Question

some residuals for a scatterplot are given. for ( x = 3 ), the residual is ( -5 ). for ( x = 5 ), the residual is ( -1 ). for ( x = 7 ), the residual is ( 3 ). for ( x = 9 ), the residual is ( 0 ). for which value of ( x ) is the data point farthest from the line of best fit? 3 5 7 9

Explanation:

Step1: Recall the definition of residual

The residual is the vertical distance between a data point and the line of best fit. The magnitude of the residual gives the distance.

Step2: Calculate the magnitudes of the residuals

For \(x = 3\), the residual is \(- 5\), and its magnitude is \(| - 5|=5\).
For \(x = 5\), the residual is \(-1\), and its magnitude is \(|-1| = 1\).
For \(x = 7\), the residual is \(3\), and its magnitude is \(|3|=3\).
For \(x = 9\), the residual is \(0\), and its magnitude is \(|0| = 0\).

Answer:

3