Monday, March 2, 2009

Fitting a Line by Eye

You did fine on the latest Fathom "fitting line" homework. But I sensed a little confusion and I should make a few comments about fitting a line by eye.

Let's return to that homework problem where you are plotting the OBP of the baseball players for two consecutive years.

Here is a plot that many of you produced.

Is this a good graph? Actually, NO since there is too much white space around the points.

You can improve this in Fathom by using the hand tool to fill up the space. Here is a better plot.

Second, it is not easy to fit a movable line. To make this process easier, plot the movable line and then add a residual graph.

A good line will remove any tilt pattern in the residual graph. I still have a downward tilt in this graph - this suggests I have to try a little harder.

This looks better -- I don't see much of an increasing or decreasing pattern in the residuals.

Does my best fit correspond to a least-squares or resistant fit? (By the way, the resistant line is called a median-median line in Fathom.) I show all three lines below. Least-squares is blue, median-median is purple, and my line is brown.

It looks like my line is closer to the resistant fit.

Generally, when one has outliers, I would anticipate that my line would be closer to the resistant median-median line.

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