The staff of a grocery products manufacturer is developing a model for the produ

Question

The staff of a grocery products manufacturer is developing a model for the production and distribution of its cereal products. The model requires transportation costs for a very large number of origins and destinations. It is impractical to do the detailed tariff analysis for every possible combination, so a random sample of 50 routes is selected. For each route, the mileage and the shipping rate (in dollars per 100 pounds) are found.

Last two rate values were not given. They were simple left blank in the data given to me.

1. Graph the data. Does it appear that shipping rate can be predicted by mileage?

2. Find the equation of a straight line that describes how shipping rate varies with mileage.

3. Test the null hypothesis that shipping rate is unaffected by mileage. State your conclusion.

4. What is the effect of each additional mile on the shipping rate? Give a 95% confidence interval estimate.

Mileage Rate 50
60
80
80
90
90
100
100
100
110
110
110
120
120
120
120
130
130
140
150
170
190
200
230
260
300
330
340
370
400
440
440
480
510
540
600
650
700
720
760
800
810
850
920
960
1050
1200
1650
300
350 12.7
13.0
13.7
14.1
14.6
14.1
15.6
14.9
14.5
15.3
15.5
15.9
16.4
11.1
16.0
15.8
16.0
16.7
17.2
17.5
18.6
19.3
20.4
21.8
24.7
24.7
18.0
27.1
28.2
30.6
31.8
32.4
34.5
35.0
36.3
41.4
46.4
45.8
46.6
48.0
51.7
50.2
53.6
57.9
56.1
58.7
75.8
89.0

Explanation / Answer

Since P-value is less than significance level i.e. 0.05 hence we reject null hypothesis and conclude that there in enough evidence to support the claim.

SUMMARY OUTPUT Regression Statistics Multiple R 0.993904208 R Square 0.987845574 Adjusted R Square 0.987581348 Standard Error 40.33149951 Observations 48 ANOVA df SS MS F Significance F Regression 1 6081366.693 6081367 3738.63 1.04625E-45 Residual 46 74824.97322 1626.63 Total 47 6156191.667 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -187.4353803 11.16936459 -16.7812 3.09E-21 -209.9181451 -164.95262 X Variable 1 19.63015595 0.321046192 61.14434 1.05E-45 18.98392348 20.2763884

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