The polynomial regression model of degree r is given by Y₁ =B₁ + B₁X₁ + B₂X² + ... + ³₂X² + U₁. Interpret the coefficient 3, in a linear regression (r = 1): Y = Bot Bi Xit and in a quadratic regression (r = 2): Y₁ =B₁ + B₁X₁ + B₂X² + U₁. How is the estimation affected if we estimate a linear regression (r = 1) when the true form of the regression function is quadratic (r = 2) or cubic (r = 3)?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 76E
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The polynomial regression model of degree r is given by
Y₁ =B₁ + B₁X₁ + ß₂X² + ··· + ß„X{ + Uj.
Interpret the coefficient 3₁ in a linear regression (r = 1):
Yi Bo + B₁X₁ + Uj
and in a quadratic regression (r = 2):
Y₁ = B₁ + B₁X₁ + B₂X² + U₂.
How is the estimation affected if we estimate a linear regression (r = 1)
when the true form of the regression function is quadratic (r = 2) or
cubic (r = 3)?
Transcribed Image Text:The polynomial regression model of degree r is given by Y₁ =B₁ + B₁X₁ + ß₂X² + ··· + ß„X{ + Uj. Interpret the coefficient 3₁ in a linear regression (r = 1): Yi Bo + B₁X₁ + Uj and in a quadratic regression (r = 2): Y₁ = B₁ + B₁X₁ + B₂X² + U₂. How is the estimation affected if we estimate a linear regression (r = 1) when the true form of the regression function is quadratic (r = 2) or cubic (r = 3)?
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