Question

A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=12N=12 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=0.01α=0.01.

X1X1	X2X2	YY
51.1	40.5	48
53.5	41	51.5
53.2	62.8	42.8
52.3	52.7	51.3
64.1	60	48.8
56.8	62.1	50
61.6	88.1	39.2
60.4	62.5	45.5
63.6	68.6	37.9
56.4	33.4	45.9
60.2	50.9	54.9
64.5	66.7	44.9

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=0.01α=0.01.
• The overall regression model is not statistically significant at α=0.01α=0.01.

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

using excel>data>data analysis >regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.612867
R Square	0.375606
Adjusted R Square	0.236852
Standard Error	4.428195
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	2	106.1623	53.08116	2.706992	0.120106
Residual	9	176.4802	19.60891
Total	11	282.6425
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	59.36817	16.8191	3.529806	0.006416	21.32072	97.41562	21.32072	97.41562
x1	-0.01376	0.339444	-0.04054	0.968549	-0.78164	0.754115	-0.78164	0.754115
x2	-0.20618	0.111283	-1.85273	0.096929	-0.45792	0.045562	-0.45792	0.045562

R2=0.3756

F=2.707
P-value for overall model =0.1201

t1=-0.041
for b1b1, P-value =0.9685
t2=-1.852
for b2b2, P-value =0.0969

r conclusion for the overall regression model

• The overall regression model is not statistically significant at α=0.01 because p value of model is greater than alpha

the regression coefficients are statistically different from zero

• neither regression coefficient is statistically significant because both p value are greater than 0.01