In polynomial regression, there is a square term in the formula of the model, so it is not linear.

Question

Options

• ATRUE
• BFALSE

• A
  29% (12)
• B
  71% (30)

Explanation

B is correct because "linear" in linear regression refers to linearity in the parameters (coefficients), not in the predictor variables. A polynomial regression model like ŷ = β₀ + β₁x + β₂x² is still linear in its coefficients (β₀, β₁, β₂), making it a special case of the general linear model. The x² term simply transforms the input feature - it doesn't make the relationship between the model and its parameters nonlinear.

Why A is wrong: Confusing "linear in the variables" with "linear in the parameters" is the classic trap here. The presence of x² looks nonlinear, but that squared term is just a fixed input feature - the model is still fit using ordinary least squares, exactly like simple linear regression.

Memory tip: Think of it this way - if you created a new variable z = x², your model becomes ŷ = β₀ + β₁x + β₂z, which is plainly a multiple linear regression with two predictors. The curve comes from the data transformation, not from a nonlinear model structure.

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