The Fat data
The Fat data contains the age, weight, height, and ten body circumf
The Fat data
The Fat data contains the age, weight, height, and ten body circumference measurements for 252 men. Each man’s percentage of body fat was accurately estimated by an underwater weighing technique.
The data frame 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 access the data using the following statement: data(fat, package = “faraway”)
Question 1
Fit a regression model with the brozek variable (percent of body fat) as a response and the following six predictors: age, neck, abdom, thigh, forearm and wrist.
Show the summary. Which predictors are significant at the 0.05 level?
Question 2
Provide interpretation to the coefficient of each significant predictor
Hints:
Hints: See Lesson 3, Slide 49 and Slide 58.
Question 3
Compute the median value of the six predictors. Store the medians in a variable named x0 and show the values .
Hint: See Lesson 4, Slide 18.
Question 4
Construct a confidence interval of the mean response based on the median values that you stored in x0.
Hint: See Lesson 4, Slide 20.
Question 5
Construct a prediction interval of the next response value based on the median values that you stored in x0.
Hint: See Lesson 4, Slide 20.
Question 6
Which of the two intervals is wider?
Question 7
Construct a confidence interval of the outcome variable for a person with the following characteristics:
Age: 49 years
Neck: circumference: 40 cm
Abdomen: circumference: 95 cm
thigh: circumference: 60 cm
forearm: circumference: 31 cm
wrist circumference: 19.5 cm
Hints:
You can store the predictor values in a new variable named x1. Here is an example of such a variable:
x1 <- c("(Intercept)" = 1, age = 25, neck =34, abdom = 84, forearm = 25, wrist = 25)
Note that the intercept should be 1, but you will need to update the values of the predictors.