Question

Question 11 (1 point)

Cardiorespiratory fitness is widely recognized as a major component of overall physical well-being. Direct measurement of maximal oxygen uptake (VO2max) is the single best measure of such fitness, but direct measurement is time-consuming and expensive. It is therefore desirable to have a prediction equation for VO2max in terms of easily obtained quantities. A sample is taken and variables measured are age (years), time necessary to walk 1 mile (mins), and heart rate at the end of the walk (bpm) in addition to the VO2 max uptake. The equation from a multiple regression is (V02) = 0.093*(age) + 0.03*(HR) + 0.08*(time) + 1.832. If a person is 40 years old, has a heart rate of 137 bpm, and a walking time of 14 minutes, and a maximum oxygen intake of 17.359 L/min, what is the residual?

Question 11 options:

	1) -29.218
	2) 8.409
	3) -6.577
	4) We do not know the observations in the data set, so we cannot answer that question.
	5) 6.577

Question 12 (1 point)

Suppose that a researcher studying the weight of female college athletes wants to predict the weights based on height, measured in inches, the percentage of body fat of an athlete, and age. The researcher calculates the regression equation as (weight) = 3.617*(height) + 1.017*(percent body fat) - 0.811*(age) - 97.656. If a female athlete is 62 inches tall, has a 23 percentage of body fat, is 24 years old, and has a weight of 193.783, the residual is 63.258. Choose the correct interpretation of the residual.

Question 12 options:

	1) The height of the athlete is 63.258 inches larger than what we would expect.
	2) The weight of the athlete is 63.258 pounds larger than what we would expect.
	3) The height of the athlete is 63.258 inches less than what we would expect.
	4) The weight of the athlete is 63.258 pounds less than what we would expect.
	5) The weight of the athlete is 193.783 pounds larger than what we would expect.

Answer 1

Solution:

Question 11)

Given:

The equation from a multiple regression is

(V02) = 0.093*(age) + 0.03*(HR) + 0.08*(time) + 1.832.

If a person is 40 years old, has a heart rate of 137 bpm, and a walking time of 14 minutes, and a maximum oxygen intake of 17.359 L/min, what is the residual?

Thus find estimated value of (V02) by substituting the values in equation.

(V02) = 0.093*(age) + 0.03*(HR) + 0.08*(time) + 1.832.

(V02) = 0.093*(40) + 0.03*(137) + 0.08*(14) + 1.832

(V02) = 3.72 + 4.11 + 1.12 + 1.832

Residual is difference between actual (V02) and estimated (V02).

This

Thus correct option is: 5) 6.577

Question 12)

Given:

the regression equation as

(weight) = 3.617*(height) + 1.017*(percent body fat) - 0.811*(age) - 97.656.

If a female athlete is 62 inches tall, has a 23 percentage of body fat, is 24 years old, and has a weight of 193.783, the residual is 63.258.

We are given that: Residual = 63.258, this is positive ,thus actual weight value should be estimated weight.

thus correct option is:

2) The weight of the athlete is 63.258 pounds larger than what we would expect.