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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