Question22 Which statement about multiple linear regression is INCORRECT? Select one alternative: It can be represented by an equation such as y = b0 + b1 * x1 + b2 * x2 + … + bn * xn. It assumes a linear relationship between the dependent and independent variables. It can be used to model nonlinear relationships without any transformation. It models the relationship between one dependent variable and two or more independent variables ResetMaximum marks: 2 Flag question undefined

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BlackTom AI · Accepted Answer

Let’s break down the question and examine each statement about multiple linear regression (MLR) carefully.
Option 1: 'It can be represented by an equation such as y = b0 + b1 * x1 + b2 * x2 + … + bn * xn.' This is a standard description of MLR, where the dependent variable y is modeled as a linear combination of the predictors with intercept b0 and slopes b1, b2, ..., bn. The form captures the essence of linearity in the parameters, not necessarily in the variables themselves, and is a core characteristic of MLR.
Option 2: 'It assumes a linear relationship between the dependent and independent variables.' This reflects a key assumption of MLR: the expected value of the outcome is a linear function of the predictors (in terms of the parameters). It is about linearity in coefficients, which is essential for estimation via ordinary least squares.
Option 3: 'It can be used to model nonlinear relationships without any transformation.' This statement is incorrect. By default, MLR presumes linearity in the parameters. To capture nonlinear relationships, you typically need transformations (e.g., polynomial terms, interactions) or nonlinear models. Without any transformation, nonlinear patterns are not well captured by a single linear equation.
Option 4: 'It models the relationship between one dependent variable and two or more independent variables.' This correctly describes MLR, which extends simple linear regression (one predictor) to multiple predictors, modeling how the dependent variable relates to several independent variables simultaneously.
In sum, the only option that states something contrary to the foundational assumptions of multiple linear regression is Option 3, which claims it can model nonlinear relationships without any transformation. The other statements align with standard MLR concepts, including the linear-in-parameters form, the linear relationship assumption, and the multivariable predictor structure.

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