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4. (Simplest linear models) a) Consider the intercept only model, y₁ = a+&; ,i = 1, ..., n. (a) Prove that the LSE of the intercept is â = y, and the residual sum satisfies res = S, yy = F1

4. (Simplest linear models) a) Consider the intercept only model, y₁ = a+&; ,i = 1, ..., n. (a) Prove that the LSE of the intercept is â = y, and the residual sum satisfies res = S, yy = F1

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 33E
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4. (Simplest linear models) a) Consider the intercept only model, y, a+ɛ,,i = 1, ..., n. (a) Prove that the LSE of the intercept is â = y, and the residual sum satisfies n SS res = Syy = y² F1 b) Consider the slope only model, y₁ = bx; + &₁, i = 1, ..., n. Derive the LSE of the slope and find the residual sum.
Transcribed Image Text:4. (Simplest linear models) a) Consider the intercept only model, y, a+ɛ,,i = 1, ..., n. (a) Prove that the LSE of the intercept is â = y, and the residual sum satisfies n SS res = Syy = y² F1 b) Consider the slope only model, y₁ = bx; + &₁, i = 1, ..., n. Derive the LSE of the slope and find the residual sum.
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