Question

I would really appreciate if you do it in SPSS, otherwise do it in Excel. Thanks!

Run the regression again without the potential confounding variable and discuss the impact on the coefficient of the primary independent variable. Did it change? If so, to what extent did it change? Based on this, do you think the added variable confounds the association between the independent and dependent variables? Interpret the results.

Independent variable: Minutes exercise

Dependent variable: Annual income

Counfonding variable: Education Level

Minutes_Exercise	Annual_Income*	Education_Level***
90	51000	2
50	23000	2
65	35000	3
20	10000	1
50	28000	1
25	5000	2
110	46000	3
50	36000	1
40	51000	2
80	12000	2
120	78000	3
80	34000	1
60	15000	1
150	28000	3
75	28000	2
80	24000	1
110	55000	2
80	62000	3
100	32000	2
0	7000	1
50	17000	2
200	64000	3
60	5000	2
65	14000	1
40	20000	1
65	72000	3
70	85000	3
45	15000	1
75	64000	3
50	27000	3

Answer 1

Independent variable: Minutes exercise

Dependent variable: Annual income

Counfonding variable: Education Level

Regression output without Counfonding variable:

Regression Statistics
Multiple R	0.50650506
R Square	0.256547376
Adjusted R Square	0.229995497
Standard Error	20073.22859
Observations	30
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3893200499	3893200499	9.662117396	0.004288622
Residual	28	11282166167	402934506
Total	29	15175366667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	13584.73078	7737.415446	1.755719448	0.09007202	-2264.64628	29434.10784
Minutes_Exercise	294.8761377	94.86444593	3.108394665	0.004288622	100.5551291	489.1971462

Annual income = 13584+294.87*Minutes exercise.

R square value is only 0.25. Hence this is not a effective equation

Regression output with Counfonding variable:

Regression Statistics
Multiple R	0.678587671
R Square	0.460481227
Adjusted R Square	0.420516873
Standard Error	17413.69747
Observations	30
ANOVA
	df	SS	MS	F	Significance F
Regression	2	6987971457	3493985728	11.52229888	0.00024104
Residual	27	8187395210	303236859.6
Total	29	15175366667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-4015.193133	8683.64939	-0.46238545	0.647509608	-21832.56995	13802.18368
Education_Level***	14595.47627	4568.724917	3.194649827	0.003546758	5221.227061	23969.72547
Minutes_Exercise	133.5161104	96.55977653	1.38273011	0.178078032	-64.60818572	331.6404066

Annual income = -4015.19+133.51*Minutes exercise + 14595.47*Education_Level

So coefficient of primary Independent variable changed from 133.51 to 294.87