Question

1. The VA has collected the past month’s data from sixteen hospitals. The VA believed the selected hospitals were efficiently run. The objective is to derive a model based on the efficient hospitals to use to comparatively evaluate questionable hospitals. The data are: y = monthly labor spent x1 = monthly X-ray exposures x2 = monthly occupied bed days x3 = average number of days of a patient’s stay SUMMARY OUTPUT Regression Statistics Multiple R 0.9981 R Square 0.9961 Adjusted R2 0.9952 Standard Error 387.1598 Observations 16 ANOVA df SS MS

   		14896.25
   		15896.25
   		16009.25
   		16896.25
   		17986.25

1. The previous multiple regression model is significant to what level?

   		It is not significant
   		0.05
   		0.01
   		0.001
   		0.0000

1. In the VA prolem which is the most significant independent variable?

   		X-ray
   		BedDays
   		Length of stay

Answer 1

We use the below F test to test the significance of the regression model:-

Where is 0.9961

k= number of independent variables = 3

n= no. of observations = 16

F= 1021.641

p value for f(1021.641) for (k, (n-k-1) df is 1.03e^14

Hence the previous regression model is significant at 0.0000 level.

Anova table can be used to find the most significant independent variable as shown below:-

Variables	df	Sum of Squares	Mean sum of squares=Sum of squares/ df	P value
X1	1	14896.25	10.57957	0.006922659
X2	1	15896.25	11.28978	0.005673905
X3	1	16009.25	11.37004	0.005550172
Residual	12 which is n-k-1	1408.021

From the above three p values we see that, 0.00555 is the least and hence the most significant of all. Therefore Length of stay (average number of days of patient stay) is the most significant independent variable.