Exercise 8-40 Interpreting Regression Results [LO 8-3] Recent research into the cost of various medical procedures has shown the impact of certain complications encountered in surgery on the total cost of a patient's stay in the hospital. The researchers used regression analysis and found the following results: Total cost for patient = Constant, plus a* Length of stay (measured in days), plus b* Presence of one or more complications (= 1 if true, O if false), plus c* Use of a laparoscope (= 1 if true, O if false) where a, b, care coefficients of the regression model. The laparoscope is an instrument somewhat like a miniature telescope with a fiber optic system that brings light into the abdomen. It is about as big around as a fountain pen and twice as long. The following table shows additional regression results presented by the researchers in the study described above. There are two regressions. The right-hand column shows the results for all patients, including those treated with laparoscopic surgery. The left-hand column shows the results for the sample of patients who were treated without the laparoscopic surgery. Nonlaparoscopic Patients Only All Patients $ 8,463 $3,284 Not significant Not applicable 844 61 Coefficients for independent variables Regression intercept Length of stay Coefficient Standard error for the coefficient Number of complications Coefficient Standard error for the coefficient Laparascopic Coefficient Standard error for the coefficient R-squared 3,690 1,238 1,637 549 Not applicable Not applicable 0.14 937 370 0.55 "Note: All independent variables are significant at the level of p=0.05 (and t-value > 2) except for the length of stay variable in the nonlaparoscopic condition. Also, the t-value for each independent variable can be calculated by dividing the coefficient of the variable *Note: All independent variables are significant at the level of p= 0.05 (and t-value > 2) except for the length of stay variable in the nonlaparoscopic condition. Also, the t-value for each independent variable can be calculated by dividing the coefficient of the variable by the standard error for the coefficient of that variable. Required: 1. Which of the two regressions has the better reliability in estimating costs? O Regression of all patients O Regression of nonlaparoscopic patients only 2. Calculate the t-value for each of the independent variables. (Round your answers to 2 decimal places.) Nonlaparoscopic Patients Only All Patients t-value t-value $ 8,463 $ 3,284 844 Not significant Not applicable 61 Coefficients for Independent Variables Regression intercept Length of stay Coefficient Standard error for the coefficient Number of Complications Coefficient Standard error for the coefficient Laparascopic Coefficient Standard error for the coefficient R-squared 1,637 3,690 1,238 549 937 Not applicable Not applicable 0.14 370 0.55
