to explore this relationship in women, a nutritionist randomly selected 60 women

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1. (40 points) A person’s muscle mass is expected to decrease with age. To explore

this relationship in women, a nutritionist randomly selected 60 women (15 women

from each 10-year age group, beginning with age 40 and ending with age 79). Let

X be age, and Y a measure of muscle mass. The data “muscle.csv”(the 1st

column includes Y and the 2nd for X) can be found on Canvas.

(a) (5 points) Draw a scatter plot of Y vs. X. Comment on the relationship

between Y and X in a sentence or two.

(b) Is there a linear association between Y and X?

i. (3 points) Please justify your answer with the estimate of correlation

coefficient, and assess it for significance by providing 95% confidence

interval.

ii. (2 points) Summarize the result in a sentence or two.

(c) (5 points) Fit the following model using PROC REG,

Yi = β0 + β1Xi + i

, i ∼ N(0, σ2

).

Provide bβ1,

bβ0, Var( bβ1), Var( bβ0), and σb

2

.

(d) (6 points) Give interpretations for bβ0 and bβ1 you obtained in (c), and provide

95% confidence intervals for β0 and β1, respectively.

1

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