Question

A researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N=13 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=0.02.

X1X1	X2X2	YY
58	64.7	35.9
45	35.4	78.8
69.4	45.5	64.1
63.2	71.9	9
58	42.8	84.3
24.5	55.5	63.5
27.5	49.3	77.3
41.8	50.5	71.5
45.9	53	23.8
55	63	27.7
38.6	51	56.1
59.6	57.6	24.9
23	50.7	70.3

R2=
F=
P-value for overall model =

t1=
for b1, P-value =
t2=
for b2, 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=0.02.
• The overall regression model is not statistically significant at α=0.02.

Which of the regression coefficients are statistically different from zero?

• neither regression coefficient is statistically significant
• the slope for the first variable b1 is the only statistically significant coefficient
• the slope for the second variable b2 is the only statistically significant coefficient
• both regression coefficients are statistically significant

Answer 1

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

Regression Statistics
Multiple R	0.8721
R Square	0.7605
Adjusted R Square	0.7126
Standard Error	13.5189
Observations	13
ANOVA
	df	SS	MS	F	Significance F
Regression	2	5803.3291	2901.6645	15.8769	0.0008
Residual	10	1827.6017	182.7602
Total	12	7630.9308
	Coefficients	Standard Error	t Stat	P-value
Intercept	180.0731	22.8844	7.8688	0.0000
X1	-0.4574	0.2636	-1.7350	0.1134
X2	-1.9901	0.4163	-4.7807	0.0007

from above:

R² =0.7605

F =15.8769

p value for overall model =0.0008

t1 =-1.7350

p value =0.1134

t2 =-4.7807

p value =0.0007

The overall regression model is statistically significant at α=0.02.

the slope for the second variable b2 is the only statistically significant coefficient