Linear regression in 3 The fitted surface in the dimension above dimension is?

Question

Options

• ACurved surface
• Bflat
• CHyperplane
• DHypersurface

• A
  6% (3)
• B
  8% (4)
• C
  84% (42)
• D
  2% (1)

Explanation

In linear regression with more than two predictors, the model defines a hyperplane - a flat, linear structure in higher-dimensional space. Just as one predictor gives a line and two predictors give a flat plane in 3D, adding more predictors extends that flatness into dimensions we can't visualize, and the technical term for that generalization is a hyperplane.

Why the distractors are wrong:

• A (Curved surface): Linear regression is linear by definition - the fitted surface has no bends or curves; that would imply a nonlinear model.
• B (Flat): "Flat" correctly describes the nature of the surface but is not the precise mathematical term for a flat structure in dimensions above 3 - it's too informal and incomplete.
• D (Hypersurface): A hypersurface is a broad term for any surface in higher dimensions and can be curved; it doesn't capture the flatness/linearity that linear regression guarantees.

Memory tip: Break it down - "hyper" means beyond and "plane" means flat. A hyperplane is simply a flat plane pushed beyond 3D. As long as your model is linear (no squared terms, no interactions), the fit stays flat - so linear = flat = hyperplane.

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