4) You have a random pair (Y, X) and Yˆ is the best linear predictor of Y based on X. (a) [1pt] We say that the regressi
Posted: Wed May 11, 2022 3:13 pm
4) You have a random pair (Y, X) and Yˆ is the best linear
predictor of Y based on X.
(a) [1pt] We say that the regression line passes through the
point of averages. Show this by setting X = μX and finding the
corresponding value of Yˆ.
(b) [1pt] Find E[Yˆ ]. This is the average of the fitted
values.
(c) [1pt] The difference Y − Yˆ is called a residual. It is the
difference between the actual and fitted values of Y. Find the
expectation of the residual and confirm that the answer justifies
the following statement: “No matter what the shape of the scatter
diagram, the average of the residuals is 0.”
(d) [1pt] Find Var(Yˆ ). Your answer can only use μX, μY , σX,
σY , or r.
(e) [1pt] Using part (d), show the following
statement:
SD of fitted values SD of Y = = lr|.
predictor of Y based on X.
(a) [1pt] We say that the regression line passes through the
point of averages. Show this by setting X = μX and finding the
corresponding value of Yˆ.
(b) [1pt] Find E[Yˆ ]. This is the average of the fitted
values.
(c) [1pt] The difference Y − Yˆ is called a residual. It is the
difference between the actual and fitted values of Y. Find the
expectation of the residual and confirm that the answer justifies
the following statement: “No matter what the shape of the scatter
diagram, the average of the residuals is 0.”
(d) [1pt] Find Var(Yˆ ). Your answer can only use μX, μY , σX,
σY , or r.
(e) [1pt] Using part (d), show the following
statement:
- 4 You Have A Random Pair Y X And Y Is The Best Linear Predictor Of Y Based On X A 1pt We Say That The Regressi 1 (22.33 KiB) Viewed 23 times