Question

A scatter plot is shown: A graph shows numbers from 0 to 10 on the x axis at increments of 1 and the numbers 0 to 15 on the y axis at increments of 1. The ordered pairs 0, 15 and 1, 10 and 2, 12 and 3, 13 and 4, 7 and 5, 8 and 6, 8 and 7, 4 and 8, 5 and 9, 3 and 10, 0 are shown on the graph Which two ordered pairs can be joined to draw the best line of best fit for this scatterplot? (0, 14) and (10, 14) (0, 14) and (10, 1) (0, 7) and (7, 0) (0, 7) and (3, 0)

Answer 1

The correct option is 2.

Explanation:

The given data points are (0, 15), (1, 10), (2, 12), (3, 13), (4, 7), (5, 8), (6, 8), (7, 4), (8, 5), (9, 3), (10,0).

The general linear regression model is

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

Using the graphing calculator, we get

a=-1.28181818..

b=14.1363636..

Put these values in equation (1).

`y=-1.28181818x+14.1363636`

At x=0,

`y=-1.28181818(0)+14.1363636=14.1363636\approx 14`

At x=10,

`y=-1.28181818(10)+14.1363636=1.3181818\approx 1`

It means the line of best fit passes through (0,14) and (10,1). Therefore the correct option is 2.