Table 5.5 gives data on average public teacher pay (annual salary in dollars) and spending on public schools per pupil (dollars) in 1985 for 50 states and the District of Columbia.
TABLE 5.5 AVERAGE SALARY AND PER PUPIL SPENDING (DOLLARS), 1985
|
Observation
|
Salary
|
Spending
|
Observation
|
Salary
|
Spending
|
|
1
|
19,583
|
3346
|
27
|
22,795
|
3366
|
|
2
|
20,263
|
3114
|
28
|
21,570
|
2920
|
|
3
|
20,325
|
3554
|
29
|
22,080
|
2980
|
|
4
|
26,800
|
4642
|
30
|
22,250
|
3731
|
|
5
|
29,470
|
4669
|
31
|
20,940
|
2853
|
|
6
|
26,610
|
4888
|
32
|
21,800
|
2533
|
|
7
|
30,678
|
5710
|
33
|
22,934
|
2729
|
|
8
|
27,170
|
5536
|
34
|
18,443
|
2305
|
|
9
|
25,853
|
4168
|
35
|
19,538
|
2642
|
|
10
|
24,500
|
3547
|
36
|
20,460
|
3124
|
|
11
|
24,274
|
3159
|
37
|
21,419
|
2752
|
|
12
|
27,170
|
3621
|
38
|
25,160
|
3429
|
|
13
|
30,168
|
3782
|
39
|
22,482
|
3947
|
|
14
|
26,525
|
4247
|
40
|
20,969
|
2509
|
|
15
|
27,360
|
3982
|
41
|
27,224
|
5440
|
|
16
|
21,690
|
3568
|
42
|
25,892
|
4042
|
|
17
|
21,974
|
3155
|
43
|
22,644
|
3402
|
|
18
|
20,816
|
3059
|
44
|
24,640
|
2829
|
|
19
|
18,095
|
2967
|
45
|
22,341
|
2297
|
|
20
|
20,939
|
3285
|
46
|
25,610
|
2932
|
|
21
|
22,644
|
3914
|
47
|
26,015
|
3705
|
|
22
|
24,624
|
4517
|
48
|
25,788
|
4123
|
|
23
|
27,186
|
4349
|
49
|
29,132
|
3608
|
|
24
|
33,990
|
5020
|
50
|
41,480
|
8349
|
|
25
|
23,382
|
3594
|
51
|
25,845
|
3766
|
|
26
|
20,627
|
2821
|
|
|
|
Source: National Education Association, as reported by Albuquerque Tribune, Nov. 7, 1986.
To ?nd out if there is any relationship between teacher's pay and per pupil expenditure in public schools, the following model was suggested: Payi = β1 + β2 Spendi + ui, where Pay stands for teacher's salary and Spend stands for per pupil expenditure.
a. Plot the data and eyeball a regression line.
b. Suppose on the basis of a you decide to estimate the above regression model. Obtain the estimates of the parameters, their standard errors, r2, RSS, and ESS.
c. Interpret the regression. Does it make economic sense?
d. Establish a 95% con?dence interval for β2 . Would you reject the hy- pothesis that the true slope coef?cient is 3.0?
e. Obtain the mean and individual forecast value of Pay if per pupil spending is $5000. Also establish 95% con?dence intervals for the true mean and individual values of Pay for the given spending ?gure.
f. How would you test the assumption of the normality of the error term? Show the test(s) you use.