| 3.5 | Least Squares Linear Regression |
- Key Idea 1: Another way of describing how well a line fits a set of data is to square the prediction errors Y – Y’ and find the mean (average) of all the squared errors...
- Consider these reading and spelling scores for 10 students
- We can use the same approach that we used in the last section - start with an arbitrary line, and find the mean square error for it and a number of other lines.
Discussion 
Slope Mean square error 1.5 7.51 1.6 7.07 1.7 6.80 1.8 6.70 Least mean square error 1.9 6.77 2.0 7.01 2.1 7.41 2.2 7.98 2.3 8.72 2.4 9.63 2.5 10.71 
Example
- Key Idea 2: For a formula that avoids the need for a trial and error approach, see the next section...
- Key Idea 3: We now have seen 3 methods of fitting a straight line to data...
- For a quick and rough idea, the visual method of Section 3.3 is adequate.
- The method used most often in standard statistical practice is to make the mean square error as small as possible (the method of least squares).
- In certain cases you should really find the smallest mean error regression line instead of the smallest mean square error regression line because of its greater robustness against undue influence from one or two data points.
Discussion