Question

1. The question asks to choose a data point in our graph (we chose 476,44) of median home prices (x) and percentage of students who scored Advanced on math MCAS (y).
We have to find the residual. I'm confused because the equation I was given is e=y-yhat
I know one is the expected value and one is what we got.
What do I plug in for y and what do I plug in for yhat?
The value of Rsquared is .72 on the calculator and if you square it it's .5184. Do I need to do anything with Rsquared or is that not involved in the residual?
2. Explain what residual measures?

Answer 1

For 1):
Y(hat) comes from substituting an x value into a regression equation and solving for y(hat). Y(hat) is also called the predicted y value in a regression equation.

Let's use an example. Suppose the regression equation is this:
y(hat) = 2.75 + .5x

If x = 1, then y(hat) = 3.25

Suppose y = 3. Then y - y(hat) would be 3 - 3.25 = -0.25 (using the above example). This would be your residual.

For 2):
The residuals in regression are measuring how far each observed y is from the regression line, y(hat), for a given value of x.

I hope this helps.