For yhat=2x+3 and x=4, calculate the prediction.
Answer and explanation
11
2×4+3=11.
Subjects
Machine learning
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Sample exercises
For prediction 7 and target 5, calculate squared error.
Answer and explanation
4
(7−5)²=4.
Residuals are 1, −1 and 2. Find MSE.
Answer and explanation
2
(1+1+4)/3=2.
What units does MSE have if the target is measured in metres?
- Seconds
- Metres only
- No units necessarily
- Square metres
Answer and explanation
Square metres
Squared residuals have squared target units.
Which claim is not established by a low regression error alone?
- The input causes the target
- The evaluated predictions fit the chosen metric
- Residuals can be inspected
- A baseline comparison is possible
Answer and explanation
The input causes the target
Prediction and causation are different.
Why can a linear model perform badly when extrapolating far beyond training inputs?
Answer and explanation
The assumed relation may not hold outside the observed region and the training data may not constrain that behaviour.
Credit model assumptions and data support.
Study notes
Linear regression, residuals and squared loss
A linear model predicts yhat=w·x+b. Linear refers to the parameters; feature transformations may make the relation nonlinear in original inputs.
UniversityLinear regression, residuals and squared loss · revision notes
A linear model predicts yhat=w·x+b. Linear refers to the parameters; feature transformations may make the relation nonlinear in original inputs.
UniversityLogistic scores, thresholds and confusion matrices
A logistic model maps a real score through σ(z)=1/(1+exp(−z)). Interpreting a score as a reliable probability requires calibration assessment.
UniversityLogistic scores, thresholds and confusion matrices · revision notes
A logistic model maps a real score through σ(z)=1/(1+exp(−z)). Interpreting a score as a reliable probability requires calibration assessment.
UniversityOverfitting, regularization and data distribution
A model can fit training-specific noise or patterns that do not generalize. Compare training and appropriately held-out performance.
UniversityOverfitting, regularization and data distribution · revision notes
A model can fit training-specific noise or patterns that do not generalize. Compare training and appropriately held-out performance.
UniversityPrediction from a linear model
A model prediction is not a guarantee about an individual outcome.
UniversityPrediction from a linear model · formula reference
A model prediction is not a guarantee about an individual outcome.
UniversityMean squared error on three cases
Average across the three observations, not only the nonzero errors.
UniversityMean squared error on three cases · formula reference
Average across the three observations, not only the nonzero errors.
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