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, 0 if false), plus c × Use of a laparoscope (= 1 if true, 0 if false) where a, b, c are 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 Coefficients for independent variables Regression intercept $8309 3783 Length of stay Coefficient* Not significant 703 Standard error for the coefficient Not applicable 71 Number of complications Coefficient 3321 1737 Standard error for the coefficient 1191 537 Laparascopic Coefficient Not applicable 911 Standard error for the coefficient Not applicable 361 R-squared 0.14 0.45 *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? multiple choice 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.)
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, 0 if false), plus
c × Use of a laparoscope (= 1 if true, 0 if false)
where a, b, c are 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 | |||||
| Coefficients for independent variables | ||||||
| Regression intercept | $8309 | 3783 | ||||
| Length of stay | ||||||
| Coefficient* | Not significant | 703 | ||||
| Standard error for the coefficient | Not applicable | 71 | ||||
| Number of complications | ||||||
| Coefficient | 3321 | 1737 | ||||
| Standard error for the coefficient | 1191 | 537 | ||||
| Laparascopic | ||||||
| Coefficient | Not applicable | 911 | ||||
| Standard error for the coefficient | Not applicable | 361 | ||||
| R-squared | 0.14 | 0.45 | ||||
*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?
multiple choice
-
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.)
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