Question

The Metro is the subway rail service in Washington, D.C. and its immediate suburbs. When a rider uses the Metro, the subway fare (or cost of the ticket) is related to how far (distance) the person travels. For example, when a rider travels 10 miles, their fare is greater than if they only travel 7 miles. The further a rider travels from a given starting point, the more they must pay.

Data is shown in the scatterplot below, along with the LSR line.

What does the LSR line's slope of 0.28 estimate?

a. The predicted fare is 28 cents per mile.

b. The predicted fare increases $0.28 for each additional mile a person rides.

c. A Metro ride of 0 miles would have a fare of $0.28.

Answer 1

LSR is Least Squares Regression line.

It tells about the relationship between an independent variable x (no of miles a person rides) amd a depend variable (fare).

Equation for regression:

y = intercept + slope (x)

Intercept is like fixed initial fare and slop is the increase in fare per extra mile.

Hence b option is correct.

The predicted fare increases $0.28 for each additional mile a person rides.

For example if we take intercept as $1 and let's calculate fare for 5 miles.

y= 1+ 0.28 x 5 = $2.4

Now let's do the same for 6 miles.

y = 1 + 0.28 x 6 = $ 2.68

If we subtract the 2 values we can find the increase in fare for 1 mile increase im distance.

= $2.68 - $2.4 = $ 0.28 (which is actually equal to our slope)

That is why option b is correct.

If it helps kindly upvote.

Comment below for doubt