A What is the Null Hypothesis for the overall model? B What is the Alternative H

Question

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

Explanation / Answer

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

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