Help to understand e i </msub> = y i </msub> −<!--
shmilybaby4i
Answered question
2022-06-09
Answer & Explanation
lodosr
Beginner2022-06-10Added 24 answers
The usual notation runs like this:
- the average of ,
- the average of ,
- , where is the th error. The values of and are unobservable because you see only the sample , and not the whole population, and is unobservable because and are unobservable.
- and are the least-squares estimates of and . The least-squares estimates are observable because you can compute them base on the sample , . They satisfy , i.e. the least-squares line passes through the point that is the average of , .
- the th "fitted value".
- the th residual, not to be confused with the ith error. The residuals are observable whereas the errors are not. The residuals necsessarily satisfy the two linear constraints and , whereas the errors, on the other hand, are often taken to be independent.
- The "regression function" is , whereas the fitted value is the value of the regression function when the input is .
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