Statistics multiple choice

Question

Which of the following statements) about errors and residuals is (are) correct? Check all that apply.

Both errors and residuals are random variables.

Errors are observed, while residuals are not observable.

Error is the difference between the observed value and the fitted value.

Errors are smaller than residuals since they reflect differences in the population.

Answer 1

I think it will be helpful to you if we start by defining what a "random variable" means: it's simply a variable whose value is unknown or a function that assigns values to each of an experiment's outcomes. You'll likely also want to refresh your memory as to what are the definitions of the following "values":error, residual, fitted, and observed. Once you understand those definitions, you should be able to answer the question as to which statements are true and which are false. For example, once you know that to calculate a residual value, you just need to subtract the observed value from the fitted value, which is Not what the third statement says, so it's not correct, so you don't put a check by it. I hope that's helpful to you.