Question

A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=11N=11 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.05α=0.05.

X1X1	X2X2	YY
55.3	51.1	56.2
72.1	51.6	76.6
35.2	41.7	51.8
70.4	58	47.9
51	71.6	39.8
66.6	60.4	61.9
61.9	48.9	63.4
46.8	54.3	41.7
47.9	48.4	48
68.8	29.3	63.8
73.4	53	79.3

R2=R2=
F=F=
P-value for overall model =

t1=t1=
for b1b1, P-value =
t2=t2=
for b2b2, P-value =

What is your conclusion for the overall regression model (also called the omnibus test)?

• The overall regression model is statistically significant at α=0.05α=0.05.
• The overall regression model is not statistically significant at α=0.05α=0.05.

Which of the regression coefficients are statistically different from zero?

• neither regression coefficient is statistically significant
• the slope for the first variable b1b1 is the only statistically significant coefficient
• the slope for the second variable b2b2 is the only statistically significant coefficient
• both regression coefficients are statistically significant

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.772011
R Square	0.596002
Adjusted R Square	0.495002
Standard Error	9.300948
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	2	1020.968	510.484	5.901028	0.026639
Residual	8	692.0611	86.50764
Total	10	1713.029
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	35.60595	19.90714	1.788602	0.111477	-10.3	81.51191	-10.3	81.51191
X1X1	0.726346	0.233464	3.111175	0.01442	0.187978	1.264715	0.187978	1.264715
X2X2	-0.40992	0.275402	-1.48843	0.17496	-1.04499	0.225162	-1.04499	0.225162

R² = 0.5960

F=5.90102828

p value= 0.026639052

t1 = 3.111175052

p value=0.01441984

t2 =  -1.488426453

p value= 0.174960123

The overall regression model is statistically significant at α=0.05α=0.05.
the slope for the first variable b1b1 is the only statistically significant coefficient