Question

A hospital would like to develop a regression model to predict the total hospital bill for a patient based on his or her length of stay, number of days in the hospital's intensive care unit (ICU), and the age of the patient. The data for these variables are in the accompanying table. Complete parts a through d below. Click the icon to view the table of hospital stay data. a. Construct a regression model using all three independent variables. Let y be the total hospital bill, Xy be the age of the patient, xz be the length of the stay in days, and xz be the number of days in the ICU. + y = (( ) + ( )x + ( x + ( ) xa (Round to the nearest whole number as needed.)

B) Calculate coefficient of determination R^2

C)Find the value of the test statistic F=

P-value=

D)Calculate adjusted multiple coefficient of determination

R^2A=

Answer 1

In order to solve this question we use R software.

R codes and output:

> d=read.table('data.csv',header=T,sep=',')

> head(d)

Costs Age Days ICU

1 1436 18    2   0

2 1966 37    2   0

3 2862 28    4   0

4 3170 39    1   0

5 3630 25    2   0

6 3962 30    1   0

> attach(d)

> fit=lm(Costs~ Age+ Days+ICU)

> summary(fit)

Call:

lm(formula = Costs ~ Age + Days + ICU)

Residuals:

    Min      1Q Median      3Q     Max

-4242.5 -1653.0   -93.3   957.3 5427.9

Coefficients:

            Estimate Std. Error t value Pr(>|t|)

(Intercept) 2228.54    1885.45   1.182    0.250

Age            69.96      46.56   1.503    0.148

Days          695.70     326.41   2.131    0.045 *

ICU          1981.63    2833.08   0.699    0.492

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2684 on 21 degrees of freedom

Multiple R-squared: 0.3054, Adjusted R-squared: 0.2062

F-statistic: 3.078 on 3 and 21 DF, p-value: 0.04975

Que.a

y = 2229  +   70 X₁ + 696 X₂ + 1982 X₃

b.

Coefficient of determination = R² = 0.3054

c.

F = 3.078

p-value: 0.04975

d.

Adjusted R-squared: 0.2062