Assignment: Physician Influence on Hospital Cost
Assignment Physician Influence on Hospital Cost
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Regression analysis refers to the set of statistical methods that are applied in the estimation of the dependent variable and one or more independent variables. Regression analysis can be applied to assess the strength of the correlation between variables and for modeling the future relationship that may be expected between independent and dependent variables. In regression analysis, there exist several variations such as multiple linear, linear, as well as nonlinear. Some of the most common models are multiple linear and simple linear (Kumari & Yadav, 2018). Nonlinear regression analysis is usually applied for complicated data sets where the independent and dependent variables indicate a nonlinear relationship (Aggarwal & Ranganathan, 2017). There are numerous applications of regression analysis, including research processes as well as financial analysis. The purpose of this assignment is to predict an outcome using regression models through the application of the dataset given.
Before conducting regression analysis, it is necessary to understand the assumptions. One of the assumptions is that the independent variable is not always random. Some other assumptions include the value of residuals is zero, the independent and dependent variables often show a linear relationship between the intercept and the slope, the value of residual is always constant across all the observations made; finally, the values of residual are not always correlated across different observations (Montgomery et al., 2021). Besides, the residual values often follow the normal distribution.
Regression analysis
From the information given, the dependent variable is hospital costs, while the independent variables include patient age, risk factors, and patient satisfaction scores. Both the independent and dependent variables are continuous.
Table 1: Descriptive Statistics  
Mean  Std. Deviation  N  
Cost

14906.51  2614.346  185 
Age

73.25  6.430  185 
risk  5.69  2.777  185 
satisfaction  50.02  28.919  185 
Table 1 indicates the descriptive statistics for both the dependent and independent variables. The means of variables, cost, age, risk, and satisfaction include $14906.51, 73.25 years, 5.69, and 50.02. The sample size used was 185.
Table 2: Correlations  
cost  age  risk  satisfaction  
Pearson Correlation  cost  1.000  .279  .199  .071 
age  .279  1.000  .152  .094  
risk  .199  .152  1.000  .037  
satisfaction  .071  .094  .037  1.000  
Sig. (1tailed)  cost  .  .000  .003  .169 
age  .000  .  .019  .101  
risk  .003  .019  .  .307  
satisfaction  .169  .101  .307  .  
N  cost  185  185  185  185 
age  185  185  185  185  
risk  185  185  185  185  
satisfaction  185  185  185  185 
Table 2 shows the correlation between dependent and independent variables. The outcomes show that there is a weak positive
correlation between the cost and age; the correlation coefficient is 0.279. The correlation between cost and risk is also weak and positive; the correlation coefficient is 0.199. Finally, the correlation between cost and the level of satisfaction is weak and negative; the correlation coefficient is .071.
Table 3: Model Summary  
Model  R  R Square  Adjusted R Square  Std. Error of the Estimate  Change Statistics  
R Square Change  F Change  df1  df2  Sig. F Change  
1  .336^{a}  .113  .098  2482.429  .113  7.692  3  181  .000 
a. Predictors: (Constant), satisfaction, risk, age 
From table 3, the RSquare is 0.113 showing a “Medium” effect size; therefore, the model attempt to explain much of the variance in the dependent variable. The significant value from the analysis is 0.000 < 0.05; therefore, we reject that null hypothesis and conclude that the model is fit or significant. Given that the analysis was done at 95% level of significance, the null hypothesis is rejected when the significant values obtained are less than 0.05.
Table 4: Coefficients^{a}  
Model  Unstandardized Coefficients  Standardized Coefficients  t  Sig.  95.0% Confidence Interval for B  
B  Std. Error  Beta  Lower Bound  Upper Bound  
1  (Constan)  6652.176  2096.818  3.173  .002  2514.825  10789.527  
age  107.036  28.911  .263  3.702  .000  49.990  164.082  
risk  153.557  66.685  .163  2.303  .022  21.978  285.136  
satisfaction  9.195  6.358  .102  1.446  .150  21.740  3.351  
a. Dependent Variable: cost 
From table 4, there is the indication of different unstandardized coefficients for the independent variables used in the study. A regression equation can therefore be formulated from the information given. Using the equation of a straight line, Y= Mx +C, at the Yintercept, x becomes 0. Therefore, the equation becomes, Y=M (0) + C, Y=C. From the table above, Y= 6652.176. To formulate a regression equation, there is the need for the analysis to consider the constant and unstandardized coefficients of the independent variables. The equation takes the form of a line equation which is Y= Mx + c,
Therefore, we find that:
Cost = 6652.176 + 107.036 (age) + 153.557 (risk) – 9.195 (satisfaction)
The above regression equation can be used to predict the costs given each of the independent variables. While determining the cost using each of the variables, we set all other independent variables to zero. The above equation shows that the cost depends on the age of the patients, risks factors, as well as the level of satisfaction of the patients after treatments.
Conclusion
Regression analysis can be applied to assess the strength of the correlation between variables and for modeling the future relationship that may be expected between independent and dependent variables. The analysis shows that the hospital costs are dependent on patient age, risk factors, and patient satisfaction scores. Both the independent and dependent variables are continuous.
References
Kumari, K., & Yadav, S. (2018). Linear regression analysis study. Journal of the practice of Cardiovascular Sciences, 4(1), 33. https://www.jpcs.org/article.asp?issn=23955414;year=2018;volume=4;issue=1;spage=33;epage=36;aulast=Kumari
Montgomery, D. C., Peck, E. A., & Vining, G. G. (2021). Introduction to linear regression analysis. John Wiley & Sons. http://sutlib2.sut.ac.th/sut_contents/H133678.pdf
Aggarwal, R., & Ranganathan, P. (2017). Common pitfalls in statistical analysis: Linear regression analysis. Perspectives in clinical research, 8(2), 100. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5384397/