Question

You will be using your Framingham dataset for the following questions.

7. Calculate a multivariable regression where the outcome is total serum cholesterol and the independent variables are BMI, age, sex and smoking status. Interpret.

8. Use the regression from question 7 to answer the following.

a. What is the predicted total serum cholesterol for a 50 year-old man who doesn’t smoke and whose BMI is 25?

b. What is the predicted total serum cholesterol for a 25 year-old woman who smokes and whose BMI is 32?

Answer 1

I have coded in R for the first part. The code is as follows:

> library(swgee)
> attach(framingham)
The following objects are masked from framingham (pos = 3):

age, bmi, BPVar, cigpday, cursmoke, female, glucose, heartrte,
outcome, time_outcome, totchol

The following objects are masked from framingham (pos = 4):

age, bmi, BPVar, cigpday, cursmoke, female, glucose, heartrte,
outcome, time_outcome, totchol

The following objects are masked from framingham (pos = 5):

age, bmi, BPVar, cigpday, cursmoke, female, glucose, heartrte,
outcome, time_outcome, totchol

The following objects are masked from framingham (pos = 6):

age, bmi, BPVar, cigpday, cursmoke, female, glucose, heartrte,
outcome, time_outcome, totchol

The following objects are masked from framingham (pos = 7):

age, bmi, BPVar, cigpday, cursmoke, female, glucose, heartrte,
outcome, time_outcome, totchol

The following objects are masked from framingham (pos = 8):

age, bmi, BPVar, cigpday, cursmoke, female, glucose, heartrte,
outcome, time_outcome, totchol

The following objects are masked from framingham (pos = 9):

age, bmi, BPVar, cigpday, cursmoke, female, glucose, heartrte,
outcome, time_outcome, totchol

The following objects are masked from framingham (pos = 10):

age, bmi, BPVar, cigpday, cursmoke, female, glucose, heartrte,
outcome, time_outcome, totchol

> data=framingham
> LinMod=lm(totchol~bmi+age+female+cursmoke,data)
> summary(LinMod)

Call:
lm(formula = totchol ~ bmi + age + female + cursmoke, data = data)

Residuals:
Min 1Q Median 3Q Max
-112.139 -27.323 -3.522 24.073 244.440

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 116.6729 8.4932 13.737 < 2e-16 ***
bmi 1.4556 0.2544 5.721 1.2e-08 ***
age 1.5196 0.1048 14.502 < 2e-16 ***
female 5.7306 1.7463 3.281 0.00105 **
cursmoke 4.3192 1.7528 2.464 0.01381 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 40.04 on 2311 degrees of freedom
Multiple R-squared: 0.09854, Adjusted R-squared: 0.09698
F-statistic: 63.15 on 4 and 2311 DF, p-value: < 2.2e-16

> LinMod

Call:
lm(formula = totchol ~ bmi + age + female + cursmoke, data = data)

Coefficients:
(Intercept) bmi age female cursmoke
116.673 1.456 1.520 5.731 4.319

Thus, the linear model is:
totchol =   116.673 +1.456*bmi+1.520*age+5.731*female+4.319*cursmoke

Now, the given values are:

	bmi	age	female	cursmoke
sample1	25	50	1	0
sample2	32	25	1	1

Thus, the first prediction is:

totchol =   116.673 +1.456*25+1.520*50+5.731*1+4.319*0
= 234.804

The second prediction is:
totchol =   116.673 +1.456*32+1.520*25+5.731*1+4.319*1
= 211.315

PS. If you do find the dataset under swgee, it will be under LocalControl

I hope this clarifies your doubt. If you're satisfied with the solution, hit the Like button. For further clarification, comment below. Thank You. :)