The statement that the algebraic expression of Linear Regression with n independent variables can be derived from the n-NN model is false.

• A. True
• B. False
• C. Not enough information
• D. Both

Answer: (B)

The main idea here is the difference between a parametric linear model and a non-parametric nearest-neighbor approach. Linear regression with multiple predictors has a single, explicit algebraic form for predictions: ŷ = β0 + β1x1 + … + βn xn, with coefficients determined by minimizing squared errors, yielding a closed-form solution like β = (XᵀX)⁻¹Xᵀy when X has full rank. n-NN predictions, on the other hand, are computed by averaging the outcomes of the k closest training points to the input, so the prediction depends on local data geometry and distance metrics rather than a fixed linear equation. There isn’t a global algebraic expression that reproduces the linear-regression model from a k-NN approach. Therefore, the statement is false.