Practice question · Fill in the blanks
Complete the definition of the least squares criterion.
Least squares chooses the line that minimises ______.
Word bank: the sum of the squared vertical distances from the points to the line · the sum of the slopes of all the data points · the number of points lying above the line · the horizontal distance from each point to the y-axis
Hints
- The quantity being minimised is built from residuals.
- Squaring stops positive and negative residuals from cancelling.
Show the answer
Least squares chooses the line that minimises the sum of the squared vertical distances from the points to the line.
Why
The residuals are vertical gaps, and squaring them prevents cancellation while penalising large misses heavily. That squaring is also why a single outlier can drag a regression line noticeably out of position.
Practise Correlation and Regression
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