Logistic Regression and the Decision Boundary · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Turning scores into yes or no answers

Computing · Machine Learning · ages 19-21
Name ______________________   Date ____________

  1. A golf model gives p equals 0.72 with threshold 0.5. What is the prediction?

    • The putt goes in
    • The putt misses
    • No prediction is possible

  2. A linear score grows large and positive. Where does the probability head?

    • Toward 0.5
    • Toward 1
    • Toward 0

  3. A score of z equals 1.1 gives e to minus z about one third. With p equals 1 over 1 plus e to minus z, what is p?

    Answer: ______________

  4. A golf model estimates a 0.72 probability that a putt goes in. Using a threshold of 0.5, what does the model predict?

    • The putt goes in
    • The putt misses

  5. Maximum likelihood picks the weights that make the observed labels most probable.

    Circle one:   True   False

  6. A logistic model with two features has linear score z = 2x1 + x2 - 6. With a threshold of 0.5, which equation describes the decision boundary?

    • 2x1 + x2 = 6
    • 2x1 + x2 = 0
    • x1 + x2 = 6
    • z = 6

  7. A medical study fits a logistic model to a biomarker. For one patient the linear score is z = 1.1, so e^-1.1 is about 1/3. The probability of success is p = 1 / (1 + e^-z). What is p? Give your answer as a decimal.

    Answer: ______________

  8. With z equals 2 x1 plus x2 minus 6 and threshold 0.5, which line is the boundary?

    • 2 x1 plus x2 equals 0
    • x1 plus x2 equals 6
    • 2 x1 plus x2 equals 6

  9. In the golf model, you raise the decision threshold from 0.5 to 0.8. What happens to the two kinds of mistakes?

    • Fewer wrong yes predictions, more wrong no predictions
    • More wrong yes predictions, fewer wrong no predictions
    • Both kinds of mistakes decrease
    • Both kinds of mistakes increase

  10. The golf threshold rises from 0.5 to 0.8. What happens to the two mistake kinds?

    • Fewer wrong yes calls, more wrong no calls
    • More wrong yes calls, fewer wrong no calls
    • Both mistake kinds fall
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Turning scores into yes or no answers W1-mt_FaVIaT7xl2-s1

  1. The putt goes in · At or above 0.5 the model answers yes.
  2. Toward 1 · The sigmoid squeezes any big score toward 1.
  3. 0.75 · One over 1 plus one third is 3 over 4, which is 0.75.
  4. The putt goes in · With a 0.5 threshold, predict yes whenever p is at least 0.5. Since 0.72 > 0.5, the model predicts the putt goes in.
  5. True · Likelihood scores how probable the data looks under the weights.
  6. 2x1 + x2 = 6 · The boundary is where p = 0.5, which happens when z = 0. Setting 2x1 + x2 - 6 = 0 gives 2x1 + x2 = 6, a straight line in the feature plane.
  7. 0.75 · Plug z = 1.1 into the sigmoid: p = 1 / (1 + 1/3) = 1 / (4/3) = 3/4 = 0.75.
  8. 2 x1 plus x2 equals 6 · The boundary is where p is 0.5, which is where z is 0.
  9. Fewer wrong yes predictions, more wrong no predictions · A higher threshold makes the model say yes less often. It wrongly says yes less, but it wrongly says no more, so one error type goes down while the other goes up.
  10. Fewer wrong yes calls, more wrong no calls · A stricter bar says yes less, so false alarms drop while misses rise.
Worksheet · LightMySky