Question: Using the Small Hospitals Only AHA sub-database, a multiple regression analysis in an attempt to predict number of personnel by births, admissions, and outpatient visits
Using the Small Hospitals Only AHA sub-database, a multiple regression analysis in an attempt to predict number of personnel by births, admissions, and outpatient visits is given below. How strong is the model? Explain. Which, if any, of the predictor variables are significant? How does R2 compare to adjusted R2 and what does it mean in this model? American Hospital Association database SUMMARY OUTPUT
| Regression Statistics | ||
| Multiple R | 0.788 | |
| R Square | 0.620 | |
| Adjusted R Square | 0.618 | |
| Standard Error | 99.769 | |
| Observations | 447 |
| ANOVA | ||||||||||
| df | SS | MS | F | Significance F | ||||||
| Regression | 3 | 7202459 | 2400820 | 241.195 | 9.53387E-93 | |||||
| Residual | 443 | 4409562 | 9953.865 | |||||||
| Total | 446 | 11612022 |
| Coefficients | Standard Error | t Stat | P-value | |||||
| Intercept | 72.2934 | 7.9538 | 9.09 | 3.36E-18 | ||||
| Admissions | 0.0563 | 0.0102 | 5.54 | 5.21E-08 | ||||
| Outpatient Visits | 0.0015 | 0.0001 | 18.81 | 2.01E-58 | ||||
| Births | 0.0696 | 0.0373 | 1.87 | 0.0624 |
In Minitab: Regression Equation Personnel = 72.29 - 0.0696 Beds + 0.0563 Admissions + 0.001478 Outpatient visits Coefficients
| Term | Coef | SE Coef | T-Value | P-Value | VIF | |||||
| Constant | 72.29 | 7.95 | 9.09 | 0.000 | ||||||
| Beds | 0.0696 | 0.0373 | 1.87 | 0.062 | 1.51 | |||||
| Admissions | 0.0563 | 0.0102 | 5.54 | 0.000 | 1.64 | |||||
| Outpatient Visits | 0.001478 | 0.000079 | 18.81 | 0.000 | 1.32 |
Model Summary
| S | R-sq | R-sq(adj) | R-sq(pred) | |||
| 99.7691 | 62.03% | 61.77% | 55.82% |
Analysis of Variance
| Source | DF | Adj SS | Adj MS | F-Value | P-Value | |||||
| Regression | 3 | 7202459 | 2400820 | 241.19 | 0.000 | |||||
| Beds | 1 | 34736 | 34736 | 3.49 | 0.062 | |||||
| Admissions | 1 | 305454 | 305454 | 30.69 | 0.000 | |||||
| Outpatient Visits | 1 | 3520026 | 3520026 | 353.63 | 0.000 | |||||
| Error | 443 | 4409562 | 9954 | |||||||
| Lack-of-Fit | 438 | 4407425 | 10063 | 23.54 | 0.001 | |||||
| Pure Error | 5 | 2137 | 427 | |||||||
| Total | 446 | 11612022 |
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