The scatterplot shows the lean body mass and metabolic rate for a sample of = adults. For each person, the lean body mass is the subject’s total weight in kilograms less any weight due to fat. The metabolic rate is the number of calories burned in a 24-hour period.

Because a person with no lean body mass should burn no calories, it makes sense to model the relationship with a direct variation function in the form y = kx. Models were tried using different values of k (k = 25, k = 26, etc.) and the sum of squared residuals (SSR) was calculated for each value of k. Here is a scatterplot showing the relationship between SSR and k:

According to the scatterplot, what is the ideal value of k to use for predicting metabolic rate?

a. 24

b. 25

c. 29

d. 31

e. 36

Step by step solution

01

Given information

02

Explanation

The $SSR$ is smallest when $k=31$ as shown in the scatterplot illustrating the relationship between SSR and $k$ because the lowest point in the scatterplot corresponds to $k=31$ Because $k=31$ is the least squares direct variation regression line between x and y, it minimizes the sum of the squares residuals, we should utilize it to make predictions when applying the model.

Thus, option (d) is the correct option.

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