Question

you run a regression analysis on a bivariate set of data $(n = 91)$. with $\overline{x}=50.6$ and $\overline{y}=28.9$, you obtain the regression equation
$y=-2.596x + 20.208$
with a correlation coefficient of $r=-0.719$. you want to predict what value (on average) for the response variable will be obtained from a value of 40 as the explanatory variable.
what is the predicted response value?
$y =$
(report answer accurate to one decimal place.)

Explanation:

Step1: Substitute \(x = 40\) into the regression equation

Given the regression equation \(y=-2.596x + 20.208\), when \(x = 40\), we have \(y=-2.596\times40+20.208\).
First, calculate \(-2.596\times40=-103.84\).

Step2: Calculate the value of \(y\)

Then, \(y=-103.84 + 20.208=-83.632\).

Answer:

\(-83.6\)