Question

5 multiple choice 1.25 points the least-squares regression line for some data is given to be \\( \hat{y} = 2.5x - 3.7 \\) find the residual for the data point \\( x = -3 \\) and \\( y = -8 \\). \\( -3.2 \\) \\( -11.8 \\) \\( 3.2 \\) \\( -19.2 \\)

Explanation:

Step1: Calculate predicted y

Substitute \(x = -3\) into \(\hat{y} = 2.5x - 3.7\):
\(\hat{y} = 2.5(-3) - 3.7 = -7.5 - 3.7 = -11.2\)

Step2: Compute residual

Residual = \(y - \hat{y}\):
Residual = \(-8 - (-11.2) = 3.2\)

Answer:

3.2