1 Suppose the following data represent the total cost and the sumber of units produced by a company.
a. Determine the linear regression line relating Y to X.
b. Compute the F statistic and its associated P-value and the 95% confidence intervals for the slope and intercept.
c. Calculate rxy, ryy, R2. Check that rxy= ryy and R2 = r2yy.
| Unit Produced (x) |
Total Cost (y) |
| 5 |
25 |
| 2 |
11 |
| 8 |
34 |
| 4 |
23 |
| 6 |
32 |
2 Skin cancer rates have been steadily increasing over recent years.
| Ozone dep % |
Melanoma % |
| 5 |
1 |
| 7 |
1 |
| 13 |
3 |
| 14 |
4 |
| 17 |
6 |
| 20 |
5 |
| 26 |
6 |
| 30 |
8 |
| 34 |
7 |
| 39 |
10 |
| 44 |
9 |
It is thought that this may be dure to ozone depletion. The following data are ozone depletion rates in various locations and the rates of melanoma in these locations.
a. Plot melanoma agains ozone depletion and fit a straight line regression model to the data.
b. Plat the residual from your regression against ozone depletion. What does this say about the fitted model?
c. What percentage of the variation in rates of melanoma is explained by the regression relationship?
d. In 1993, scientist discovered that 40% of ozone was depleted in the region of Hamburg, Germany. What would you expect to be the rate of melanoma in the area? Give 95% confidence interval.
3. Electricity comsuption was recorded for a small town on 12 randomly chosen days.The following mamimum temperatures and comsuption were recorded for each day.
| Day |
Mwh |
temp |
| 1 |
16.3 |
29.3 |
| 2 |
16.8 |
21.7 |
| 3 |
15.5 |
23.7 |
| 4 |
18.2 |
10.4 |
| 5 |
15.2 |
29.7 |
| 6 |
17.5 |
11.9 |
| 7 |
19.8 |
9 |
| 8 |
19 |
23.4 |
| 9 |
17.5 |
17.8 |
| 10 |
16 |
30 |
| 11 |
19.6 |
8.6 |
| 12 |
18 |
11.8 |
a. Plot the data and find the regression model for Mwh with temperature as explanatory cariable. Why is there a negative relationship?
b. Find the correlation coefficient, r.
c. Produce a residual plot. Is the model adequate? Are there any outliers or influential observations?
d. Use the model to perdict the electricity consumption that you would expect for a day with maximum temperature 10° and a day with maximum temperature 35°.
Do you believe these perdictions?