Question

question #9
use the regression equation ( y = - 2.3 + 2.5x ) and the table below to calculate the residual when ( x = 7 ).

1.3
2.2
1.8
-2.5

Explanation:

Step1: Calculate the predicted value

Substitute \(x = 7\) into the regression equation \(y=-2.3 + 2.5x\).
\(y_{predicted}=-2.3+2.5\times7=-2.3 + 17.5=15.2\)

Step2: Find the actual value

From the table, when \(x = 7\), the actual value \(y_{actual}=17\)

Step3: Calculate the residual

The formula for residual is \(Residual=y_{actual}-y_{predicted}\)
\(Residual = 17-15.2 = 1.8\)

Answer:

1.8