▶Linear model
Predictions are a weighted sum of features plus an intercept.
Linear Regression
Estimating parameters by least squares
Linear regression chooses parameters so that a model minimizes squared vertical residuals between observations and predictions.
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The essential idea: linearity refers to the parameters, so transformed predictors can still fit nonlinear shapes.
One Concept · One Example
What to notice
- Residuals are vertical prediction errors.
- Least squares gives large errors extra weight.
- Features may be nonlinear while coefficients remain linear.
Fit by minimizing residual energy
Least-squares objective
Training minimizes the sum of squared residuals.
Feel the least-squares objective
Change slope and intercept, then compare your residual sum of squares with the optimal line.
Linear regression estimates parameter coefficients by minimizing squared prediction residuals.