Question

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Data were collected on the distance a baseball will travel when hit by a baseball bat at a certain speed. The speed, s, is measured in miles per hour, and distance, y, is measured in yards. The regression line is given by ŷ = 4.17 + 52.45s.

Identify the slope and y-intercept of the regression line. Interpret each value in context.
The slope, b = 52.45, indicates that the distance increases by 52.45 yards for every one mile per hour of speed. The y-intercept, a = 4.17, is the distance estimated by this model if the speed is zero miles per hour.
The slope, b = 4.17, indicates that the distance increases by 4.17 yards for every one mile per hour of speed. The y-intercept, a = 52.45, is the distance estimated by this model if the speed is zero miles per hour.
The slope, b = 4.17, indicates that the distance decreases by 4.17 yards for every one mile per hour of speed. The y-intercept, a = 52.45, is the distance estimated by this model if the speed is one mile per hour.
The slope, b = 52.45, indicates that the distance decreases by 52.45 yards for every one mile per hour of speed. The y-intercept, a = 4.17, is the distance estimated by this model if the speed is one mile per hour.
The slope and y-intercept are unable to be determined from the regression line given.

Answer 1

B

Explanation:

The formula is y=mx+b. M is the slope while b is the y intercept. The y intercept is what y is when the x axis is 0. In this case 4.17 is the slope and 52.45s is the y intercept.

Answer 2

Given:

The speed, s, is measured in miles per hour, and distance, y, is measured in yards.

The regression line is given by

`\hat{Y}=4.17+52.45s` ...(i)

To find:

The slope and y-intercept of the regression line.

Solution:

The general form of linear regression line is

`y=a+bx` ...(ii)

where x is variable. In the given equation the variable is denoted by s.

On comparing (i) and (ii), we get

`a=4.17, b=52.45`

It means slope is 52.45 and y-intercept is 4.17.

The slope, b = 52.45, indicates that the distance increases by 52.45 yards for every one mile per hour of speed.

The y-intercept, a = 4.17, is the distance estimated by this model if the speed is zero miles per hour.

Therefore, the correct option is A.