Question

Statistics Homework

The management staff of a grocery products manufacturer collects data on 50 routes. For each route the factor variable is the mileage and response variable is the shipping rate (dollars per 100 pound). 1. Make a scatterplot and add the regression line. 2. Interpret the slope in the words of the problem. 3. Find the coefficient of determination and interpret. 4. Find the correlation coefficient and interpret. 5. Find and interpret a 95% Confidence Interval for the true slope. 6. Plot the standardized residuals vs. mileage. Interpret. 7. Plot the predicted values vs. shipping rate. Interpret. 8. Make a normality plot. Interpret. 9. Find the predicted values for Mileage = 400 and Mileage = 800. 10. Find the residuals values for Mileage = 400 and Mileage = 800

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

Answer 1

1)

2)

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 9.793 0.439 22.30 0.000
Mileage 0.050323 0.000823 61.14 0.000 1.00

Regression Equation

Rate = 9.793 + 0.050323 Mileage

Here slope=0.050323

3) by, minitab,

Model Summary

S R-sq R-sq(adj) R-sq(pred)
2.04204 98.78% 98.76% 98.57%
Coefficient of determination = R^2= 0.9878

4) Pearson correlation of Mileage and Rate = 0.994

5)

6)

Mileage	Rate	RESI1
50	12.7	0.390688
60	13	0.187459
80	13.7	-0.119
80	14.1	0.281002
90	14.6	0.277773
90	14.1	-0.22223
100	15.6	0.774545
100	14.9	0.074545
100	14.5	-0.32546
110	15.3	-0.02868
110	15.5	0.171316
110	15.9	0.571316
120	16.4	0.568087
120	11.1	-4.73191
120	16	0.168087
120	15.8	-0.03191
130	16	-0.33514
130	16.7	0.364859
140	17.2	0.36163
150	17.5	0.158402
170	18.6	0.251945
190	19.3	-0.05451
200	20.4	0.542259
230	21.8	0.432573
260	24.7	1.822887
300	24.7	-0.19003
330	18	-8.39971
340	27.1	0.197058
370	28.2	-0.21263
400	30.6	0.677687
440	31.8	-0.13523
440	32.4	0.464773
480	34.5	0.551858
510	35	-0.45783
540	36.3	-0.66751
600	41.4	1.413115
650	46.4	3.896972
700	45.8	0.780829
720	46.6	0.574372
760	48	-0.03854
800	51.7	1.648543
810	50.2	-0.35469
850	53.6	1.0324
920	57.9	1.8098
960	56.1	-2.00311
1050	58.7	-3.93217
1200	75.8	5.6194
1650	89	-3.82589

8)

9)

Regression Equation

Rate = 9.793 + 0.050323 Mileage

Mileage=400 then Rate =29.9222

Mileage=800 then Rate =50.0514