In: Statistics and Probability
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) 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 )