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Re: Fit vs Regress

  • To: mathgroup at
  • Subject: [mg4356] Re: Fit vs Regress
  • From: rubin at (Paul A. Rubin)
  • Date: Thu, 11 Jul 1996 01:02:01 -0400
  • Organization: Michigan State University
  • Sender: owner-wri-mathgroup at

In article <4qqnlu$49m at>,
   "Prof. L. Seiford, IEOR, UMass, 413/545-1658" <SEIFORD at> 
->I received the following from a colleague. 
->I'm not that familiar with the package.
->Does anyone have an explanation?
->>Wayne and I are trying to do a little linear regression, and having 
->>What we want is to fit a linear form to 49 independent variables.  We 
succeed in
->>using the Fit[ ] function as follows:
->>  A = ReadList["test3624.mat", Number, RecordLists ->True]
->>  y = Array[x,49]
->>  z = Fit[A, y, y]
->>which results in
->>  z = 0.178173 x[1] + 0.178173 x[2] - 0.0380162 x[3] + 
->>      0.0713675 x[4] + 0.178173 x[5] ET CETERA ... x[49]
->>However, the Function Browser window shows us that we can load in the 
->>  <<"Statistics`LinearRegression`"
->>and use the Regress[ ] function. We tried this on a super-small data set 
->>without using any subscripting of the independent variables, and it 
->>nicely and gave us lots more data about the fit than Fit[ ] gives.
->>However, if we try the full data set with the subscripted variables as 
->>to wit:
->>  A = ReadList["test3624.mat", Number, RecordLists ->True]
->>  y = Array[x,49]
->>  z = Regress[A, y, y]
->>we get nothing but error messages, in spite of the fact that the 
->>browser suggests that Fit[ ] and Regress[ ] have identical input 
->>Any ideas?

Regress[ ..., ..., {x, y, z, ...} ] uses Function[ {x, y, z, ...}, ... ], 
in which the variables names from the regression equation are used as 
formal parameters to Function.  When the variable list has the form y = 
{x[1], x[2], ..., x[49]}, those formal parameters are actually function 
calls; e.g., x[1] is the (undefined) function x evaluated at argument 1.  
This is ok mathematically (after all, subscripting is just treating a 
symbol as a function of an integer argument), but syntactically it causes 
Function[] indigestion, hence the error messages.

One workaround is to type in the variable names they want:  y = {x1, x2, 
..}.  Another is to change y = Array[ x, 49 ] to y0 = 
Table[ Unique["x"], 49 ] both places it occurs in the call to Regress, 
which will give them 49 symbols of the form x$nnn (but not necessarily x$1, 
x$2, ...).  If that's a big deal, they can convert to the other notation 
after Regress gets done with

  Regress[ A, y0, y0 ] /. Thread[ Rule[ y0, y ] ]


* Paul A. Rubin                                  Phone: (517) 432-3509   *
* Department of Management                       Fax:   (517) 432-1111   *
* Eli Broad Graduate School of Management        Net:   RUBIN at MSU.EDU    *
* Michigan State University                                              *
* East Lansing, MI  48824-1122  (USA)                                    *
Mathematicians are like Frenchmen:  whenever you say something to them,
they translate it into their own language, and at once it is something
entirely different.                                    J. W. v. GOETHE


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