Question

The CFO of the hospital ABC wants to predict the toud endiges UJUM of stay for the patients. The sample data for 5 randomly selected patients are given below. (000) Length of Charges Stay EXY - NXY EX-nX 22 6 Table 2 16. = 7 -6,X| Y 18 Observati 26 (a) Using the method of least squares, determine the equation for the estimated regression line Y-b+b, X (b) State the meaning of slope b, in this regression line.le, what does b, tell? (c) What is the regression prediction of the charge for a patient who stayed in the hospital for 5 days? (d) If you used the sample average charge as the estimate for the hospital charges for each patient, what would be the total squared errors for these 5 observations (SST)? (e) If you use regression prediction values as your estimate for the charges, what would be the (unexplained) squared errors (SSE)? (1) How much of the total variation is explained by the regression (SSR)? (8) What percentage of the total (squared) errors was explained by the the length of stay? Table 3 (h) Part of the regression output for this problem is given in Table 3. Regression Statistics Construct approximate 95 percent confidence interval for the R Square average charges for patients who stayed in the hospital 5 days (LOS 5). Standard Error 0.000 Question 6 (5.0 pts) A 10-year study by the World Heart Association (WHA) provided data on how age, blood pressure, smoking college degree, and citizenship relate to the risk of strokes The data in Table 3 (on page 3) are from a portion of this study, Risk is interpreted as the probability (times 100) that the person will have a stroke over the next 10 year period The estimated regression output to predict the risk of stroke by using person's age (X) and blood pressure (X2) is given in Exhibit A. (on page 4 of exam) Use 3 decimals in your answers. (a) What is the estimated regression equation? Y = b + b X, + b X2 (b) What is the interpretation of b, in this regression equation? What does it tell? (c) What is the probability of a stroke over 10 years for Adam Brown, a 68-vear old with a blood pressure of 2007 (d) What percentage of the total squared error in the risk of strokes is explained by this regression? (e) is blood pressure (X) a significant factor or not in the risk of a stroke? Why? Use a = 0.05. Question 7 (5.0 pts) The estimated regression output to predict the risk of stroke by using person's age (X). blood pressure (X), smoke (X), and college degree (X) is given in Exhibit B. (Page 4) Note:X, 1 if the person is a smoker and X=1 if the person has a college degree. (a) What is the estimated regression equation? Y=b+b.X. +b,X,.b,X,+bX (b) What is the interpretation of b, in this regression equation? i.e., what does it tell? (d) What is the interpretation of b, in this regression equation? i.e., what does it tell? d) What percentage of the total squared error in the risk of strokes is explained by this regression? (e) is smoke (X,) a significant factor or not in predicting the risk of a stroke? Why? Use a 0.05. Is college degree (X.) a significant factor or not in the risk of a stroke? Why? Use a = 0.05. What is the prediction for the probability of a stroke over 10 years for Adam Brown, a 68-year old smoker who has a blood pressure of 200 and has a college degree?

Answer 1

Que.5

In order to solve this question I used R software.

R codes and output:

> y=c(18,22,20,24,26)
> x=c(4,6,5,7,8)
> fit=lm(y~x)
> summary(fit)

Call:
lm(formula = y ~ x)

Residuals:
1 2 3 4 5
-1.050e-15 3.345e-16 1.228e-15 -1.524e-16 -3.599e-16

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.000e+01 1.909e-15 5.24e+15 <2e-16 ***
x 2.000e+00 3.096e-16 6.46e+15 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9.79e-16 on 3 degrees of freedom
Multiple R-squared: 1, Adjusted R-squared: 1
F-statistic: 4.173e+31 on 1 and 3 DF, p-value: < 2.2e-16

Warning message:
In summary.lm(fit) : essentially perfect fit: summary may be unreliable
> anova(fit)
Analysis of Variance Table

Response: y
Df Sum Sq Mean Sq F value Pr(>F)
x 1 40 40 4.1731e+31 < 2.2e-16 ***
Residuals 3 0 0   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Warning message:
In anova.lm(fit) :
ANOVA F-tests on an essentially perfect fit are unreliable
>

a.

Least square regression equation is,

Y = 1 + 2X

b.

Meaning of slope:

If X is increase (or decrease ) by 1 day then Y also increase (or decrease) by 2 units.

c.

When X = 5 Days, charge Y is

Y = 1 + 2X

= 1 + 2 * 5

= 11

d. From ANOVA output,

SST = 40

e.

SSE = 0

f.

SSR = 40

g.

100% of total (squared) errors was explained by the length of stay .