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!**

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