# Multiple Regressions

Multiple Regressions

Descriptive analysis

From the data the mean and the standard deviation of the Staffed beds is 216.59 and 21.15 respectively.

Variable Mean Standard Deviation

Medicare Days_05 25092.15 2601.991

Medicaid Days_05 10467.28 1484.689

Total Surgeries_05 8979.778 1046.17

RN FTE_05 309.1728 41.295

Occupancy 89276.4 2908.932

Ownership 0.1975 0.0445

System Membership 0.642 0.054

Rural/Urban 0.296 0.051

Teaching Affiliation 0.2222 0.046

Age 65 Plus 2005 14199.51 2056.83

Crime Rate/100,00 population 6779.716 564.833

Uninsured 2005 17508.98 2591.95

Total Operating expense_05 1.2E+08 16492479

Multiple Regression

From the multiple regressions, this is the model

Y = 0.85 + 0.18×1 – 1.13×2 -0.20×3 +1.84×4 + 0.33×5 +0.23×6 – 12.89×7 + 5.39×8 -4.60×9 -20.37×10 -0.26×11 – 0.1×12 + 0.35×13

Note: Total Operating Expenses_05 is y Staffed beds_05 is x1 Medicare Days_05 is x2 Medicaid Days are x3 Total Surgeries_05 is x4 RN FTE_05 is x5 Occupancy is x6 Ownership is x7 System Membership is x8 Rural/Urban is x9 Teaching Affiliation is x10 Age 65 Plus 2005 is x11 Crime rate/100,000 population is x12 Uninsured 2005 is x13

Note: The regression coefficients have been reduced by scaling the data. Using the data, the way they are, one gets ridiculous coefficients. The total expenses_05 have been reduced by 1000000, Age 65 Plus, Uninsured 2005, Crime Rate, Total Surgeries, Medicaid day_05, Medicare days_05, and Occupancy has been reduced by 1000.

From the data a unit (1000) increase in staffed bed would result in a 170,000 increase in total operating expense. This variable has p value of 0.26, which is greater than 0.05 showing that this variable is not significant. A unit (1000) increase in Medicare days would result in a 1131 decrease in total operating expenses. Medicare days has a p value of 0.004 which is less than 0.05 showing that this variable is significant. A unit (1000) increase in Medicaid days would lead to 201 decreases in total operating expenses. Medicaid days is an insignificant variable because it has a p value greater than 0.05. A unit (1000) increase in total surgeries would result in a 1836 increase in the total operating expenses. Total surgeries is an insignificant variable because its p value is greater than 0.05. A unit increase in RN FTE would lead to a 329112 increase in total operating expenses. RN FTE has less than the critical value; this shows that the variable is significant. A unit (1000) increase in occupancy would lead to a 239 increase in total operating expenses. Occupancy is insignificant because it has a p value greater than 0.05. A unit expense in Ownership results into a 12890000 decrease in total operating expense. The variable ownership is insignificant because it is greater than the critical value 0.05. A unit increase in System membership results into a 4600000 decrease in total operating expense. System membership has a p value of 0.4 which is greater than 0.05 which shows that the variable is insignificant. A unit increase in Teaching Affiliation would lead to a 20370000 decrease in total operating expense. The p value of teaching affiliation is greater than the significant value 0.05 showing that the variable is insignificant. A unit (1000) increase in Age above 65 would result in a 260000 decrease in total expenses. The variable age has a p value greater than 0.05 showing that the variable age is insignificant. A unit (1000) increase in Crime rate would lead to a 100000 increase in total operating expenses. Crime rate has a p value of 0.89 which is greater than the critical value, demonstrating that the variable is insignificant. Lastly a unit increase in uninsured would lead to a 350000 increase in total expenses. Uninsured has a p value greater than 0.05 showing that the variable is insignificant. According to Allen (1997), if p value is greater than the critical value reject the variable is not significant.

Hypothesis Testing

From the data the null hypothesis is H0 = β1= β2= β3……= β13 = 0 against the alternative hypothesis H1 = β1= β2= β3……= β13≠0. From the anova table the calculated Fstatistics is 167.55 with 13 an 67 degrees of freedom. The tabulated Fstatistics is 1.797 which is below the Fcalculated. This means that we reject the null hypothesis and accept the alternative hypothesis. According to Cohen & Cohen (1983), if the f calculated is greater than the tabulated f value reject the null hypothesis.

R Square and Adjusted R Square

From the data, the adjusted R Square is 0.96 showing that the model explains 96% of the variation. This is a good fit. It is better to report adjusted R Square because it changes slightly if the variable is not significant. The value of R Square is 0.98 showing that the model is a good fit. This value is not commonly used because it fluctuates greatly, even if the variable is not significant (Hearley, 2010).

Interpretation

From the data, the Medicaid days_05, RN FTE_05, and Staffed beds_05 are the most significant variables in the model. This means to professionals that increasing the number of staffed beds in hospitals will increase the number of patients increasing the total operating expenses. Increasing the number of medicare days will decrease the total operating expenses in hosptials.

References

Allen, M. P. (1997). Understanding regression analysis. Plenum Press, Spring Street:New York

Cohen,J.,& Cohen, P. (1983). Applied multiple regression/correlation analysis for the behavioral sciences. Lawrence Erlbaum Associates, Hillsdale: New Jersey.

Healey, J. F. (2010). The essentials of statistics: a tool or social research. Wadworth/Cengage Learning, Australia: Belmont, CA.

Johnson, R., Freund, J., & Miller, I. (2011). Probability and statitics for engineers.Pearson Education:Prentice Hall, New York

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