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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=0.05. X1 X2 Y 31.9 50.2 89.2 12.7 25.5 33.5 41.2 46.4 44.5 29.2 42.9 76.3 22.9 36.6 56 39.4 46.6 55.3 36.4 46.2 43 56.1 49.6 7.6 21 39.7 58.2 58 48.3 22.6 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

- August 24, 2022 - Edwin Tunner

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=0.05.

X1 X2 Y
31.9 50.2 89.2
12.7 25.5 33.5
41.2 46.4 44.5
29.2 42.9 76.3
22.9 36.6 56
39.4 46.6 55.3
36.4 46.2 43
56.1 49.6 7.6
21 39.7 58.2
58 48.3 22.6

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
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