The total expenses of a hospital are related to many factors. Two of these factors are...

The total expenses of a hospital are related to many factors. Two of these factors are the number of beds in the hospital and the number of admissions. Data were collected on 14 hospitals, as shown in the following table:Find the best regression model to predict the total expenses of a hospital. Discuss the accuracy of this model. Should both variables be included in the model? Why or why not?

Hospital	# Beds	Admissx1000	Total Exp x$1mil
1	120	77	57
2	336	160	127
3	310	230	157
4	55	33	24
5	30	19	14
6	190	155	93
7	110	53	45
8	40	6	6
9	210	159	99
10	25	18	12

Expert Solution

Regression Statistics
Multiple R	0.997641
R Square	0.995288
Adjusted R Square	0.993942
Standard Error	4.12342
Observations	10

ANOVA
	df	SS	MS	F	Significance F
Regression	2	25139.38	12569.69	739.2809	7.18E-09
Residual	7	119.0181	17.00259
Total	9	25258.4

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-0.62223	2.149332	-0.2895	0.780585	-5.70459	4.46013	-5.70459	4.46013
X Variable 1	0.1953	0.035172	5.552634	0.000858	0.11213	0.27847	0.11213	0.27847
X Variable 2	0.3975	0.051374	7.737414	0.000113	0.27602	0.518979	0.27602	0.518979

Total expenses=-0.62223+0.1953 beds+0.3975 admission

Here R2=0.99 i.e. 99% .The model is 99% good fit. The 99% variation in the total expenses explained by the regressors.

For bed p-value is 0.000858 <0.05 and for admission 0.000113<0.05.

Therefore number of bed and number of admission both are contributing significantly. So both variables should included in the model.

orchestra answered 2 years ago

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