A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=11N=11 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=0.05α=0.05.
| X1X1 | X2X2 | YY |
|---|---|---|
| 52.3 | 45.6 | 49.1 |
| 55.9 | 48.7 | 53.1 |
| 46.5 | 47.4 | 45.9 |
| 52 | 45.6 | 59.8 |
| 48.9 | 45.5 | 52.6 |
| 46.2 | 35.1 | 71.2 |
| 28.8 | 32.6 | 33.5 |
| 40.7 | 41 | 40.3 |
| 43.7 | 40 | 65.8 |
| 47 | 37.8 | 52.8 |
| 34.2 | 28 | 53.5 |
R2=R2= (Not the adjusted R2R2)
FF test statistic =
P-value for overall model =
test statistic for b1b1
p-value for the two-tailed test =
test statistic for b2b2
p-value for the two-tailed test =
What is your conclusion for the overall regression model at the 0.05 alpha level (also called the omnibus test)?
Which of the regression coefficients are statistically different from zero at the 0.05 alpha level?
A researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N=15 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level α=0.01.
| X1X1 | X2X2 | YY |
|---|---|---|
| 44.5 | 64.2 | 39.3 |
| 27.4 | 58.2 | 18.8 |
| 37.6 | 74 | 40.2 |
| 40.5 | 12.1 | 73.3 |
| 33.4 | 60.8 | 15.5 |
| 0.3 | 21.7 | 27.4 |
| 91.4 | 57 | 69.8 |
| 56.4 | 58.9 | 98.4 |
| 30.8 | 46.8 | 40 |
| 54 | 83.2 | 31.5 |
| 31.6 | 66.2 | 29.8 |
| 37.5 | 57.1 | 46.7 |
| 55.3 | 38.7 | 99.8 |
| 66 | 61.2 | 84.1 |
| 53.7 | 37.9 | 45.9 |
SSreg=
SSres=
R2=
F=
P-value =
| X1X1 | X2X2 | YY |
|---|---|---|
| 58.8 | 29.9 | 63.1 |
| 64.1 | 57.3 | 40.1 |
| 51.4 | 35.3 | 46.2 |
| 77.1 | 88.5 | 30 |
| 60.6 | 67.5 | 16.2 |
| 68.3 | 63.4 | 62 |
| 44.8 | 6.6 | 77.6 |
| 49 | 29.3 | 65.5 |
| 55.5 | 25.8 | 62.5 |
| 57.5 | 30.2 | 62 |
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)?
Which of the regression coefficients are statistically different from zero?
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)?
Which of the regression coefficients are statistically different from zero?
A researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N=15 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level α=0.02.
| X1 | X2 | Y |
|---|---|---|
| 55.1 | 69.4 | 72.2 |
| 31.4 | 54.3 | 36.2 |
| 57.9 | 50 | 103.4 |
| 41.3 | 53.7 | 43.9 |
| 50.7 | 36.6 | 98.5 |
| 50.1 | 53.3 | 65.3 |
| 39.8 | 60.5 | 55.2 |
| 59.6 | 80.8 | 43.6 |
| 24.2 | 8.2 | 77 |
| 32.4 | 69.8 | 31 |
| 34.4 | 35.3 | 82.6 |
| 70.3 | 79.6 | 66.2 |
| 31.5 | 36.1 | 43.6 |
| 42.3 | 48.7 | 73.3 |
| 25.9 | 70.2 | 21.6 |
SSreg=
SSres=
R2=
F=
P-value =
What is your decision for the hypothesis test?
What is your final conclusion?
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