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)

wherea,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

Coefficients for independent variables

Regression intercept $8,675 $3,157

Length of stay

Coefficient* Not significant 823

Standard error for the coefficient Not applicable 73

Number of complications

Coefficient 3,641 1,958

Standard error for the coefficient 1,274 485

Laparascopic

Coefficient Not applicable 921

Standard error for the coefficient Not applicable 390

R-squared0.270.59

*Note: All independent variables are significant at the level ofp= 0.05 (andt-value > 2) except for the length of stay variable in the nonlaparoscopic condition. Also, thet-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?

• Regression of nonlaparoscopic patients only
• Regression of all patients

2. Calculate thet-value for each of the independent variables.(Round your answers to 2 decimal places.)

Nonlaparoscopic All patient

Patient Only

Coefficients for independent Variables T-Value T-value

Regression Intercept $8675 $3157

lent if stay

Coefficient no significant 823

Standard error for Coefficient no applicable 73 ?

Number of complications

Coefficient 3641 1958

Standard error for Coefficient 1274. ? 485 ?

laparoscopic

Coefficient no applicable 921

Standard error for Coefficient no applicable 390 ?

R-squared 0.27 0.59