Question

The equation of the linear regression line represents the relationship between the score a student earned on an aptitude test, x, and their final score in a statistics class, y. yˆ=1625x+24.9 What does the slope of the line represent? For every 16 points earned on the aptitude test, the student earned 25 fewer points in the statistics class. A For every 25 points earned on the aptitude test, the student earned 16 additional points in the statistics class. B For

C every 16 points earned on the aptitude test, the student earned 25 additional points in the statistics class. D For every 25 points earned on the aptitude test, the student earned 16 fewer points in the statistics class.

Answer 1

The correct option is B. For every 25 points earned on the aptitude test, the student earned 16 additional points in the statistics class.

Explanation:

The point slope form of a line is

`y=mx+b` .... (1)

where, m is the slope and b is y-intersect.

The given equation of the linear regression is

`\hat{y}=(16)/(25)x+24.9` .... (2)

where, x is the score a student earned on an aptitude test and y is their final score in a statistics class.

On comparing (1) and (2), we get

`m=(16)/(25),b=24.9`

It means the slope of the line is
`(16)/(25)`. It represents for every 25 points earned on the aptitude test, the student earned 16 additional points in the statistics class.

Therefore, the correct option is B.

Answer 2

For this case, the equation of the line is given by:
y = (16/25) x + 24.9
We observed that:
The slope of the line is given by:
m = 16/25
Therefore, we have:
For every 25 points in the attitude test, the student earns 16 additional points in the statistics class.
Answer:
For every 25 points earned on the aptitude test, the student earned 16 additional points in the statistics class.