🚀 go-pugleaf

In article <1992Sep9.150541.15735@cbfsb.cb.att.com> rizzo@cbnewsf.cb.att.com (anthony.r.rizzo) writes:

(description of polynomial regression problem greatly abstracted by current
poster)

>with which the data were collected was zeroed at 20 C.  So, the
>curve, ideally, should pass through (20,0).  

>Two options are available to me.  First, I can simply change the
>value of the constant term in my polynomial, so as to shift
>the curve up or down by the required amount.  But this will give
>me a new curve that DOES NOT minimize the squares of the errors.

Right you are. Don't do this, you don't have to.

>Second, I can re-derive the equations such that the fitted curve
>is CONSTRAINED to pass through (20,0). . . .

You can easily do this by recoding the predictors and running the regression
without an intercept term. Instead of X, X**2, X**3, X**4, create a new
predictor Q = X - 20, and run your regression on Q, Q**2, Q**3, and Q**4.

Run it with the intercept term first. Check the partial t-statistic for the
intercept term. If it's not statistically significant, it should be okay to
run the regression again, this time without the intercept. You'll get the
answer you want.

You can expand the polynomial in Q to get a polynomial in X without
too much trouble; it's only fourth degree.

> Now my questions:  

>1) Is this legitimate, or am I just whistling Dixie?  

It is completely legitimate to recode the predictors in any way you like.
You must be careful when you recode the response. You only need to recode
the predictors in this case. (What's wrong with "Dixie"? Don't you like
Dan Emmett?) Be sure to test the significance of the intercept term, though.
If it is significant, it indicates either (a) lack of fit, or (b) the
system drifted during the process, rendering the zeroing at 20 degrees
invalid. (If you made subsequent measurements at 20 degrees throughout the
process you can get an idea of how likely (b) is.)

>2) Is this a common thing to do?  If so, any references?

Sure, it's common. It's so common, I do it without even thinking too much
about it, so I don't have a reference for you. Sorry!

==Doctor FORTRAN