Question

In: Statistics and Probability

Use Excel to prepare a Linear Regression Analysis. Use data samples below for populations and determine...

Use Excel to prepare a Linear Regression Analysis.

Use data samples below for populations and determine if the selected independent variable is affecting the dependent variable. Use an alpha of 5% for ANOVA and Correlation Coefficient. Explain the results.

Data samples

Group A

104,103,101,99,97,101,101

Group B

101,100,95,99,101,103,97

Group C

100,96,99,95,99,102,106

Group D

97,99,99,101,105,100,99

Expert Solution

i) Group A and Group B

Regression line equation: y=98.11304347828+0.013043478260679x

Correlation coefficient (r): 0.01130828

SUMMARY OUTPUT	A&B

Regression Statistics
Multiple R	0.011308
R Square	0.000128
Adjusted R Square	-0.19985
Standard Error	2.563316
Observations	7

ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.004202	0.004202	0.000639	0.980804
Residual	5	32.85294	6.570588
Total	6	32.85714

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	99.88235	38.56015	2.5903	0.048819	0.760322	199.0044
X Variable 1	0.009804	0.387695	0.025288	0.980804	-0.9868	1.006406

ii) Group A and Group C

Regression line equation: y=82.469565217373+0.16956521739148x

Correlation coefficient (r): 0.107523

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.107523
R Square	0.011561
Adjusted R Square	-0.18613
Standard Error	2.548618
Observations	7

ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.37987	0.37987	0.058482	0.818516
Residual	5	32.47727	6.495455
Total	6	32.85714

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 5.0%	Upper 5.0%
Intercept	94.06818	28.08963	3.348858	0.020354	21.86149	166.2749	92.21666	95.91971
X Variable 1	0.068182	0.281939	0.241831	0.818516	-0.65657	0.79293	0.049598	0.086766

iii) Group A and Group D

Correlation coefficient (r): -0.9339

Regression line equation: y=201.29565217391-1.0043478260869x

SUMMARY OUTPUT	A&D

Regression Statistics
Multiple R	0.933915
R Square	0.872197
Adjusted R Square	0.846636
Standard Error	0.916433
Observations	7

ANOVA
	df	SS	MS	F	Significance F
Regression	1	28.65789	28.65789	34.12265	0.00208
Residual	5	4.199248	0.83985
Total	6	32.85714

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 5.0%	Upper 5.0%
Intercept	187.6992	14.87054	12.62222	5.54E-05	149.4733	225.9252	186.7191	188.6794
X Variable 1	-0.86842	0.148665	-5.84146	0.00208	-1.25058	-0.48627	-0.87822	-0.85862

iv) Group B and Group C

Regression line equation: y=110.29411764707-0.10784313725499x

Correlation coefficient (r): -0.0788778

SUMMARY OUTPUT	b&C

Regression Statistics
Multiple R	0.078878
R Square	0.006222
Adjusted R Square	-0.19253
Standard Error	2.94762
Observations	7

ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.271978	0.271978	0.031303	0.866509
Residual	5	43.44231	8.688462
Total	6	43.71429

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 5.0%	Upper 5.0%
Intercept	105.1731	32.48723	3.237367	0.023017	21.66199	188.6842	103.0317	107.3145
X Variable 1	-0.05769	0.326079	-0.17693	0.866509	-0.8959	0.78052	-0.07919	-0.0362

v) Group B and Group D

Correlation coefficient (r): 0.2208203

Regression line equation: y=79.529411764708+0.20588235294116x

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.22082
R Square	0.048762
Adjusted R Square	-0.14149
Standard Error	2.883841
Observations	7

ANOVA
	df	SS	MS	F	Significance F
Regression	1	2.131579	2.131579	0.256306	0.634196
Residual	5	41.58271	8.316541
Total	6	43.71429

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 5.0%	Upper 5.0%
Intercept	75.74436	46.79478	1.61865	0.166447	-44.5455	196.0342	72.65989	78.82883
X Variable 1	0.236842	0.467821	0.506267	0.634196	-0.96573	1.439414	0.206006	0.267678

vi) Group C and Group D

Regression line equation: y=113.40384615385-0.13461538461538x

Correlation coefficient (r): -0.19740215

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.197402
R Square	0.038968
Adjusted R Square	-0.15324
Standard Error	3.963082
Observations	7

ANOVA
	df	SS	MS	F	Significance F
Regression	1	3.184211	3.184211	0.202738	0.671371
Residual	5	78.53008	15.70602
Total	6	81.71429

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 5.0%	Upper 5.0%
Intercept	128.5188	64.30712	1.998516	0.102133	-36.7879	293.8255	124.28	132.7576
X Variable 1	-0.28947	0.642897	-0.45026	0.671371	-1.94209	1.363145	-0.33185	-0.2471

a) we have to conclude that Relation between

i) Group A and Group B

ii)Group A and Group C

iii) Group B and Group D this data has no correation between them beacause there correlation value is very low

b) Group A and Group D this two group is strong negative correlation

c) Group B and Group C is moderate neagative correlation between them

d) Group C and Group C is very low negative correlation between them

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