Least Squares

Description

Six data points have been placed in the coordinate plane and a line is drawn through them. Move the line by dragging its y-intercept or by dragging the point that determines its slope until it appears to be a good fit to the six data points.

From each data point the square of the residual from the point to the line has been constructed. The sum of these squares results in a larger square whose area can be minimized by dragging the line. This then becomes a criteria of best fit; that is, the least squares best fit of a line through the points is that line which minimizes the sum of the squares of the residuals.

Questions

1. Press the Show Regression Line button to compare your estimate of the best fit with the actual best fit.
2. With both lines hidden, arrange the points so that you think the r² value is:
   • less than 0.2,
   • greater than 0.8,
   • between 0.4 and 0.6

   Check your estimates by showing the regression line and the correlation coefficient.

3. With the regression line hidden, move the points so that there is an outlier. Attempt to find the best fit regression line and compare your result with the actual. Describe the effect that the outlier has on the least squares line. Why is it that the least squares regression line is said not to be resistant to outliers?

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