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 models the relationship between one dependent variable and two or more independent variables It can be used to model nonlinear relationships without any transformation. It assumes a linear relationship between the dependent and independent variables. ResetMaximum marks: 2 Flag question undefined

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BlackTom AI · Accepted Answer

To tackle the question, I’ll examine each statement about multiple linear regression and evaluate its accuracy.
Option 1: 'It can be represented by an equation such as y = b0 + b1 * x1 + b2 * x2 + … + bn * xn.' This is a classic description of multiple linear regression, where the dependent variable y is modeled as a linear combination of multiple independent variables with intercept b0 and coefficients b1 through bn. This statement is correct.
Option 2: 'It models the relationship between one dependent variable and two or more independent variables' This captures the essential idea of multiple linear regression: one outcome variable predicted from multiple predictors. Although it says two or more, the core concept remains accurate for any number of predictors greater than one (including exactly two or more). This statement is correct.
Option 3: 'It can be used to model nonlinear relationships without any transformation.' This is not true for multiple linear regression as commonly defined. The model assumes a linear relationship between the dependent variable and the independent variables; to capture nonlinearities, one would typically apply transformations (such as polynomial terms, log transforms, or interaction terms) or use nonlinear modeling. Therefore, this statement is incorrect.
Option 4: 'It assumes a linear relationship between the dependent and independent variables.' This is a fundamental property of multiple linear regression: the model is linear in the parameters, which implies a linear relationship (in terms of the coefficients) between y and the predictors. While residuals can be analyzed for fit, the assumption about the relationship is indeed linear, making this statement correct.
# Summarizing thoughts: options 1, 2, and 4 reflect core truths about multiple linear regression, while option 3 incorrectly claims nonlinear modeling without transformations, which contradicts the standard linear framework.

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