In a study to determine the relationship between ambient outdoor temperature and the rate of evaporation of water from soil, measurements of average daytime temperature in ? C and evaporation in mm/day were taken for 40 days. The results are shown in the following table.
|
Temp.
|
Evap.
|
Temp.
|
Evap.
|
Temp.
|
Evap.
|
Temp.
|
Evap.
|
|
11.8
|
2.4
|
11.8
|
3.8
|
18.6
|
3.5
|
14.0
|
1.1
|
|
21.5
|
4.4
|
24.2
|
5.0
|
25.4
|
5.5
|
13.6
|
3.5
|
|
16.5
|
5.0
|
15.8
|
2.6
|
22.1
|
4.8
|
25.4
|
5.1
|
|
23.6
|
4.1
|
26.8
|
8.0
|
25.4
|
4.8
|
17.7
|
2.0
|
|
19.1
|
6.0
|
24.8
|
5.4
|
22.6
|
3.2
|
24.7
|
5.7
|
|
21.6
|
5.9
|
26.2
|
4.2
|
24.4
|
5.1
|
24.3
|
4.7
|
|
31.0
|
4.8
|
14.2
|
4.4
|
15.8
|
3.3
|
25.8
|
5.8
|
|
18.9
|
3.0
|
14.1
|
2.2
|
22.3
|
4.9
|
28.3
|
5.8
|
|
24.2
|
7.1
|
30.3
|
5.7
|
23.2
|
7.4
|
29.8
|
7.8
|
|
19.1
|
1.6
|
15.2
|
1.2
|
19.7
|
3.3
|
26.5
|
5.1
|
a. Compute the least-squares line for predicting evaporation (y) from temperature (x).
b. Compute 95% confidence intervals for β0 and β1 .
c. Predict the evaporation rate when the temperature is 20? C.
d. Find a 95% confidence interval for the mean evaporation rate for all days with a temperature of 20? C.
e.Find a 95% prediction interval for the evaporation rate on a given day with a temperature of 20? C.