Question

A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=18N=18 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level α=0.05α=0.05.

X1X1	X2X2	YY
48.6	52.9	39.2
40.8	58.8	45.5
43.5	64.3	50.1
45.3	32.7	40.8
50.4	47.4	42.9
46.9	44.1	38.4
90.6	46.6	49.3
50.2	33.6	37.3
54.2	28.2	38.8
24.9	62.7	50.9
61.9	34.5	43
44.3	58.2	47.6
59.1	57	55.3
53.6	55.1	49.6
38.2	35.9	35.4
72.3	33.8	33.1
86.3	20.2	42.8
52	58.1	61.1

SSreg=SSreg=  
SSres=SSres=  
R2=R2=  
F=F=  
P-value =

What is your decision for the hypothesis test?

• Reject the null hypothesis, H0:β1=β2=0H0:β1=β2=0
• Fail to reject H0H0

What is your final conclusion?

• The evidence supports the claim that one or more of the regression coefficients is non-zero
• The evidence supports the claim that all of the regression coefficients are zero
• There is insufficient evidence to support the claim that at least one of the regression coefficients is non-zero
• There is insufficient evidence to support the claim that all of the regression coefficients are equal to zero

Answer 1

Applying regression from excel: data-data analysis: regression:

Regression Statistics
Multiple R	0.758254
R Square	0.574949
Adjusted R Square	0.518275
Standard Error	5.072367
Observations	18
ANOVA
	df	SS	MS	F	Significance F
Regression	2	522.0359	261.0179	10.14493	0.001634
Residual	15	385.9336	25.7289
Total	17	907.9694
	Coefficients	Standard Error	t Stat	P-value	\
Intercept	13.80948	8.233633	1.677203	0.114212
X1	0.168493	0.086699	1.943421	0.070973
X2	0.473551	0.105306	4.496895	0.000426

SSreg= 522.0359

SSres= 385.9336

R2=   0.5749

F= 10.1449

p value =0.0016

since p value <0.05

Reject the null hypothesis, H0:β1=β2=0H0:β1=β2=0

The evidence supports the claim that one or more of the regression coefficients is non-zero