A set of data includes the point \( (7,-2) \) and has the regression equation \( y=-12.5 x+81.4 \). What is the residual for this point?

To find the residual for the point \( (7, -2) \) using the regression equation \( y = -12.5x + 81.4 \), we start by calculating the predicted \( y \) value when \( x = 7 \): \[ y = -12.5(7) + 81.4 = -87.5 + 81.4 = -6.1 \] Now, we find the residual by subtracting the predicted \( y \) value from the actual \( y \) value: \[ \text{Residual} = \text{Actual } y - \text{Predicted } y = -2 - (-6.1) = -2 + 6.1 = 4.1 \] Thus, the residual for the point \( (7, -2) \) is \( 4.1 \).