Question

the data shown has a least squares regression line of ( y = -1.5x + 34.3 ).
use the drop - down menus to complete the statements and identify the residual of the
data point ( (4,36) )
point ( (4,36) ) is the least squares regression line.
the value of the least squares regression line at ( x = 4 ) is
so, the residual of the data point ( (4,36) ) is

Explanation:

Step1: Find the predicted value at \(x = 4\)

Substitute \(x = 4\) into the regression line equation \(y=-1.5x + 34.3\).
\(y=-1.5\times4+34.3\)
\(y=-6 + 34.3\)
\(y = 28.3\)

Step2: Calculate the residual

The formula for the residual \(e=y_{actual}-y_{predicted}\).
Given \(y_{actual}=36\) and \(y_{predicted}=28.3\)
\(e=36 - 28.3\)
\(e = 7.7\)

Answer:

Point \((4,36)\) is above the least - squares regression line.
The value of the least - squares regression line at \(x = 4\) is \(28.3\).
So, the residual of the data point \((4,36)\) is \(7.7\).