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 ax Length of stay (measured in days), plus bx 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. Nonlaparoscopie Patients Only All Patients $ 8,043 $3,719 861 BO 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 Not significant Not applicable 3,393 1,239 1,986 406 Not applicable Not applicable 0.11 908 358 0.53 "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 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? R-squaluu U. V.35 "Note: All independent variables are significant at the level of p=0.05 (and -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 nonlaparoscopic patients only Regression of all patients 2. Calculate the t-value for each of the independent variables. (Round your answers to 2 decimal places.) nces Nonlaparoscopic Patients Only All Patients t-value t-value $ 8,043 $ 3.719 861 Not significant Not applicable 80 Coefficients for Independent Variables Regression intercept Length of stay Coefficient Standard error for the coefficient Number of Complications Coefficient Standard error for the coefficient Laparoscopic Coefficient Standard error for the coefficient R-squared 3,393 1.239 1,986 406 908 Not applicable Not applicable 0.11 0.53
