Recent research into the cost of various medical procedures has shown the impact
ID: 3178446 • Letter: R
Question
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:
The laparoscope is an instrument somewhat like a miniature telescope with a fiber optic system which 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, and the related costs.
*Note: All independent variables are significant at the level of p = .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.
Regression of all patients
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:
2. Calculate the t-value for each of the independent variables. (Round your answers to 2 decimal places.) Nonlaparoscopic All Patients Patients Only Coefficients for Independent Variables t-value 8,676 3,158 Regression intercept Length of stay 822 Coefficient Not significant Standard error for the coefficient 73 Not applicable Number of complications 3,661 1,978 Coefficient Standard error for the coefficient 485 1,274 Laparascopic Not applicable 971 Coefficient Standard error for the coefficient 390 Not applicable R-squared 0.27 0.59 t-valueExplanation / Answer
1. Regression of all patients have better reliability and precision in estimating the cost because the R-squared is higher in 'regression for all patients' as this value indicates that percent of variance in the dependent variable that can be explained by the independent variable.
2. The t-vlaue for independent variables are as follows:
For Non-laproscopic patients
a. Number of complications - t-value= 3661/1274 = 2.87
For all patients
a. Length of stay - t-value = 822/73 = 11.26
b. Number of complications - t-value= 1978/485 = 4.08
c. Laproscopic - t-value = 971/390 = 2.49
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