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,care coefficients of the regression model, and
?	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.

	Nonlaparoscopic Patients Only		All Patients
Coefficients for independent variables
Regression intercept		$8,318			$3,809
Length of stay
Coefficient*		Not significant			850
Standard error for the coefficient		Not applicable			83
Number of complications
Coefficient		3,914			1,955
Standard error for the coefficient		1,259			497
Laparascopic
Coefficient		Not applicable			920
Standard error for the coefficient		Not applicable			347
R-squared		0.23			0.53

*Note: All independent variables are significant at the level ofp= .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 and precision in estimating cost?
	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.)

Average Wages Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Average tax liability 41028 Mean 1772.9030703 Standard Error 41101 Median #N/A Mode 8864.5153515 Standard Deviation 78579632.417 Sample Variance -1.308490111 Kurtosis -0.131080672 Skewness 28227 Range 26873 Minimum 55100 Maximum 1025700 Sum 25 Count 8757.52 464.30866931 8973 #N/A 2321.5433466 5389563.51 -0.853636305 -0.114166729 8150 4952 13102 218938 25 WAGES 3545.806 equals 2 standard errors fr 41028 mean 37482.19 confidence interval starts a 44573.81 confidence interval ends a equals 2 standard errors from the mean confidence interval starts at confidence interval ends at SUMMARY OUTPUT Regression Statistics Multiple R 0.9701953506 R Square 0.9412790183 Adjusted R Square 0.9387259321 Standard Error 574.66553779 Observations 25 ANOVA df Regression Residual Total Intercept Average Wages SS MS F Significance F 1 121753993.192 121753993.19 368.6828249 1.17366E-015 23 7595531.04755 330240.48033 24 129349524.24 Coefficients Standard Error t Stat P-value Lower 95% -1667.126487 554.950850271 -3.004097545 0.006329142 -2815.129787 0.2540861482 0.0132328849 19.2011152 1.17366E-015 0.22671184 Upper 95% Lower 95.0% Upper 95.0% -519.1231871 -2815.129787 -519.1231871 0.2814604563 0.22671184 0.2814604563 Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Average Wages Average tax liability 26,873 4952 27,551 4998 29,146 5404 29,510 5682 30,464 5926 31,654 6371 32,865 6954 34,614 7506 36,418 8200 38,199 8973 40,449 9764 41,044 9071 41,101 8437 41,932 8103 43,800 8969 45,195 9876 46,996 10537 48,345 11001 49,763 10600 48,917 9639 49,545 10223 50,647 10604 52,577 11834 52,995 12212 55,100 13102 Average tax liability 14000 12000 10000 8000 6000 4000 2000 0 25,000 30,000 35,000 40,000 45,000 50 Average tax liability 5,000 40,000 45,000 50,000 55,000 60,000