Question

Finally, the researcher considers using regression analysis to establish a linear relationship between the two variables – hours worked per week and income earned per year.

c) Estimate a simple linear regression model and present the estimated linear equation. Display the regression summary table and interpret the intercept and slope coefficient estimates of the linear model.                                                           

Yearly Income ('000's)	Hours Per Week
43.8	18
44.5	13
44.8	18
46.0	25.5
41.4	11.6
43.3	18
43.6	16
46.2	27
46.8	27.5
48.2	30.5
49.3	24.5
53.8	32.5
53.9	25
54.2	23.5
50.5	30.5
51.2	27.5
51.5	28
52.6	26
52.8	25.5
52.9	26.5
49.5	33
49.8	15
50.3	27.5
54.3	36
55.1	27
55.3	34.5
61.7	39
62.3	37
63.4	31.5
63.7	37
55.5	24.5
55.6	28
55.7	19
58.2	38.5
58.3	37.5
58.4	18.5
59.2	32
59.3	35
59.4	36
60.5	39
56.7	24.5
57.8	26
63.8	38
64.2	44.2
55.8	34.5
56.2	34.5
64.3	40
64.5	41.5
64.7	34.5
66.1	42.3
72.3	34.5
73.2	28
74.2	38
68.5	31.5
69.7	36
71.2	37.5
66.3	22
66.5	33.5
66.7	37
74.6	43.5
62.0	20
57.3	35
55.3	24

Answer 1

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SUMMARY OUTPUT
Regression Statistics
Multiple R	0.6715
R Square	0.4509
Adjusted R Square	0.4419
Standard Error	6.2518
Observations	63
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1957.439918	1957.44	50.0822	1.7094E-09
Residual	61	2384.157225	39.0845
Total	62	4341.597143
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	36.157	3.087	11.712	0.000	29.984	42.330
Hours Per Week()	0.708	0.100	7.077	0.000	0.508	0.908

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Where y(hat) is yearly income, x is hours per week

Interpretation - By increasing one unit in hours per week there is on an average $ 0.708 increase in yearly income