Question

The equation of the linear regression line represents the relationship between the body weight of a sample of land mammals in kilograms, x, and their brain weight in grams, y. yˆ=213/100x+0.68 What does the slope of the line represent? 

A. For every 100 kg of body weight, the brain weight decreases by 213 g.



B. For every 213 kg of body weight, the brain weight decreases by 100 g.

C. For every 100 kg of body weight, the brain weight increases by 213 g.

D. For every 213 kg of body weight, the brain weight increases by 100 g.

Answer 1

C. For every 100 kg of body weight, the brain weight increases by 213 g.

Explanation:

To answer this question we must analyze the slope formula.

The formula for the slope of a line is:

`m = (y_2-y_1)/(x_2-x_1)`

Where m is the Slope of the line

The slope of the line represents the rate of change of the equation. If the slope is m = 3, then:

`3 = (y_2-y_1)/(x_2-x_1)`

`3(x_2-x_1) = y_2-y_1`

This means that when x increases 1, y increases 3.

For the studied case
`m = (213)/(100)`

`(213)/(100) = (y_2-y_1)/(x_2-x_1)`

`(213)/(100)(x_2-x_1) = y_2-y_1`

This means that when x (the body weight) increases by a value of 100, y (the brain weight) increases by a value of 213.

Therefore the correct answer is option C