REGRESSION ANALYSIS

An analyst at Blue Cross/Blue Shield wants to estimate the linear relationship between the number of days of hospitalization a patient would require and the total medical cost actually incurred.Results of the analysis are to be used for predicting medical costs based on a physician's preliminary report.The analyst envisages that the relationship can be modeled as:

COST=b+b(DAYS)+e

A random sample of 11 accounts reveals the following set of data:

DAYS 562714

COST$2,535$3,090$1,704$3,864$981$2,898

DAYS 83259

COST $5,280$1,740$2,316$3,597$4,460

COMPUTER OUTPUT - RESULTS

Hospitalization Days Vs Cost

REGRESSION FUNCTION & ANOVA FOR COST

COST=782.184+460.788 DAYS

R-Squared= 0.863568

Adjusted R-Squared= 0.848409

Standard error of estimate= 504.1076

Number of cases used= 11

Analysis of Variance

(p-value)

SourceSSdfMSF ValueSig Prob

Regression1.44767E+0711.44767E+0756.967130.000035

Residual2.28712E+069254124.50000

Total1.67639E+0710

Hospitalization Days Vs Cost

REGRESSION COEFFICIENTS FOR COST

Two-Sided

(p-value)

VariableCoefficientStd Errort ValueSig Prob

Constant782.18400326.180102.398010.040028

DAYS460.7880061.050477.547660.000035 *

Standard error of estimate=504.1076

Durbin-Watson statistic=1.843576

Use the computer output to respond to the following questions:

(a)What sort of relationship exists between the number of days of hospitalization and the cost of hospitalization?Does this relationship make sense to you, why or why not?

(b)The model assumed is: COST= b+b(DAYS) + e.What are the estimated values for coefficients bandb?What do these coefficients represent?

(c)What are the estimated costs for a (i) one week (7 days) hospitalization, (ii) two weeks (14 days) hospitalization?