Question

Consider the following data for two variables,  and .

7	30	21	18	25
10	27	23	16	21

a. Develop an estimated regression equation for the data of the form . Comment on the adequacy of this equation for predicting . Enter negative value as negative number.

The regression equation is

s= (to 3 decimals)   R2= % (to 1 decimal)   R Adjusted= % (to 1 decimal)

Analysis of Variance

SOURCE DF SS (to 2 decimals) MS (to 2 decimals) (to 2 decimals) -value (to 4 decimals) Regression           Residual Error           Total

b. Develop an estimated regression equation for the data of the form y=b0+b1x+b2x2 . Comment on the adequacy of this equation for predicting y . Enter negative value as negative number. If your answer is zero, enter "0".

The regression equation is

s= (to 3 decimals)   r2= % (to 1 decimal)   adjusted r= % (to 1 decimal)

Analysis of Variance

SOURCE DF SS (to 3 decimals) MS (to 3 decimals) (to 2 decimals) -value (to 4 decimals) Regression           Residual Error           Total

c.Using the appropriate regression model, predict the value of y when x=2 .

Answer 1

a)

excel o/p for regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.952126
R Square	0.906543
Adjusted R Square	0.875391
Standard Error	2.322839
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	157.0133	157.0133	29.10033	0.012484
Residual	3	16.18675	5.395582
Total	4	173.2
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	4.757028	2.906424	1.636729	0.200208	-4.49251	14.00657	-4.49251	14.00657
X	0.7249	0.134378	5.394473	0.012484	0.297248	1.152551	0.297248	1.152551

Y=4.76 + 0.72*X

s=2.323

R²=90.7%

R² adj = 87.5%

ANOVA
	df	SS	MS	F	p-value
Regression	1	157.01	157.01	29.10	0.0125
Residual	3	16.19	5.40
Total	4	173.20

b)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.952255
R Square	0.906789
Adjusted R Square	0.813579
Standard Error	2.841134
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	2	157.0559	78.52796	9.728385	0.093211
Residual	2	16.14409	8.072044
Total	4	173.2
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	5.174194	6.750391	0.766503	0.523491	-23.8704	34.21878	-23.8704	34.21878
X	0.667544	0.805915	0.828306	0.494605	-2.80003	4.135115	-2.80003	4.135115
X²	0.001585	0.021802	0.072696	0.948664	-0.09222	0.09539	-0.09222	0.09539

Y=5.17 + 0.67*X + 0.00*X²

s=2.841

R²=90.7%

R² adj = 81.4%

ANOVA
	df	SS	MS	F	p-value
Regression	2	157.06	78.53	9.73	0.0932
Residual	2	16.14	8.07
Total	4	173.20

c)

first model is appropriate because p-value <α=0.05

when x=2

Y=4.76 + 0.72*2 = 6.21