Practice question · Fill in the blanks
Complete the definition of least-squares fitting.
Least-squares fitting chooses the curve that minimises ______.
Word bank: the largest single residual · the sum of the squared residuals · the number of points missed · the degree of the polynomial
Hints
- The name of the method states the quantity being minimised.
- Squaring the residuals is what removes the signs.
Show the answer
Least-squares fitting chooses the curve that minimises the sum of the squared residuals.
Why
The total of the squared vertical distances is minimised, every point contributes, and large misses are penalised disproportionately. Minimising the largest residual instead is a different, legitimate criterion, but it is not least squares.
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