apture Pro Question 4 The cost of treating individual surgical patients in hospital varies widely. The cost is believed to depend to some extent on the length of time that the patient stays in hospital and the seriousness of the operation they undergo. Data has been collected on the cost of treating 200 such patients and is summarised at the end of the question in the form of descriptive statistics, produced using SPSS. The cost of hospital treatment (in Es) has been regressed separately against their length of stay (in days) and against their operation duration (in minutes) using SPSS, with the results shown in the following pages under the headings MODEL 1 and MODEL 2 respectively. (a) Which of these models show evidence of a significant linear relationship between treatment cost and the explanatory variable? Justify your answer. Express any significant relationship(s) in words. (5 marks) (b) On the basis of the output provided, comment on the apparent quality of the two models. (4 marks) (c) The results of using SPSS to predict the cost of treating a patient who stays in hospital for 4 days and has an operation duration of 55 minutes for the two models are shown below. Cost (8) Prediction LMCI UMCI LICI UIC MODEL 1 1042.97333 1022.35681 1063.58985 797.36504 1288.58161 MODEL 2 1246.70921 1220.05476 1273.36367 879.59543 1613.82299 Use your preferred model to advise the hospital management on the likely cost of an average patient with these characteristics, and of an individual patient with these characteristics. Comment on the level of accuracy of your predictions. (5 marks) (d) Assuming that the model implied by your preferred regression is appropriate, sketch a diagram showing how the data would be spread in comparison to the regression line. Indicate the correct scales on your diagram, as far as possible. (7 marks) (e) Explain in terms of the diagram you created in part (d) of this question what you would expect to see that would indicate that the errors in the model did not obey the regression assumption concerning constant variance. (4 marks)ture Pro Descriptive Statistics N Minimum Maximum Mear Std. Deviation Length_Stay 200 1.00 2.00 5.3500 2.09030 Op Dur 200 9.51 144.29 61.1986 25.39098 Cost 200 441.80 3126.40 1362.8520 510.52680 Valid N (listwise) 200 MODEL 1 (Length of Stay) Model Summary Adjusted R Std. Error of Model R R Square Square the Estimate 970(a) 941 941 24.10715 a Predictors: (Constant), Length_Stay ANOVA(b) Model Sum of Squares df Mean Square F Sig Regression 18817172.367 48817172.367 3169.414 000(a) Residual 3049711.892 198 15402.585 Total 51866884.259 199 a Predictors: (Constant), Length Stay b Dependent Variable: Cost Coefficients(a) Unstandardized Standardized Coefficients Coefficients Sig. Model B Std. Error Beta Std. Error Constant) 95.185 24.167 3.939 .000 Length Stay 236.947 4.209 970 56.298 000 a Dependent Variable: CostApowersoft Screen Capture Pro MODEL 2 (Operation Duration) Model Summary Adjusted R Std. Error of Model R R Square Square the Estimate 932(a) 868 868 85.67020 a Predictors: (Constant), Op_Dur ANOVA(b) Model Sum of Squares df Mean Square F Sig Regression 45041 146.688 45041 146.688 1306.547 .000(a) Residual 6825737.571 198 34473.422 Total 51866884.259 199 a Predictors: (Constant), Op Dur b Dependent Variable: Cost Coefficients(a) Unstandardized Standardized Coefficients Coefficients # Sig. Model B Std. Error Beta Std. Error (Constant) 216.178 34.333 6.297 000 Op Dur 18.737 518 932 36.146 000 a Dependent Variable: Cost