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Consider a regression analysis with three independent variables x₁, x₂, and X.. Select all possible equations for the following regression models. (a) The model that includes as predictors all independent variables but no quadratic or interaction terms. Oyna+Pix, +РуX2 +Рухуче 2^2 Oy=a+Pixa + Ружа + Ружа + Paxs=+. Oy=a+Pixa+Ружа + Руху + РаХаХа+ Oy=a+fix, +Руха + Руху +РахуXste Oyna+Pix, +Dz*а Oyna+Pix1 + рух2 + Руху+Paxi2+Psxy2+ Роху? +Рухах2+ Рухажу+PдXaXy+e Boxy2+e (b) The model that includes as predictors all independent variables and all quadratic terms. Oy=a+Pixe+P2х2 + вужуте Oy=a+Pix, +Pzx2+Руху +Рах,2+Pѕ Oy=a+AјX, +Ружа + вужу+ РаХаХан Oy=a+BiX1 + Руха + Ружа + РахуX, +e Oy=a+fix, +Pyx2 +Руха + Рахаха те Oyna+Pixi + Ружа + вужу + Paxi2+Psx22+ гружах2 + Рухуху + Рухажу те (c) All models that include as predictors all independent variables, no quadratic terms, and exactly one interaction term. Oy=a+Pix2+B2x2+ вужуте Oy=a+Pixa + Руха + Руху + Рах,2 Oy=a+fix, +Ружа +Руху +РљX,X2 Oy=a+BiX, +Ружа + Ружу + Рах, Ха+e Oy=a+BјX, +вуха + Ружа + Ражажут Dy=a+fix1 (d) The model that includes as predictors all independent variables, all quadratic terms, and all interaction terms (the full quadratic model). Oy=a+Pix, +Pzx2 +Руху те +e Oyna+Pix1+Pyx2 + Руху + Рах,2+P; Oy=a+Pix,+Ружа + Ружу+ РахјХ2+ Oy=a+Pix, +Ружа +Рухз+ Рах,Жу+ Oy=a+Pixa + руху + Руху + Ражажут Oyna+Pixa+ража + Руху + Раx12+B Poxy2+e Раху? + вухах2 + Руху Ху+ ВдXzХу+0

Consider a regression analysis with three independent variables x₁, x₂, and X.. Select all possible equations for the following regression models. (a) The model that includes as predictors all independent variables but no quadratic or interaction terms. Oyna+Pix, +РуX2 +Рухуче 2^2 Oy=a+Pixa + Ружа + Ружа + Paxs=+. Oy=a+Pixa+Ружа + Руху + РаХаХа+ Oy=a+fix, +Руха + Руху +РахуXste Oyna+Pix, +Dz*а Oyna+Pix1 + рух2 + Руху+Paxi2+Psxy2+ Роху? +Рухах2+ Рухажу+PдXaXy+e Boxy2+e (b) The model that includes as predictors all independent variables and all quadratic terms. Oy=a+Pixe+P2х2 + вужуте Oy=a+Pix, +Pzx2+Руху +Рах,2+Pѕ Oy=a+AјX, +Ружа + вужу+ РаХаХан Oy=a+BiX1 + Руха + Ружа + РахуX, +e Oy=a+fix, +Pyx2 +Руха + Рахаха те Oyna+Pixi + Ружа + вужу + Paxi2+Psx22+ гружах2 + Рухуху + Рухажу те (c) All models that include as predictors all independent variables, no quadratic terms, and exactly one interaction term. Oy=a+Pix2+B2x2+ вужуте Oy=a+Pixa + Руха + Руху + Рах,2 Oy=a+fix, +Ружа +Руху +РљX,X2 Oy=a+BiX, +Ружа + Ружу + Рах, Ха+e Oy=a+BјX, +вуха + Ружа + Ражажут Dy=a+fix1 (d) The model that includes as predictors all independent variables, all quadratic terms, and all interaction terms (the full quadratic model). Oy=a+Pix, +Pzx2 +Руху те +e Oyna+Pix1+Pyx2 + Руху + Рах,2+P; Oy=a+Pix,+Ружа + Ружу+ РахјХ2+ Oy=a+Pix, +Ружа +Рухз+ Рах,Жу+ Oy=a+Pixa + руху + Руху + Ражажут Oyna+Pixa+ража + Руху + Раx12+B Poxy2+e Раху? + вухах2 + Руху Ху+ ВдXzХу+0

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Consider a regression analysis with three independent variables X₁, X₂, and X3. Select all possible equations for the following regression models. (a) The model that includes as predictors all independent variables but no quadratic or interaction terms. Oy=a+B₁₂x₁₂ + ₂x₂ + B 3x3 + e 2 2 Oy=a + ₁x₁ + B₂X₂ + B3×3 + B₁X₁² + P5X₂² + P6x3² + e Oy=a +₁x₁ + ₂×₂ + B3X3 + B₁X₁ X₂ + e Oy=a +₁x₁ + 1 ₂x2 + B 3×3 + B₁X1 X3 + e Oy=a +₁x₁ + ₂X2 + B 3×3 + ₁*₂*3 + e 1 "2" Oy=a + B₁X₁ + B₂X₂ + B3×3 + B₁X1² + P5X₂² + B6X3² + B₂X₁ X₂ + B8X₁ X3 + PgX₂ X3 + e (b) The model that includes as predictors all independent variables and all quadratic terms. Oy=a + B₁X₁ + B₂x₂ + 3x3 + e 2 Oy=a+B₁₂x₁₂ + ₂x₂ + B 3×3 + B₁ × ₁² + B₂ × ₂² + B6 x 3² + e 1 Oy=a + ₁x₁ + P₂X₂ + B3×3 + B₁X₁ X₂ + e Oy=a + ₁x₁ + 1 ₂×₂ + B3×3 + B₁X₁ X3 + e ₂×2 + P3×3 + ₁*2*3+e 2 2 ₂x₂ + B3X3 + BAX₁²³² + P5X₂²² + B6X3² + B₂X₁ X₂ + B8X₁ X3 + PgX₂ X3 + e Oy=a +₁x₁ + 1 Oy=a + P₁x₁ + (c) All models that include as predictors all independent variables, no quadratic terms, and exactly one interaction term. Oy=a + ₁x₁ + B₂X₂ + B3×3 + e 2 Oy=a+P₁X₁ + P₂X₂ + B3X3 + B₁ × ₁² + P5X₂² + B6 x 3² + e Oy=a +₁x₁ + a+ ₂x₂ + B3 x 3 + B₁X₁ X₂ + e ₂×₂ + B3×3 + B₁X₁ X3 + e ₂×₂ + B3X3 + B₁ X₂ X3 + e Oy=a +₁x₁ + Oy=a +₁x₁ + Oy=a + ₁x₂ + ₂x2 +P3×3 + B4X1² 5 2 2 + P8X₁ X3 +₂×₂×3 + e Oy = a + ₁x₁ + ×₁×₂² (d) The model that includes as predictors all independent variables, all quadratic terms, and all interaction terms (the full quadratic model). Oy=a +₁x₁ + ₂x₂ +Bzx3 + e P3 2 Oy=a +₁x₁ +₂X₂ + P3×3 + P₁x₁² + P5X₂² + B6 x 3² + e 1 Oy=a+B₁X₁ + B₂X₂ + B 3×3 + B₁X1 X₂ + e 1 1 Oy=a +₁x₁ + ₂ x ₂ + B 3 x 3 + B ₁ X ₁ X3 + e Oy=a + ₁x₁ + ₂x₂ + B3X3 + B₁ X₂ X3 + e 2 2 e ₂x₂ + P3×3 + P₁x₁² + P5×₂² + P6x3² + B7×1×₂ + BgX1 X3 + BgX₂×3 + @
Transcribed Image Text:Consider a regression analysis with three independent variables X₁, X₂, and X3. Select all possible equations for the following regression models. (a) The model that includes as predictors all independent variables but no quadratic or interaction terms. Oy=a+B₁₂x₁₂ + ₂x₂ + B 3x3 + e 2 2 Oy=a + ₁x₁ + B₂X₂ + B3×3 + B₁X₁² + P5X₂² + P6x3² + e Oy=a +₁x₁ + ₂×₂ + B3X3 + B₁X₁ X₂ + e Oy=a +₁x₁ + 1 ₂x2 + B 3×3 + B₁X1 X3 + e Oy=a +₁x₁ + ₂X2 + B 3×3 + ₁*₂*3 + e 1 "2" Oy=a + B₁X₁ + B₂X₂ + B3×3 + B₁X1² + P5X₂² + B6X3² + B₂X₁ X₂ + B8X₁ X3 + PgX₂ X3 + e (b) The model that includes as predictors all independent variables and all quadratic terms. Oy=a + B₁X₁ + B₂x₂ + 3x3 + e 2 Oy=a+B₁₂x₁₂ + ₂x₂ + B 3×3 + B₁ × ₁² + B₂ × ₂² + B6 x 3² + e 1 Oy=a + ₁x₁ + P₂X₂ + B3×3 + B₁X₁ X₂ + e Oy=a + ₁x₁ + 1 ₂×₂ + B3×3 + B₁X₁ X3 + e ₂×2 + P3×3 + ₁*2*3+e 2 2 ₂x₂ + B3X3 + BAX₁²³² + P5X₂²² + B6X3² + B₂X₁ X₂ + B8X₁ X3 + PgX₂ X3 + e Oy=a +₁x₁ + 1 Oy=a + P₁x₁ + (c) All models that include as predictors all independent variables, no quadratic terms, and exactly one interaction term. Oy=a + ₁x₁ + B₂X₂ + B3×3 + e 2 Oy=a+P₁X₁ + P₂X₂ + B3X3 + B₁ × ₁² + P5X₂² + B6 x 3² + e Oy=a +₁x₁ + a+ ₂x₂ + B3 x 3 + B₁X₁ X₂ + e ₂×₂ + B3×3 + B₁X₁ X3 + e ₂×₂ + B3X3 + B₁ X₂ X3 + e Oy=a +₁x₁ + Oy=a +₁x₁ + Oy=a + ₁x₂ + ₂x2 +P3×3 + B4X1² 5 2 2 + P8X₁ X3 +₂×₂×3 + e Oy = a + ₁x₁ + ×₁×₂² (d) The model that includes as predictors all independent variables, all quadratic terms, and all interaction terms (the full quadratic model). Oy=a +₁x₁ + ₂x₂ +Bzx3 + e P3 2 Oy=a +₁x₁ +₂X₂ + P3×3 + P₁x₁² + P5X₂² + B6 x 3² + e 1 Oy=a+B₁X₁ + B₂X₂ + B 3×3 + B₁X1 X₂ + e 1 1 Oy=a +₁x₁ + ₂ x ₂ + B 3 x 3 + B ₁ X ₁ X3 + e Oy=a + ₁x₁ + ₂x₂ + B3X3 + B₁ X₂ X3 + e 2 2 e ₂x₂ + P3×3 + P₁x₁² + P5×₂² + P6x3² + B7×1×₂ + BgX1 X3 + BgX₂×3 + @
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