One of the biggest changes in higher education in recent years has been the grow

Question

One of the biggest changes in higher education in recent years has been the growth of online universities. The Online Education Database is an independent organization whose mission is to build a comprehensive list of the top accredited online colleges. The following table shows the retention rate (%) and the graduation rate (%) for 29 online colleges.

Write the regression equation. Interpret the regression constant and regression coefficient. Forecast a value for the dependent variable. Test the significant of the regression coefficient using alpha = .05. Test the overall significant of the regression model. Interpret the coefficient of determination. Are there any indications of a violation of the general linear model? Be specific.

Retention Rate (%)      Graduation Rate (%)

            7                                    25

           51                                   25

             4                                   28

           29                                   32

           33                                   33

           47                                   33

           63                                   34

           45                                   36

           60                                   36

           62                                   36

           67                                   36

           65                                   37

           78                                   37

           75                                   38

           54                                   39

           45                                   41

           38                                   44

           51                                   45

           69                                   46

           60                                   47

           37                                   48

           63                                   50

           73                                   51

           78                                   52

           48                                   53

           95                                   55

           68                                   56

          100                                  57

          100                                  61

Explanation / Answer

Independent variable: Retention Rate

Dependent variable: Graduation Rate

Following is the output of regression analysis:

Slope of the regression equation: 0.2845

For each unit increase in independent variable, dependent variable is increased by 0.2845.

Intercept of regression equation: 25.4229

When retention rate is 0% then graduation rate is 25.42%.

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P-value of the slope is 0.0000

Since p-value is less than 0.05 so we reject the null hypothesis.

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P-value of F test is 0.0000

Since p-value is less than 0.05 so model is significant.

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The R-square is 0.4492

It shows that 44.92% of variation in dependent variable is explained by independent variable.

SUMMARY OUTPUT Regression Statistics Multiple R 0.670244797 R Square 0.449228088 Adjusted R Square 0.428829129 Standard Error 7.456104604 Observations 29 ANOVA df SS MS F Significance F Regression 1 1224.285956 1224.285956 22.02210775 6.95491E-05 Residual 27 1501.024388 55.59349587 Total 28 2725.310345 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 25.42290363 3.746283822 6.786165928 2.7441E-07 17.73616425 33.10964301 Retention Rate (%), X 0.284526003 0.060630691 4.692771862 6.95491E-05 0.160122101 0.408929904

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