Question

1. Consider the following data set. Cl is years of education, C2 is years of job experience, C3 is age, and C4 is annual salary.

a. Estimate the relationship:

C4 = a + b(Cl)+c(C2)+d(C3)

b. Test the hypothesis that the entire model (C1, C2, and C3 combined) does not explain a significant amount of variation in the dependent variable at the 5% level of significance.

c. What fraction of the variation in annual salary is explained by education, experience, and age?

Row	Education	Experience	Age	Salary
1	10	20	45	55139
2	10	5	23	48937
3	10	19	36	57624
4	11	15	50	58170
5	11	16	42	62202
6	11	8	30	51646
7	11	4	21	52563
8	12	10	34	49434
9	12	8	27	55153
10	12	18	38	63882
11	13	6	25	46067
12	13	10	46	60886
13	14	10	38	57190
14	14	2	22	52094
15	15	8	32	60620
16	16	5	49	59843
17	16	4	28	57288
18	17	7	33	67151
19	18	3	27	61313
20	19	3	32	64175

Answer 1

(a) C4 = 22,228.5143 + 1,959.5483*C1 + 696.0572*C2 + 76.0178*C3

(b) The hypothesis being tested is:

H0: β1 = β2 = β3 = 0

H1: At least one βi ≠ 0

The p-value is 0.0003.

Since the p-value (0.0003) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the model is significant.

(c) 0.679

	R²	0.679
	Adjusted R²	0.619
	R	0.824
	Std. Error	3489.559
	n	20
	k	3
	Dep. Var.	Salary
ANOVA table
Source	SS	df	MS	F	p-value
Regression	41,18,69,047.7521	3	13,72,89,682.5840	11.27	.0003
Residual	19,48,32,298.7979	16	1,21,77,018.6749
Total	60,67,01,346.5500	19
Regression output				confidence interval
variables	coefficients	std. error	t (df=16)	p-value	95% lower	95% upper
Intercept	22,228.5143
Education	1,959.5483	409.9821	4.780	.0002	1,090.4251	2,828.6715
Experience	696.0572	256.1168	2.718	.0152	153.1138	1,239.0006
Age	76.0178	128.6253	0.591	.5628	-196.6556	348.6912