Question

Data from n = 113 hospitals in the United States are used to assess factors related to the likelihood that a hospital patients acquires an infection while hospitalized. The variables here are y = infection risk, x₁ = average length of patient stay, x₂ = average patient age, x₃ = measure of how many x-rays are given in the hospital. The Minitab output is as follows:

Regression Analysis: InfctRsk versus Stay, Age, Xray

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	3	73.099	24.366	20.70	0.000
Stay	1	31.684	31.684	26.92	0.000
Age	1	1.126	1.126	0.96	0.330
Xray	1	13.719	13.719	11.66	0.001
Error	109	128.281	1.177
Total	112	201.380

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
1.08484	36.30%	34.55%	30.64%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	1.00	1.31	0.76	0.448
Stay	0.3082	0.0594	5.19	0.000	1.23
Age	-0.0230	0.0235	-0.98	0.330	1.05
Xray	0.01966	0.00576	3.41	0.001	1.18

Regression Equation

InfctRsk

=

1.00 + 0.3082 Stay - 0.0230 Age + 0.01966 Xray

1. Set up the hypothesis test to decide whether there is a connection between the infection risk and the group of predictors.
2. Then, decide, using tests, which of the predictors and constant should be in the final relationship.
3. Give the value of the coefficient of determination and tell what it means.

Answer 1

Answer The hypothesis test (interpretation) is given as under Connection between the infection risk and group of predictors is as follows The value of P-value for Stay and x-rays are at significant level i.e. 0.000 and 0.001 respectively. But P-value for Age is 0.330 which is not good for rejecting the null hypothesis Ho:B2 = 0 thus variable Age is not useful predictor within the model, and both variables stay and x-rays are useful for prediction of infection risk. For constant the p-value is not significant to model as it is representing intercept only Thus stay and x-rays are the predictors that should be in final relationship The coefficient of determination value of R2 36.30% means that model explains the 36.30% of the observed variation in Infection risk.