# Simple Linear Regression, residual and observed value

"A simple linear regression model was fitted with an intercept equal to -17 and slope equal to 2.37. Calculate the value of the residual when X = 11 and the observed value of Y at that value of X is 12. Use 2 decimal places. "

Got this question from a lecturer in an exam and nobody got it emailed her after and she said all the info was in the question.

Is the residual not the error in the observed minus the predicted value, and if so how do you get it if we are not given an observed value to start with.

My guess is just the increase in Y of 2.37 from where when x=11 y=9.07 to when x=12 y=11.44

• "the observed value of $Y$ at that value of $X$ is $12$" -- it seems like you are indeed given the observed value – jld Apr 20 '17 at 21:36

The lecturer states that the observed value of Y is 12 (when X is 11).

• This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review – kjetil b halvorsen Apr 20 '17 at 22:10
• Please let the OP know why they were wrong to accept the answer so that they can better use Cross Validated in the future. – James Phillips Apr 20 '17 at 23:40

From the question we can see that the modeled relationship between Y and X is:

$Y = a + bX +u$, where a is the intercept, b is the slope coefficient, and u is the error.

This equation was estimated and the predicted values are:

$\hat{Y} = -17 + 2.37*X$

Residuals = $Y - \hat{Y}$

In this case:

Residual = 12 - (-17 + 2.37*(11)) = 29 - 26.07 = 2.93