Question

In: Statistics and Probability

Statistics Homework The management staff of a grocery products manufacturer collects data on 50 routes. For...

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

Solutions

Expert Solution

Answer :- 1) scatter plot

1) Please follow the below steps to create the scatter plot.

Steps -1 ) First type the data in excel.

2) Then select all the data.

3) Insert--->> Insert scatter plot (x,y) ---->> Scatter with straight lines and markers.

2) Interpretation the slope.

The slope of regression line is almost important for interpreting the data. The slope is the rate of change when x increase by 1 unit then yhat change by slope units. If the value of slope is positive the yhat increases and if the slope is negative then yhat decreases.

Now find the slope by using the excel.

Path : data--->> data analysis-->> regression.

Give the inputs .

Inputs Y range :Mileage

Input X range : Rate   

Output : give the cell where you want to the output------->> OK.

Therefore slope = 0.050323

3) coefficient of determination :-

4) Correlation coefficient :-

Interpretation :- Coefficient of determination measures the proportion of the total variation in y is explained by x.

r= 0.993904 R^2= 0.9878456  

Approximately 98% of variation in rate (y) is explained by the linear relationship with x ( mileage)

And less than 2% is explained by other causes.

5 ) Confidence interval -

Please see the excel sheet and see the confidence interval for slope.

So C.I (for slope ) = ( 0.048666, 0.05198 )

​​​​​​​


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