Question

A researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N=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=0.05.

   X1          X2         Y

34.4	26.4	59.4
53.7	38.3	90.4
72.8	43.2	71.3
25.4	21.2	64.5
75.9	46.5	71.1
60.4	27.9	72.6
28	56.4	29.9
40.1	43.6	53.7
27.2	64.5	61.5
48.2	60	43.8
78.6	53.6	53.5
69	43.9	85.5

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=0.05

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

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

using excel data analysis tool for regression,steps are:

write data>menu>data>data analysis>regression>enter required labels>ok> and following o/p is obtained

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.645566
R Square	0.416756
Adjusted R Square	0.287146
Standard Error	14.26945
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	2	1309.446	654.7232	3.215463	0.088375
Residual	9	1832.554	203.6171
Total	11	3142
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	67.90951	17.56506	3.866171	0.003811	28.17459	107.6444	28.17459	107.6444
X1	0.402109	0.214897	1.871172	0.094123	-0.08402	0.888239	-0.08402	0.888239
X2	-0.57943	0.315883	-1.83431	0.099811	-1.294	0.13515	-1.294	0.13515

R2=0.4168
F=3.2155
P-value for overall model =0.0884

t1=1.8712
for b1, P-value =0.0941
t2= -1.8343
for b2, P-value =0.0998

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

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neither regression coefficient is statistically significant