Statistics: Essential Tool for Informed Decision-Making Essay Example

Introduction

Statistics is an essential tool in the decision-making process as it helps the organization executives to make informed decisions and faced the uncertainties with confidence regardless of the available amount of data as stated in Statsoft.com. Hence providing their staff with stable leadership. There is numerous regression model that has over the years gained a lot of attention from the different researchers and scholars (Casson & Farmer, 2014). With their abilities to put different information together to create significant variables, formulate an actual model as well as analyze the appropriateness of the model to align with the data gathered or collected. Additionally, the data analysis is formed from the hospital patients' age, costs, the risk factor, and the patient's level of satisfaction scores. All the dataset was from the previous year's records. The purpose of this paper is to predict the sum of reimbursement needed to provide for the expenditure of the subsequent year. Also, the p-value will be computed in addition to the beta value along with the R-square and the goodness of fit. The analysis is aimed at giving the relation between hospital costs and patient age, risk factors, and patient satisfaction scores, and then generate a prediction to support this healthcare decision. Therefore, various regression models will be employed in this analysis.

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The Analysis

The Effect Size Analyses and Statistical Significance

The statistical significance is essential; however, it is not the sole determinant when evaluating the results of a statistical test. And this is because the statistical significance shows the likelihood that the results obtained are just a coincidence or a lucky guess. Therefore, it is essential to take into consideration the effect size. The effect size shows how reliable or necessary the results are (Sullivan & Feinn, 2012). The p-value measures the null proposition that the coefficient is correspondent to a zero. A p-value, which is low than 0.05 shows that the null supposition is not significant and should be rejected. In simple terms, this means that a predictor with a lower p-value is probably to be a meaningful addition to the model, and this is because the alterations in the predictor's value are linked to the modifications in the response variables. On the contrary, a p-value that is above the significance levels shows that it is not enough evidence to draw a conclusion that nob zero correlation exists. The beta coefficient, on the one hand, is the degree of change in the results owing to a one-unit difference in the predictor variables.

Input the Output Summary Here

Anova

From the above outputs, it can be observed that the regression for both age and risk predictors is below the 0.05 significance level meaning that these two are statistically significant to the data analysis. However, the regression for the patient's satisfaction is at 0.1499/0.150, which is above 0.05, and hence it, means that it is not statistically significant to the analysis.

Beta Coefficient

To attain the beta coefficient, it is essential to make a comparison between the independent individual variables to the dependent variables. Therefore, all the variables within the regression models should be converted to Z-score before running the analysis to get the beta coefficients.

The Regression and The Goodness Fit

For a linear regression model analysis, a measure of goodness of fit is represented by R-square. The statistical analysis “shows the percentage of the change in the dependent variable that is independent variables interpreted accurately” (Frey, 2018). The study conducted above shows the R-square as 0.1131, and that in percentage is 11%, therefore because R-square is considerably high, it is thus used as the measure of goodness. The adjusted R-square was recorded at 0.098. Using the linear regression model, it can, therefore, be determined on how accurate the data fits the model.

Regression Equation Prediction of Statistical Data

The regression is mainly used to predict the results of the data given. the independent variables are incorporated in the regression equation to predict the mean values of the dependent variables. from the data given Y represents the cost, a represent the age, b is the risk factor and c represent the satisfaction scores. therefore, the data is presented as: “Y=6652.176+107.036* (age) +153.557*(risk)-9.195* (satisfaction)”

Decision Making

The multiple regression equation that was employed in this case was "Y=6652.176+107.036* (age) +153.557*(risk)-9.195* (satisfaction)" the total reimbursement total that was achieved in the previous year was 14,906.51, and this was achieved using both the predicted costs as well as the actual costs. It is important to note that this data showed no effect or change in the costs for hospitals in the coming year. Therefore, the hospital can concentrate on minimizing other expenses while maintaining a cost of 14906.51. Thus, the hospital management should implement strategies that are aimed at increasing the patient's satisfaction while at the same time reducing risks, which reduced the annual hospital budget. These strategies would, therefore, increase the overall hospital revenue, cut on operational costs, and yearly budget.

Narrative summary

To evaluate the cost for a patient, it is vital, to sum up, the intercept, the age of the patient, the risk factor, and then subtract the satisfaction score to arrive at Y. From the estimation of the model, the model is appropriate since the values are within the given range. However, patient satisfaction needs to be improved to increase in the following year's reimbursements. The analysis shows that age is statistically significant, so it is for risk since they have a p-value, which is below the alpha level of 0.05 while satisfaction is not. Therefore, for the management to make a decision that is best for the hospital, the satisfaction variable should be eliminated from the data set. However, while looking at the long sustainability of the hospital, the satisfaction variable should be included.

References

Casson, R. J., & Farmer, L. D. M. (2014). Understanding and checking the assumptions of linear regression: A primer for medical researchers. Clinical & Experimental Ophthalmology, 42(6), 590–596. https://doi.org/10.1111/ceo.12358

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

Statsoft.com. (n.d.). How to find relationship between variables, multiple regression. Retrieved from http://www.statsoft.com/Textbook/Multiple-Regression

Sullivan, G. M., & Feinn, R. (2012). Using effect size—or why the P value is not enough. Journal of Graduate Medical Education, 4(3), 279–282.