(d) Let b and b be the least squares estimate of ẞ with and without the i-th observation included in the data, respectively. Show that b - b(¹)(1)where e₁ = y -hat(y), = y₁-xb is the i - th residual when fitted on the whole data.3Ćb-b(i)(X¹X) - ¹xiei1 - hiiwhere ei = Yi - ŷi = yi - ab is the i-th residual when fitted on the whole data.=1-h(d) Let b and b) be the least squares estimate of 3 with and without the i-th observation included in thedata, respectively. Show thati i

Given that b andb(i) are the least squares estimate of β with and without the ith observation…

(d) Let b and b(₁) be the least squares estimate of 3 with and without the i-th observation included in the data, respectively. Show that b-b(i): (XX)-¹xili 1-hii where e; = y₁ - yi = yi-b is the i-th residual when fitted on the whole data. =

(d) Let b and b(₁) be the least squares estimate of 3 with and without the i-th observation included in the data, respectively. Show that b-b(i): (XX)-¹xili 1-hii where e; = y₁ - yi = yi-b is the i-th residual when fitted on the whole data. =

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

Section2.CR: Chapter 2 Review

Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...

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Question

(d) Let b and b be the least squares estimate of ẞ with and without the i-th observation included in the data, respectively. Show that b - b
(¹)
(1)
where e₁ = y -hat(y), = y₁-xb is the i - th residual when fitted on the whole data.
3
Ć
b-b(i)
(X¹X) - ¹xiei
1 - hii
where ei = Yi - ŷi = yi - ab is the i-th residual when fitted on the whole data.
=
1-h
(d) Let b and b) be the least squares estimate of 3 with and without the i-th observation included in the
data, respectively. Show that
i i

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