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 + B₁₂ x₁ + B₂ × ₂ + B 3×3 + e22Oy = a + B₁₂ x₁ + B₂×₂ + B3×3 + B4×₁² + B5×₂² + B6×3² + eOy = a + B₁x₁ + B₂x₂ + B 3×3 +Oy = a + B₁x₁ + B₂x₂ + B3X3 +Oy = a + B₁₂ x₁ + B₂×2 + B 3×3 + B4×₂×3 + e4×₁×₂ + eB4X₁ X3 + e2Oy = a + B₁x₁ + B₂×₂ + B3×3 + B4x₁² + B 5x₂+(b) The model that includes as predictors all independent variables and all quadratic terms.Oy = a + B₁₂ x₁ + B₂×₂ + B 3×3 + e22Oy = a + B₁x₁ + B₂×₂ + B 3×3 + B ₁×₁² + √5 x ₂²23 +B7x1x₂ + B8X1 X3 + B9x₂x3 + e22Oy = a + B₁₂ x₁ + B₂×₂ + B 3×3 + B ₁×₁² + B5 × ₂ ² + B6 × 3² + e+ eOy = a + B₁x₁ + B₂×₂ + B 3×3 + B₁x1x₂ +Oy = a + B₁x₁ + B₂×₂ + B3X3 + B4X1X3Oy = a + B₁₂x₁₂ + B ₂x₂ + B3X3 + B4x2x3 + e2+ B6x3² + B7x₁x(c) All models that include as predictors all independent variables, no quadratic terms, and exactly one interaction term.Oy = a + B₁x₁ + B₂×₂ + B 3×3 + e222+ B₂x₂ + B3×3 + B₁×₁² + B 5x₂² + B6X3² + e22Oy = a + B₁x₁ + ₂×₂ + B3×3 + B₁×₁² + B 5x₂²Oy = a + B₁₂x₁₂ + B₂×₂ + B 3×3 + B₁x1x2 + eOy = a + B₁x₁ + B₂×₂ + B 3×3 + B4X1X3 + eOy = a + B₁₂ x₁ + B₂×₂ + B 3×3 + B4×2×3 + eOy = a + B₁x₁Oy = a + B₁x₁ + B₂x₂ + 3x3 + 4×1×₂ + eOy = a + B₁x₁ + B₂×₂ + B 3×3 + B₁X1 X3 + eOy = a + B₁x₁ + B₂×₂ + B 3×3 + B4×₂×3 + e22Oy = a + B₁x₁ + B₂×₂ + B 3×3 + B ₁×₁² + B 5x X₂²+ B6x3² + B7×₁×₂ + B8×₁×3 + B9×₂×3 + e(d) The model that includes as predictors all independent variables, all quadratic terms, and all interaction terms (the full quadratic model).Oy = a + B₁x₁ + B₂×₂ + B 3×3 + e+ B8X₁ X3 + B9x2. te2+ B6X3+ e22Oy = a + B₁×₁ + B₂×₂ + B3×3 + B4×1² +B5x2² + B6 x 3² + B₁x₁x₂ + B8 x₁ x3 + B9×₂×3 + e

As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted...…

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 + B₁x₁ + B₂×₂ + B3×3 + e Oy = a + B₁x₁ + B₂X₂ + B3X3 + B4x1² + B5×₂² + B6 x 3². + e Oy = a + B₁x₁ + B₂X₂ + B 3×3 + B₁x₁x₂ + e Oy = a + B₁x₁ + B₂X₂ + B3X3 + B4X1 X3 + e С y = a + B₁x₁ + B₂X₂ + B 3×3 + B4X2 X3 + e 2 2 · B₁x₁ + B₂ × ₂ + B 3×3 + B4×₁² + B5×₂² + B6×3² + B7 × ₁ × ₂ + B8 X₁ X3 + B9×₂×3 + e Oy = a + (b) The model that includes as predictors all independent variables and all quadratic terms. Oy = a + B₁x₁ + ₂x₂ + 3x3 + e 2 Oy = a + B₁₂ x₁ + B₂X₂ + B 3×3 + B₁ × ₁² + B 5 x ₂² + B6 x 3² + e Oy = a + B₁x₁ + B₂X₂ + B 3×3 + B₁X1 X₂ + e Oy = a + B₁x₁ + B₂X₂ + B 3×3 + B4X1 X3 + e Oy = a + B₁x₁ + B₂X₂ + B3X3 + B4X₂ X3 + e Oy = a + B₁x₁ + B₂×₂ + B 3×3 + B4×₁² + B 5x₂² + B6 × 3² + B₂×₁×₂ + B8 × 1 ×3 + B9×₂×3 + e (c) All models that include as predictors all independent variables, no quadratic terms, and exactly one interaction term. Oy = a + B₁x₁ + B₂x₂ + 3x3 + e 2 2 Oy = a + B₁x₁ + B₂x₂ + B3X3 + Ba Xí + B5x₂² + B6x3² + e Oy = a + B₁x₁ + B₂X₂ + B3X3 + B4X1X2 + e Oy = a + B₁x₁ + B₂X₂ + B3X3 + B₁X₁ X3 + e Oy = a + B₁x₁ + B₂X₂ + B3x3 + B4×2×3 + e Oy = a + B₁₂ x₁ + B₂X₂ + B3X3 + B4X₁² + B 5 x ₂² + B6 1 (d) The model that includes as predictors all independent variables, all quadratic terms, and all interaction terms (the full quadratic model). Oy=a + B₁x₁ + B₂x₂ + 3x3 + e Oy = a + B₁₂ x₁ + B₂X₂ + B3X3 + B 4x₁² + B 5x₂² Oy = a + B₁x₁ + B₂X₂ + B3X3 + B4x1x₂ + e Oy = a + B₁x₁ + B₂×₂ + B3×3 + B4X₁ X3 + e Oy = a + B₁x₁ + B₂x₂ + B3X3 + B4×2×3 + e Oy = a + B₁₂ x₁ + B₂x₂ + B 3×3 + B4x₁² + B5x₂² + B6X3 +B7x₁x₂ + B8X1 X3 + 9x₂x3 + e +B6x + e + B7 X₁ X₂ + B8X₁ X3 + B9x₂x3 + e