Estimate the regression model

Question

Problem: To find 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 base of  “a.)” you decide to estimate the above regression model. Obtain the estimates of parameters, their standard errors,  r², RSS, and ESS.

c) Interpret the regression. DOES it make economic sense?

d) Establish a 95% confidence interval for β2. Would you reject the hypothesis that the true slope coefficient is 3.0?

e) Obtain the mean and individual forecast value of Pay if per pupil spending is $5000. Also establish 95% confidence intervals for the true mean and individual values of Pay for the given spending figure.

f) How would you test the assumption of the normality of the error term? Show the test(s) you use.

Average Salary and per pupil spending (Dollar), 1985

Observation		Salary	Spending		Observation		Salary	Spending
1		19583	3346		27		22795	3366
2		20263	3114		28		21570	2920
3		20325	3554		29		20080	2980
4		26800	4642		30		22250	3731
5		29470	4669		31		20940	2853
6		26610	4888		32		21800	2533
7		30678	5710		33		2934	2729
8		27170	5536		34		18443	2305
9		25853	4168		35		19538	2642
10		24500	3547		36		20460	3124
11		24274	3159		37		21419	2752
12		27170	3621		38		25160	3429
13		30168	3782		39		22482	3947
14		26525	4247		40		20969	2509
15		27360	3982		41		27224	5440
16		21690	3568		42		28892	4042
17		21974	3155		43		22644	3402
18		20816	3059		44		24640	2829
19		18095	2967		45		22341	2297
20		20939	3285		46		25610	2932
21		22644	3914		47		26015	3705
22		24624	4517		48		25788	4123
23		27186	4349		49		29132	3608
24		33990	5020		50		41480	8349
25		23382	3594		51		25845	3766
26		20627	2821