Question

A statistical program is recommended.

Consider the following data for two variables, x and y.

x	9	32	18	15	26
y	9	20	22	16	23

(a)Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x. (Round b₀ to two decimal places and b₁ to three decimal places.)

(b) Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x + b₂x². (Round b₀ to two decimal places and b₁ to three decimal places and b₂ to four decimal places.)

Answer 1

(a)

Following is the output of regression analysis generated by excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.748347052
R Square	0.56002331
Adjusted R Square	0.413364413
Standard Error	4.366423773
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	72.8030303	72.8030303	3.81854305	0.14568764
Residual	3	57.1969697	19.06565657
Total	4	130
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	8.606060606	5.188739544	1.658603314	0.19577684	-7.9068244	25.1189456
X	0.46969697	0.240363718	1.954109272	0.14568764	-0.2952477	1.234641595

The  estimated regression equation for the data of the form ŷ = b₀ + b₁x is

(b)

Following is the output of regression analysis generated by excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.980796243
R Square	0.961961271
Adjusted R Square	0.923922542
Standard Error	1.572424043
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	2	125.0549653	62.52748263	25.2889963	0.038038729
Residual	2	4.945034744	2.472517372
Total	4	130
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-12.94213023	5.046081471	-2.564788202	0.12430075	-34.65366644	8.76940599
X	2.929881001	0.542117992	5.404507959	0.03257284	0.597335544	5.262426457
X^2	-0.059346545	0.012909634	-4.597074193	0.04420517	-0.114892216	-0.003800873

An estimated regression equation for the data of the form ŷ = b₀ + b₁x + b₂x²

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