7 98
$8.00 4.4 202
$3.90 3.2 145
$4.40 0.75 280
$5.00 2.4 209

1. Use the F test to determine the overall significance of the regression relationship for the expanded model. What is the conclusion at the 0.01 level of significance?

2. Use the t test to determine the significance of each independent variable. What is the conclusion for each test at the 0.01 level of significance?  

Solutions

Expert Solution

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.931476
R Square 0.867647
Adjusted R Square 0.860493
Standard Error 1.847203
Observations 40
ANOVA
df SS MS F Significance F
Regression 2 827.6411 413.8206 121.2782 5.65E-17
Residual 37 126.2499 3.412159
Total 39 953.891
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -5.08357 0.830332 -6.12233 4.29E-07 -6.76598 -3.40116 -6.76598 -3.40116
Package_Weight 1.347949 0.119289 11.29982 1.48E-13 1.106246 1.589653 1.106246 1.589653
Distance_Shipped 0.036372 0.00387 9.397333 2.43E-11 0.02853 0.044214 0.02853 0.044214

a)

Ho: overall model is not significant

ha: overall model is significant

F=121.28

p value=0.000<0.01

so, reject Ho

hence, overall regression model is significant

b)

for Package_Weight

t=11.29982287

p value =0.00<0.01, reject Ho

hence, variable Package_Weight is significant predictor

-------------

similarly , for Distance_Shipped

p value=0.00<α=0.01

hence, variable distance shipped , is significant predictor


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