Question about Least Squares Fitting

A colleague showed me a plot of y vs. x data that he fit to a straight
line using linear least squares in Excel. It had a fairly low
correlation coefficient, about R^2 = 0.5. He wasn't quite happy with
the visual, qualitative fit of the straight line through his data
points. In particular there were some points at large x and y that the
straight line didn't go through. Not that it necessarily should have,
since there was a greater density of points at lower x and y.

Anyhow, he then did a fit of the same data points but plotting x vs.
y. The R^2 was similar. The straight line went a little differently
through the data, this time going through the extreme points that it
missed before. I noticed that if you inverted the y vs. x least
squares equation from the first fit to solve for x as a function of y,
the slope and intercept were somewhat different from what you got
directly from the fit of the x vs. y plot.

So we were wondering...If you consider just the data as points in
space and look at how the straight line goes through them, should you
expect a similar pattern if you just change the plot from y vs. x to x
vs. y. Is there something fundamental here about least squares
fitting, or is it an Excel thing?

Thanks.

.

Relevant Pages

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