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A researcher would like to predict the dependent variable Y from the two independent variables X1...

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Statistics

A researcher would like to predict the dependent variable Y fromthe two independent variables X1 and X2 for a sample of N=16subjects. Use multiple linear regression to calculate thecoefficient of multiple determination and test the significance ofthe overall regression model. Use a significance level α=0.05.

X1            X2            Y

4842.347.1
36.358.765.4
43.440.263.6
49.537.945.6
45.537.250.8
40.664.742.4
42.546.763.1
42.74035.8
55.810.652.1
40.96360.3
39.656.544
43.545.161.2
3968.867.2
50.443.740.6
46.142.658
55.219.149.1

SSreg=
SSres=
R2=
F=
P-value =

What is your decision for the hypothesis test?

  • Reject the null hypothesis, H0:β1=β2=0
  • Fail to reject H0


What is your final conclusion?

  • The evidence supports the claim that one or more of theregression coefficients is non-zero
  • The evidence supports the claim that all of the regressioncoefficients are zero
  • There is insufficient evidence to support the claim that atleast one of the regression coefficients is non-zero
  • There is insufficient evidence to support the claim that all ofthe regression coefficients are equal to zero

Answer & Explanation Solved by verified expert
4.3 Ratings (716 Votes)

Applying regression on above data:

Regression Statistics
Multiple R 0.3911
R Square 0.1530
Adjusted R Square 0.0227
Standard Error 9.7816
Observations 16
ANOVA
df SS MS F Significance F
Regression 2 224.6738 112.3369 1.1741 0.3398
Residual 13 1243.8355 95.6797
Total 15 1468.5094
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 110.5744 57.4787 1.9237 0.0766 -13.6007 234.7496 -13.6007 234.7496
x1 -1.0988 0.9613 -1.1430 0.2737 -3.1756 0.9781 -3.1756 0.9781
x2 -0.1853 0.3474 -0.5333 0.6028 -0.9357 0.5652 -0.9357 0.5652

from above\"

SSreg =224.6738

SSres=1243.8355

R2= 0.1530

F =1.1741

p value =0.3398

Fail to reject H0

There is insufficient evidence to support the claim that at least one of the regression coefficients is non-zero
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