In order to adjust for gender, height and age, multiple regression was used to b

ID: 3226663 • Letter: I

Question

In order to adjust for gender, height and age, multiple regression was used to build a second model. The output from this multivariate model is given below. Based on this model:

a. What percentage of the variability in cholesterol is explained by its linear relationship with age, gender, height and weight?

b. What is the predicted difference in cholesterol between two men who are one pound different in weight, but the same height and age?

c. Does weight significantly (at alpha=.05) predict cholesterol, after adjusting for gender, height and age?

d. Compare you answers to parts (b) and (c) on this question to parts (b) and (e) on question 5. Do you draw the same conclusions about the effect of weight when you adjust for other covariates as when you do not? (Yes or No) How do you interpret this?

e. What is the predicted cholesterol of a 60 year old woman who weighs 140 lbs. and is 5'9" (69")?

f. Looking at the regression plot, do you see any reason to be concerned about the validity of your model? If yes, describe.

> summary(lm(Cholesterol~., temp))

Call:
lm(formula = Cholesterol ~ ., data = temp)

Coefficients Estimate Std. error t-value Pr(>|t|) (Intercept)

         -69.740

62.008 -1.12 0.26355 Age 1.651 0.379 4.36 3.3e-05 Female -7.975 7.934 -1.01 0.31739 Weight -0.318 0.119 -2.68 0.00858 Height 3.168 0.886 3.58 0.00055

Explanation / Answer

a. 27.1% of variability in cholestrol is explained by the linear model.

b. There will be predicted difference of 0.318 units in cholesterol between two men who are one pound different in weight, but the same height and age. More the weight less the cholestrol (although counter-intuitive; may be some other effect)

c. Yes, since p-value for weight<0.05.

d. [question 5 not mentioned]

e.cholestrol= 195.42 (i.e. =-69.74+1.651*60-7.975*1 - .318*140+3.168*69)

f. F-value< 0.05 indicating regression is significant.

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In order to adjust for gender, height and age, multiple regression was used to b

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