Artificial intelligence · University
Linear 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.
Key ideas and conditions
Prediction
A linear model predicts yhat=w·x+b. Linear refers to the parameters; feature transformations may make the relation nonlinear in original inputs.
Residual
Define residual consistently, for example yhat−y. Squared loss penalizes larger residuals more heavily.
Mean loss
MSE is the mean squared residual over the evaluated examples. It has squared target units and is not the same as mean absolute error.
Interpretation
Good fit on observed data does not establish causation or reliable extrapolation. Inspect residual patterns and the intended data range.
Explain without looking
- For loss (w−3)² at w=1, find derivative with respect to w.
- Describe one useful residual diagnostic.
Further reading and review references
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