Question

Hello! I am a bit confused about this question,, I was under the impression that a residual in statistics is the difference between the observed and predicted values of the dependent variable Y for a given value of X. Here is the question along with my choices...

A residual is:

The difference between a data point and the regression line.

A value that can be 1 or zero.

A value that is always negative because it is a difference

The difference between two different lines.

Answer 1

The answer is:

Your understanding is correct. The residual is given by:

i.e. the difference between the observed and predicted values of the dependent variable Y for a given value of X.

But think of it like this:

• The data point is actually the predicted value of the dependent variable Y for a given value of X i.e.
• The regression line is Y = a+b*x

The residual is the linear distance between the data point and the regression line. This option is perfectly encapsulated by OPTION A. Hope this helps!

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!