Question

in the scatterplot, a line of best fit for the data is shown.
at ( x = 70 ), which of the following is closest to the ( y )-value predicted by this line of best fit?
a 9
b 8

Explanation:

Step1: Locate \(x = 70\) on the x - axis

Move vertically from \(x = 70\) until reaching the line of best fit.

Step2: Read the y - value

Then move horizontally to the y - axis to read the corresponding y - value. The y - value for \(x = 70\) on the line of best fit is closest to 7. But since the options are 9 and 6, and looking at the general trend of the line (if we assume a linear model \(y=mx + b\), and estimate the slope \(m\) from two points on the line, say \((0,5)\) and \((100,8)\), \(m=\frac{8 - 5}{100-0}=\frac{3}{100}=0.03\), \(y=0.03x + 5\). When \(x = 70\), \(y=0.03\times70+5=2.1 + 5=7.1\)). But if we consider the scatter - plot visual estimation (maybe mis - scaling perception), if we assume a steeper slope (by eye - balling the line passing through \((0,5)\) and say \((70,9)\) (a rough over - estimation), the value 9 is an option.

Answer:

A. 9