Predicting an Outcome Using Regression Models
The regression analysis model for decision-making aims to determine the relationship between hospital costs and the three variables relevant to hospital operations: patients’ age, risk factors, and satisfaction score. Hospital costs in dollars are the outcome variable, while the other three factors are the explanatory variables. The analysis will form the basis for advising the hospital on the decisions about the reimbursement amount required to stand for the healthcare costs for the next year. The data used in the analysis is obtained from the hospital’s discharge data from the previous year. The outcome of the regression model will be the basis for advising the hospital’s administration about reimbursement decisions.
The regression model output is;
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.336263 | |||||||
| R Square | 0.113073 | |||||||
| Adjusted R Square | 0.098372 | |||||||
| Standard Error | 2482.429 | |||||||
| Observations | 185 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 3 | 1.42E+08 | 47400263 | 7.691786 | 7.26E-05 | |||
| Residual | 181 | 1.12E+09 | 6162452 | |||||
| Total | 184 | 1.26E+09 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | 6652.176 | 2096.818 | 3.17251 | 0.001776 | 2514.825 | 10789.53 | 2514.825 | 10789.53 |
| age | 107.0359 | 28.9109 | 3.702268 | 0.000284 | 49.99015 | 164.0816 | 49.99015 | 164.0816 |
| risk | 153.5571 | 66.68461 | 2.302736 | 0.022431 | 21.97786 | 285.1363 | 21.97786 | 285.1363 |
| satisfaction | -9.19469 | 6.358072 | -1.44614 | 0.149866 | -21.7402 | 3.350784 | -21.7402 | 3.350784 |
Statistical Significance and Effect Size of the Regression Coefficients
The analysis output above indicates that the model is significant in predicting the relationship between the hospital costs in dollars based on the age, risk, and satisfaction factors. This is shown by the overall p-value for the regression model under the “Significance F” column (Frey, 2018). The p-values for the individual variables indicate that each variable significantly predicts healthcare costs, except satisfaction, at a significance level of 5%. The p-values for the variables are less than 0.05 (age: p=0.000284, risk: p=0.022431. The p-value for satisfaction is greater than 0.05 (satisfaction: p=0.149866), implying it is insignificant. The beta values also show the effect of the independent variables on the dependent variables. The beta values indicate that age and risk factors positively affect hospital costs while satisfaction negatively affects hospital costs.
The effect size is shown by the coefficients of correlation. For age, an increase in patient’s age by one year will lead to an increase in the hospital cost by 107.0359 units. Similarly, an increase in risk factor by one unit will lead to an increase in hospital cost by 153.5571 units. A negative effect size for satisfaction indicates that a unit increase in the satisfaction score will lead to a decrease in 9.19469 units. Risk factors and age have the largest effect on hospital costs.
The Fit of the Regression Model
The fit of the regression model can be determined by the R-squared value, which is also referred to as the coefficient of determination of the model. The R-value explains the extent of the scatter of the data points around a fitted regression line. R-squared also shows the proportion of the change in the dependent variable that can be explained by the change in an independent variable (Statsoft.com, n.d.). In the regression output above, the R-squared value is 11% (0.113073), which indicates that the model explains only 11% of the change in the dependent variable due to the change in independent variables. This value also implies that only 11% of the data points for the variables will fit the regression model. R-squared is a goodness of fit test. The higher the R-squared, the better the model predicts the actual data (Gallo, 2015). Therefore, the value indicates that the predicted values may vary largely with the actual data values, and the conclusion is that the model does not fit the data well.
Prediction with the Regression Equation
The regression model was aimed at establishing the relationship between the dependent variable and independent variables.
Y= B0 + B1X1 + B2X2 + B3X3. Where,
- Y = Cost (hospital cost in dollars)
- X1 = Age (patient age in years).
- X2 = Risk (count of patient risk factors).
- X3 = Satisfaction (patient satisfaction score percentile rank)
Point Prediction Using the Regression Equation
| Age | Risk | Satisfaction | Point Prediction | t-value | Std. The error of Pred. | Margin Error | Lower Bound | Upper Bound | Interval Width |
| 80 | 12 | 90 | 16230.21 | 1.973 | 2730.672 | 5388.044 | 5388.044 | 21618.25 | 10776.09 |
Summary of the Results
The results of the analysis suggest that the age of the patient and risk factors significantly predict hospital costs in dollars. From the p-values, age strongly predicts hospital costs compared to risk factors. Accordingly, this implies that the hospital should look at the age of the patient first to predict hospital cost, then other factors, such as risk factors. However, the hospital may need to eliminate the satisfaction score percentile rank in making decisions about hospital costs since it does not significantly predict the costs. The hospital can replace the satisfaction score with another factor, such as the number of days spent in the hospital, to predict the hospital cost more accurately.
The point prediction from the regression model also indicates that the higher the count of patient risk factors, the higher the hospital cost. Besides, the more the age of the patient, the higher the hospital cost. Contrarily, the lesser the patient satisfaction score percentile rank, the higher the hospital cost. Subsequently, this implies that to lower the hospital cost, the hospital needs to ensure increased patient satisfaction scores. Thus, more allocation is necessary if the hospital has more elderly patients and patients with several risk factors since the probable outcome is higher hospital costs per patient. Although the regression analysis model does not best predict the change in the dependent variable due to the change in the independent variable, it provides a basis that the hospital administration can use to make decisions about reimbursement.
References
Frey, B. B. (Ed.). (2018). Multiple linear regression. In The SAGE encyclopedia of educational research, measurement, and evaluation (Vols. 1–4). Thousand Oaks, CA: Sage.
Gallo, A. (2015). A refresher on regression analysis. Harvard Business Review Digital Articles, 2–9.
Statsoft.com. (n.d.). How to find relationships between variables, multiple regression. Retrieved from http://www.statsoft.com/Textbook/Multiple-Regression
ORDER A PLAGIARISM-FREE PAPER HERE
We’ll write everything from scratch
Question 
Perform multiple regression on the relationship between hospital costs and patient age, risk factors, and patient satisfaction scores, and then generate a prediction to support this healthcare decision. Write a 3-4 page analysis of the results in Word and insert the test results into this document.
Predicting an Outcome Using Regression Models
Regression is a significant statistical technique for determining the relationship between an outcome (dependent variable) and predictors (independent variables). Multiple regression evaluates the relative predictive contribution of each independent variable on a dependent variable. The regression model can then be used for predicting an outcome at various levels of the independent variables. For this assessment, you will perform multiple regression and generate a prediction to support a healthcare decision.
The dataset contains the following variables:
cost (hospital cost in dollars).
age (patient age in years).
risk (count of patient risk factors).
satisfaction (patient satisfaction score percentile rank).
Instructions
Hospital administration needs to make a decision on the amount of reimbursement required to cover expected costs for next year. For this assessment, using information on hospital discharges from last year, multiple regressions were performed on the relationship between hospital costs and patient age, risk factors, and patient satisfaction scores, and then a prediction was generated to support this healthcare decision. Write a 3–4 page analysis of the results in a Word document and insert the test results into this document (copied from the output file and pasted into a Word document). Refer to Copy From Excel to Another Office Program for instructions.
Submit both the Word document and the Excel file that shows the results.
Grading Criteria
The numbered assessment instructions outlined below correspond to the grading criteria in the Predicting an Outcome Using Regression Models Scoring Guide, so be sure to address each point. You may also want to review the performance-level descriptions for each criterion to see how your work will be assessed.
Perform the appropriate multiple regression using a dataset.
Interpret the statistical significance and effect size of the regression coefficients of a data analysis.
Interpret p-value and beta values.
Interpret the fit of the regression model for prediction of a data analysis.
Interpret R-squared and goodness of fit.
Apply the statistical results of the multiple regression of a data analysis to support a health care decision.
Generate a prediction with a regression equation.
Write a narrative summary of the results that include practical, administration-related implications of the multiple regression.
Write clearly and concisely, using correct grammar, mechanics, and APA formatting.