Homework SourseA What is the Null Hypothesis for the overall model B What i
A What is the Null Hypothesis for the overall model?
B What is the Alternative Hypothesis for the overall model?
C What is the multiple regression equation?
D What is the standard error? Describe what this means as related to the problem.
E For your initial model equation, discuss whether R2 or Adjusted R2 should be used in interpreting
how good the linear equation is. Then, interpret the appropriate R2 value.
F What does the overall statistical significance explain with respect to the model?
G Evaluate the p-value for each independent variable. Should any of the independent variables be
dropped? Why or why not?
H Develop a correlation matrix for the independent variables. Should any of the independent
variables be dropped? Why or why not?
I What is the dependent variable?
J What are the independent variables?
| Subscriptions | Population | Adv | Income |
| 37.95 | 588.90 | 13.06 | 33.51 |
| 37.66 | 585.30 | 13.24 | 33.63 |
| 37.55 | 566.30 | 13.43 | 33.68 |
| 38.78 | 642.90 | 13.61 | 33.75 |
| 37.67 | 624.20 | 13.99 | 33.86 |
| 38.23 | 603.90 | 14.18 | 33.90 |
| 36.90 | 571.90 | 14.86 | 34.05 |
| 38.28 | 584.30 | 17.64 | 34.11 |
| 38.95 | 605.00 | 17.72 | 34.17 |
| 39.27 | 676.30 | 17.73 | 34.21 |
| 38.30 | 587.40 | 18.20 | 34.25 |
| 38.84 | 576.40 | 18.53 | 34.27 |
| 38.14 | 570.80 | 19.82 | 34.45 |
| 38.39 | 586.50 | 20.24 | 34.66 |
| 37.29 | 544.00 | 20.94 | 34.72 |
| 39.15 | 611.10 | 21.38 | 34.84 |
| 38.29 | 643.30 | 21.61 | 34.88 |
| 38.09 | 635.60 | 21.68 | 35.20 |
| 37.83 | 598.90 | 21.70 | 35.26 |
| 39.37 | 657.00 | 22.35 | 35.44 |
| 37.81 | 595.20 | 23.41 | 35.72 |
| 37.42 | 520.00 | 23.69 | 35.76 |
| 38.83 | 629.60 | 23.81 | 35.81 |
| 38.33 | 680.00 | 25.39 | 35.85 |
| 40.24 | 651.20 | 25.92 | 35.87 |
Solution
A What is the Null Hypothesis for the overall model?
Null hypothesis: The overall model is not significant.
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B What is the Alternative Hypothesis for the overall model?
Alternative hyppothesis: The overall model is significant.
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C What is the multiple regression equation?
Subscriptions =65.6862+0.0118*Population+0.2500*Adv-1.1343*Income
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D What is the standard error? Describe what this means as related to the problem.
standard error=0.538
The standard error of the estimate is a measure of the accuracy of predictions.
So the accuracy of predictions is 0.538
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E For your initial model equation, discuss whether R2 or Adjusted R2 should be used in interpreting
how good the linear equation is. Then, interpret the appropriate R2 value.
R2 =0.5527 should be used in interpreting how good the linear equation is.
55.27% of variance can be explained by the regression line.
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F What does the overall statistical significance explain with respect to the model?
Since the p-value of F test is very small, we can conclude that the overall model is significant.
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G Evaluate the p-value for each independent variable. Should any of the independent variables be
dropped? Why or why not?
Assume that the significant level a=0.05
Since all p-value for each independent variable are less than 0.05, we can conclude that all independent variable are significant. So no independent variables should be
dropped
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H Develop a correlation matrix for the independent variables. Should any of the independent
variables be dropped? Why or why not?
No independent variables should be dropped because all of them are correlation.
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I What is the dependent variable?
Subscriptions
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J What are the independent variables?
Population, Adv and Income
| Regression output | confidence interval | |||||
| variables | coefficients | std. error | t (df=21) | p-value | 95% lower | 95% upper |
| Intercept | 65.6862 | 16.6915 | 3.935 | .0008 | 30.9744 | 100.3981 |
| Population | 0.0118 | 0.0029 | 4.120 | .0005 | 0.0058 | 0.0177 |
| Adv | 0.2500 | 0.1034 | 2.417 | .0248 | 0.0349 | 0.4651 |
| Income | -1.1343 | 0.5388 | -2.105 | .0475 | -2.2548 | -0.0139 |
