Question

A researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N=10 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.

X1	X2	Y
40.5	62.9	21.8
16.4	51.3	31.8
62.5	44.4	29.6
60.4	53.6	40.6
50.2	54	33.7
39.2	51.5	37
80.9	16.9	58.1
41.6	52.6	34.6
48.5	50	34.7
35.6	57.2	33.8

R2=0.747
F=10.33
P-value for overall model = 0.0082

b1=0.04, t1=0.29, P-value = 0.7802
b2=−0.61, t2=−3.05, P-value = 0.0186


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