An express delivery service company recently conducted a study to investigate th
ID: 3172853 • Letter: A
Question
An express delivery service company recently conducted a study to investigate the relationship between the cost of shipping a package (Y), the package weight (x1), and the distance shipped (X2). 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. The sample information is shown in the table below:
Cost of shipment
Package weight
Distance shipped
3.4
4.3
100
2.1
0.5
165
11.1
5.3
245
2.7
6.1
52
2
4.7
58
8.1
3.7
255
15.6
7.2
265
5.1
2.6
214
1.1
0.8
105
4.5
0.95
285
6.1
6.4
120
1.8
1.3
95
14.6
6.7
245
14.1
7.7
195
9.3
6.8
165
1.2
2.9
50
12.2
8.3
165
1.6
0.9
85
8.1
4.6
207
4
3.4
150
Estimate a simple linear regression model involving shipping cost and package weight. Interpret the slope coefficient of the least squares line.
a. As the package weight increases by one pound, the shipping cost increases by $1.49 on average.
b. As the package weight increases by 1.49 lbs, the shipping cost increases by $1 on average.
c. As the package weight increases by one pound, the shipping cost increases by $0.08.
d. We cannot determine this effect with this regression as the results are insignificant.
Cost of shipment
Package weight
Distance shipped
3.4
4.3
100
2.1
0.5
165
11.1
5.3
245
2.7
6.1
52
2
4.7
58
8.1
3.7
255
15.6
7.2
265
5.1
2.6
214
1.1
0.8
105
4.5
0.95
285
6.1
6.4
120
1.8
1.3
95
14.6
6.7
245
14.1
7.7
195
9.3
6.8
165
1.2
2.9
50
12.2
8.3
165
1.6
0.9
85
8.1
4.6
207
4
3.4
150
Explanation / Answer
Following is the outcome of regression analysis:
The coefficient of slope is 1.49
Following option is correct:
a. As the package weight increases by one pound, the shipping cost increases by $1.49 on average.
SUMMARY OUTPUT Regression Statistics Multiple R 0.773598901 R Square 0.59845526 Adjusted R Square 0.576147219 Standard Error 3.175711247 Observations 20 ANOVA df SS MS F Significance F Regression 1 270.5529453 270.5529453 26.82688527 6.30606E-05 Residual 18 181.5325547 10.08514193 Total 19 452.0855 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 0.077515914 1.418049803 0.054663746 0.957008517 -2.901696166 3.056727994 Package weight,X 1.493243473 0.288300569 5.179467662 6.30606E-05 0.887546455 2.098940491Related Questions
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