w = (mx, + b – yı)² + ... + (mx, + b - yn). (1) (See the accompanying figure.) Show that the values of m and b that do this are (E»)(E») - -E» (E»)' - »E»² (E» - -Ex). m (2) b= Σχ (3)

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 33EQ
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Problem 2. Sketch a proof of these formulas for linear regression, described on
the following page.
P;(x1, y1)
y = mx + b
P2(x2, y2)
w = (mx + b – y)² +
... + (mxr, + b –
(1)
(See the accompanying figure.) Show that the values of m and b
that do this are
(E»)(E») - »>»»
(E.) - »>«?
т
(2)
b= Σχ
(3)
- m
Transcribed Image Text:2 Problem 2. Sketch a proof of these formulas for linear regression, described on the following page. P;(x1, y1) y = mx + b P2(x2, y2) w = (mx + b – y)² + ... + (mxr, + b – (1) (See the accompanying figure.) Show that the values of m and b that do this are (E»)(E») - »>»» (E.) - »>«? т (2) b= Σχ (3) - m
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