Question

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

x	10	34	20	11	24
y	11	30	22	19	21

a. Develop an estimated regression equation for the data of the form y=b₀+b₁x. Comment on the adequacy of this equation for predicting . Enter negative value as negative number.

The regression equation is

Y=___________+___________ (to 2 decimals)

s=__________ (to 3 decimals) r2=_________% (to 1 decimal) r2 adj=_______ % (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 ----------------- -------------- ------------

Using a .05 significance level, the p-value indicates a (- Select your answer -weak, strong or no relationship); note that ______________ (to 1 decimal) of the variability in y has been explained by x.

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

y=_________+__________X+_________x2 (to 2 decimals)

s=_________ (to 3 decimals) r2=_____________% (to 1 decimal) r2 adj=________ % (to 1 decimal)

Analysis of Variance

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

At the a= .05 level of significance, the relationship (- Select your answer - is, is not) _______________ (to 1 decimal) of the variability in y has been explained by x.

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

_______________ (to 2 decimals)

Answer 1

a)

using excel data analysis tool for regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.903173
R Square	0.815722
Adjusted R Square	0.754296
Standard Error	3.372848
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	151.0717	151.0717	13.27974	0.035638
Residual	3	34.12831	11.3761
Total	4	185.2
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	8.320774	3.69179	2.253859	0.109546	-3.42815	20.0697	-3.42815	20.0697
X	0.620163	0.170181	3.644138	0.035638	0.078571	1.161755	0.078571	1.161755

so, regression line is   Ŷ =   8.32 +   0.62 *x

s=3.373

R²=81.6%

R² adj = 75.4%

ANOVA
	df	SS	MS	F	p-value
Regression	1	151.072	151.072	13.28	0.0356
Residual	3	34.128	11.376
Total	4	185.200

Using a .05 significance level, the p-value indicates a (, strong relationship) ; note that _____81.6%_________ (to 1 decimal) of the variability in y has been explained by x.

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b)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.903417
R Square	0.816162
Adjusted R Square	0.632324
Standard Error	4.125944
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	2	151.1532	75.57659	4.439568	0.183838
Residual	2	34.04682	17.02341
Total	4	185.2
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	9.070045	11.7337	0.772991	0.520382	-41.416	59.5561	-41.416	59.5561
X	0.535426	1.242336	0.430983	0.708485	-4.80991	5.880767	-4.80991	5.880767
X²	0.001973	0.028518	0.069186	0.951137	-0.12073	0.124677	-0.12073	0.124677

Y = 9.07 + 0.54*X + 0.00*X²

s=4.126

R²=81.6%

R² adj = 63.2%

ANOVA
	df	SS	MS	F	p-value
Regression	2	151.153	75.577	4.44	0.1838
Residual	2	34.047	17.023
Total	4	185.200

At the a= .05 level of significance, the relationship is not . ______81.6%_________ (to 1 decimal) of the variability in y has been explained by x

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c)

first model is appropriate

so, when x=2

Ŷ =   8.3208   +   0.6202   *2 = 9.56