MHA5017_RebeccaOjo_Assessment3

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Jan 9, 2024

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1 Predicting an Outcome Using Regression Models Rebecca Ojo Capella University MHA-5017: Data Analytics Healthcare Decisions Dr. Michael Furukwawa December 23, 2023
2 Introduction Regression analysis is a popular tool for data modeling and analysis. Most survey analysts use it to comprehend how the variables relate to one another, which they may then use to forecast the exact result. Finding the variables that have an impact on an interest issue can be done with confidence using regression analysis (Palmer and O’Connell, 2009). Regression analysis gives you the confidence to identify the aspects that are most important, the factors that may be disregarded, and the relationships between these components. In this assessment, I will perform a multiple regression test on the relationship between hospital costs and patient age, risk factors, and patient satisfaction scores, and then generate a prediction to support this health care decision. Descriptive Statistics Table & Analysis Predicting future reimbursement costs to make decisions based on the hospital's existing finances requires a multiple regression test. Results must have statistical significance to be interpreted. Using the statistical tool software in Excel, the following results were provided based on costs, patient age, risk factors, and patient satisfaction scores from the hospitals discharges from the previous year:
3 Regression Statistics Multiple R 0.336262892 R Square 0.113072733 Adjusted R Square 0.098372281 Standard Error 2482.428639 Observations 185 ANOVA df SS MS F Significance F Regression 3 142200787.6 47400262.5 7.69178615 7.25547E-05 Residual 181 1115403803 6162451.95 Total 184 1257604590 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 6652.176243 2096.817927 3.17251019 0.00177571 2514.825184 10789.5273 2514.825184 10789.5273 age 107.0358985 28.91090095 3.70226783 0.0002835 49.99015068 164.0816463 49.99015068 164.0816463 risk 153.5570698 66.68461014 2.30273626 0.02243122 21.97786172 285.1362779 21.97786172 285.1362779 satisfaction -9.194689858 6.358071506 -1.4461445 0.14986607 -21.74016342 3.350783708 -21.74016342 3.350783708 According to Xia (2020), variance analysis aids hospital researchers in determining the equality of three or more groups. This is demonstrated by the ANOVA value in the tables above. Accepting this regression model might be wise, for instance, if the value of F (significance) is smaller than alpha, or.05. Here, 7.25547E-05, the significance factor, is less than alpha. This number indicates a p-value of 0.0002835 and a beta coefficient of 107.04 for age. This demonstrates how cost and age relate to one another can have important consequences (Wang et al., 2019). A p-value of 0.14987 and a beta value of -9.19469 are displayed when viewing the satisfaction beta value. The association between the independent and outcome variables (cost) is negative, as indicated by the negative value, while the p-value is positive. The variable in this instance therefore has no significant link with, as indicated by a larger p-value than the alpha value.
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4 Additionally, with a p-value of 0.0224, the beta coefficient of risk is displayed as 153.56 in rounded figures. This statistical result once more emphasizes the connection between the two variables, risk and cost. F value 7.691786146 is sufficient to reject the null hypothesis because it is bigger than 3.95. Interpretation of Fit of Regression Model The relationship between one or more independent variables and a response, dependent, or target variable is described by a function that is provided by a regression model (IMSL, 2016). Understanding the variance in the dependent variables described by predictors is easier by looking at the R-squared value, which is a crucial result of the regression study. The R-squared, for instance, is 0.1131 according to the data results, and the dependent values have an 11% influence on the dependent y variable, or the result. R-squared is used to quantify the fit of the data. As a result, the regression analysis model indicates that age and risk are statistically significant, but customer happiness is not. A scatterplot with a linear regression is an excellent option to measure how close the data is fitted to the regression line for Age, see chart below. 5000 10000 15000 20000 25000 30000 35000 0 10 20 30 40 50 60 70 80 90 100 f(x) = 0 x + 63.04 R² = 0.08 Age Cost Age Application of Results for Decision Making
5 The following regression equation, for example, might be used to forecast the expense of hospitalization: y=β0+β1 X X1+β2 X X2 +β3 x X3. Here, X1, X2, and X3 are noted as coefficients, and the values of Y stand in for the Cost. Cost Prediction Equation 6652.17624314191+107.035898490796(Age)+153.5570698(Risk)+9.194689858 (Satisfaction) Cost Prediction Solved 6652.17624314191+107.035898490796(72) +153.5570698(9) +9.194689858(20) = 15924.67 Based on information on population, birth, and death rates, it is anticipated that the hospital will see a greater number of senior patients in 2024 (Li et al., 2022). It is also anticipated that senior patients' chronic health issues will have a higher risk factor. Moreover, it is also anticipated that this year will see a rise in the value of patient satisfaction due to the hospital's effective implementation of a marketing campaign aimed at raising satisfaction levels. The equation provides a formula to measure the predictive Cost; for instance, the overall predictive yearly Cost of $14,998 * 185 ($2,774,630) and the anticipated Cost of $14,998 per patient indicate that the hospital's costs will be significantly impacted by the patient's age and hazards. It follows that when the degree of satisfaction increases, costs also tend to decrease.
6 References IMSL. (2021, June 16). What Is a Regression Model? IMSL by Perforce. https://www.imsl.com/blog/what-is-regression-model Li, Y., Wang, Y., Gu, N., Cao, Y., & Ye, M. (2022). Application of multiple regression analysis model in table tennis competition. Journal of environmental and public health, 2022, 6748465. https://doi.org/10.1155/2022/6748465 Palmer, P. B., & O'Connell, D. G. (2009). Regression analysis for prediction: understanding the process.   Cardiopulmonary physical therapy journal ,   20 (3), 23–26. Wang, Q. Q., Yu, S. C., Qi, X., Hu, Y. H., Zheng, W. J., Shi, J. X., & Yao, H. Y. (2019). Zhonghuayu fang yixuezazhi [Chinese Journal of Preventive Medicine], 53(9), 955–960. https://doi.org/10.3760/cma.j.issn.0253-9624.2019.09.018 Xia, M., Murray, S., &Tayob, N. (2020). Regression analysis of recurrent-event-free time from multiple follow-up windows. Statistics in medicine, 39(1), 1–15. https://doi.org/10.1002/sim.8385
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