Question

a set of data points has a line of best fit of $y = 2.5x - 1.5$. what is the residual for the point $(4,7)$? a. $8.5$ b. $-1.5$ c. $1.5$ d. $7$

Explanation:

Step1: Calculate the predicted value

Substitute \(x = 4\) into the line of best - fit equation \(y=2.5x - 1.5\).
\(y_{predicted}=2.5\times4-1.5\)
\(y_{predicted}=10 - 1.5\)
\(y_{predicted}=8.5\)

Step2: Calculate the residual

The formula for the residual is \(y_{residual}=y_{actual}-y_{predicted}\).
Given \(y_{actual} = 7\) and \(y_{predicted}=8.5\), then \(y_{residual}=7 - 8.5=-1.5\)

Answer:

B. - 1.5