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Claude Linear Regression and Supervised Learning — practice questions

Explore 13 free Linear Regression and Supervised Learning questions in Claude Aifoundations. Open each question or exercise to read its content, reference answers and available explanation.

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Linear Regression and Supervised Learning questions and exercises with answers

Showing questions 1–13 of 13.

The SUPERVISED-learning setup gives the learnerRead the answer and worked solution →Linear regression assumes the hypothesis function h_θ(x) takes the formRead the answer and worked solution →The least-squares cost function in CS229 linear-regression notes isRead the answer and worked solution →The gradient-descent update rule for parameter θⱼ in linear regression isRead the answer and worked solution →'Α' in θⱼ := θⱼ − α·∂J/∂θⱼ is called theRead the answer and worked solution →The LMS (Widrow–Hoff) update rule on a single training example isRead the answer and worked solution →The closed-form 'normal equations' solution for least-squares linear regression isRead the answer and worked solution →The design matrix X for n training examples with d features (plus intercept) has shapeRead the answer and worked solution →The PROBABILISTIC justification for the least-squares cost assumes the noise ε⁽ⁱ⁾ in y⁽ⁱ⁾ = θᵀx⁽ⁱ⁾ + ε⁽ⁱ⁾ isRead the answer and worked solution →Logistic regression uses which hypothesis function?Read the answer and worked solution →Closed-form normal equations require XᵀX to beRead the answer and worked solution →The resulting per-example log-likelihood is, up to constantsRead the answer and worked solution →Split batch from stochastic descentRead the answer and worked solution →

Worked practice questions

The SUPERVISED-learning setup gives the learner

  1. Labelled (x, y) pairs and asks the learner to predict y on new x
  2. Only a reward signal, no inputs
  3. A graph structure with no node labels
  4. Only inputs x without any labels
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Correct answer: A. Labelled (x, y) pairs and asks the learner to predict y on new x

Supervised learning is parametrised by a labelled training set {(x⁽ⁱ⁾, y⁽ⁱ⁾)} and learns h(x) ≈ y. Unsupervised has only x; reinforcement learns from a reward signal.

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Linear regression assumes the hypothesis function h_θ(x) takes the form

  1. h_θ(x) = θ⁰ · 2^x
  2. h_θ(x) = θᵀx (with x₀ = 1 to absorb the intercept)
  3. h_θ(x) = sin(θᵀx)
  4. h_θ(x) = 1 / (1 + exp(−θᵀx))
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Correct answer: B. h_θ(x) = θᵀx (with x₀ = 1 to absorb the intercept)

h(x) = θᵀx with x₀ = 1 convention. **Option D is the LOGISTIC sigmoid (used for logistic regression), not linear regression.**

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The least-squares cost function in CS229 linear-regression notes is

  1. J(θ) = Σ y⁽ⁱ⁾
  2. J(θ) = Σ log(h(x⁽ⁱ⁾))
  3. J(θ) = Σ |h(x⁽ⁱ⁾) − y⁽ⁱ⁾|
  4. J(θ) = ½ Σ (h(x⁽ⁱ⁾) − y⁽ⁱ⁾)²
Show answer and solution

Correct answer: D. J(θ) = ½ Σ (h(x⁽ⁱ⁾) − y⁽ⁱ⁾)²

Least-squares cost J(θ) = ½ Σᵢ (h_θ(x⁽ⁱ⁾) − y⁽ⁱ⁾)². The ½ disappears under differentiation, making the gradient cleaner.

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