5. In the regression model, Y₁ = ẞ0+ ẞ₁xi1 + B₂xi2 + ... + ßpxip +Єi, n = 1, . . ., n. Suppose we correct Y₁,..., Yn for their arithmetic average Ỹ, to obtain Y₁ = Y₁ – Ỹ. Then V₁,, have average zero, i.e., they are centred on zero. Similary, correct the values of the jth explanatory variable, x1,...,xnj, by subtracting their average, Ã¡: Xij = Xij − Ñj. Define the n× 1 vector, y = (1, №2...Vn), and the n xp matrix (no intercept column), X11 Xip -(1-5) x = We also define the vector of slop parameters (no intercept), ß₁:p = (ß₁, . . ., ßp). (a). (b). (c). (d). written as Please show that the least squares estimate for the slope parameters can be = (xTx)¯¹xy. B1P = SS(B₁,..., Bp Bo) in the ANOVA Table (with the intercept ignored) can be written as Σ(Ŷ - Ÿ)². 3) SS (B₁, ..., ßp|ẞ0) can also be written as Tŷ, and hence as Show that E[SS(B1, ..., ßp |ẞo)] = po² +ß{ :pXT Xß₁:p· T

5. In the regression model, Y₁ = ẞ0+ ẞ₁xi1 + B₂xi2 + ... + ßpxip +Єi, n = 1, . . ., n. Suppose we correct Y₁,..., Yn for their arithmetic average Ỹ, to obtain Y₁ = Y₁ – Ỹ. Then V₁,, have average zero, i.e., they are centred on zero. Similary, correct the values of the jth explanatory variable, x1,...,xnj, by subtracting their average, Ã¡: Xij = Xij − Ñj. Define the n× 1 vector, y = (1, №2...Vn), and the n xp matrix (no intercept column), X11 Xip -(1-5) x = We also define the vector of slop parameters (no intercept), ß₁:p = (ß₁, . . ., ßp). (a). (b). (c). (d). written as Please show that the least squares estimate for the slope parameters can be = (xTx)¯¹xy. B1P = SS(B₁,..., Bp Bo) in the ANOVA Table (with the intercept ignored) can be written as Σ(Ŷ - Ÿ)². 3) SS (B₁, ..., ßp|ẞ0) can also be written as Tŷ, and hence as Show that E[SS(B1, ..., ßp |ẞo)] = po² +ß{ :pXT Xß₁:p· T

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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