don steward
mathematics teaching 10 ~ 16

Monday, 15 March 2010

line of best fit

"a line of best fit is a straight road that passes as close as you can to all of the 'houses'
it is not like science where you try to pass through as many points as you can; the line need not pass through any of the 'houses'
we may draw slightly different lines of best fit - and that's fine"

problems commonly occurring:
  • students often force the line of best fit to pass through the origin
  • they want it to pass through as many of the plotted points as possible
  • the notion of having as many points above the line as below can lead to some strange lines
to obtain a reasonably good line of best fit you can ask students to draw an ellipse around the points on a scatter graph and then chop this ellipse in half (i.e. along the major axis)

[this links with confidence ellipses]

the skinnier the ellipse the better the correlation

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