Please help me answer these question according to the slides provided.

Please help me answer these question according to the slides provided. Thank you!

PThe Fat Data

The fat data contains the age, weight, height, and ten body circumference measurements for 252 men. An underwater weighing technique accurately estimated each man’s body fat percentage.

The data contains the following variables:

brozek: Percent of body fat using Brozek’s equation, 457/Density – 414.2

siri: Percent body fat using Siri’s equation, 495/Density – 450/ density: Density (gm/cm3)

age: Age (yrs)

weight: Weight (lbs)

height: Height (inches)

adipos: Adiposity index = Weight/Height2 (kg/m2)

free: Fat Free Weight = (1 – fraction of body fat) * Weight, using Brozek’s formula (lbs)

neck: Neck circumference (cm)

chest: Chest circumference (cm)

abdom: Abdomen circumference (cm) at the umbilicus and level with the iliac crest hip: Hip circumference (cm)

thigh: Thigh circumference (cm)

knee: Knee circumference (cm)

ankle: Ankle circumference (cm)

biceps: Extended biceps circumference (cm)

forearm: Forearm circumference (cm)

wrist: Wrist circumference (cm) distal to the styloid processes

You can assess the data using the following statement: data(fat, package = “faraway”)

Question 1

Create a new data frame that contains the following subset of variables:

brozek, age, weight, height, neck, chest, abdom, knee, ankle, forearm, and wrist.

Make sure to use the new data frame in all questions below.

Hint: In the following example, we select two variables (agegp and alcgp) from the esoph data frame and name the new data frame esophSubDf

esophSubDf <- esoph[c(“agegp”, “alcgp”)]

Question 2

Fit a regression model with the brozek variable (percent of body fat) as a response and the rest of the variables as predictors. Show the model summary.

Question 3

Calculate pairwise correlations between the predictors (correlation matrix).

Hint: See Lesson 7, Slide 31.

Question 4

Evaluate the collinearity by calculating the condition numbers of the eigenvalues.

Are there any condition numbers above 30?

Hint: See Lesson 7, Slide 33.

Question 5

Calculate the variance inflation factor for each predictor. Which inflation factors are greater than 10?

Hint: Go to Lesson 7. Slide 35.

Question 6

Fit a model with brozek as the response and age, weight, and height as predictors.

Show the summary.

Question 7

Evaluate the collinearity by calculating the condition numbers of the eigenvalues. Are there any condition numbers above 30?

Question 8

Calculate the variance inflation factor for each predictor. Which inflation factors are greater than 10?