Question

the equation for the line of best fit for a data set is ( y = 2x + 1.5 ). if the point ( (1, 4) ) is in the data set, what is the residual of 1?
0.5
3.5
4.0
7.5

Explanation:

Step1: Calculate the predicted value

Substitute \(x = 1\) into the line of best - fit equation \(y=2x + 1.5\).
\(y_{predicted}=2\times1+1.5=3.5\)

Step2: Calculate the residual

The formula for the residual is \(residual=y_{actual}-y_{predicted}\).
Given \(y_{actual} = 4\) and \(y_{predicted}=3.5\), then \(residual = 4 - 3.5\).
\(residual=0.5\)

Answer:

A. \(0.5\)