Re: Fitting data on a vertical line

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg1565] Re: Fitting data on a vertical line*From*: rubin at msu.edu (Paul A. Rubin)*Date*: Sat, 24 Jun 1995 06:39:26 -0400*Organization*: Michigan State University

In article <3sd9dm$n5n at news0.cybernetics.net>, phpull at unix1.sncc.lsu.edu (Joe Wade Pulley) wrote: ->Hello, -> I have recently accidentally asked Mathematica to do a linear ->least squares fit to a set of data which were exactly vertically ->placed. Instead of giving me an error or an infinite slope, ->Mathematica spits out some sort of fit which is totally wrong. ->For example, if I make up a list of data which is similar to mine, I ->get the following results. -> -> -> ->In[1]:= ->ls={{2.1,3},{2.1,4},{2.1,5},{2.1,6},{2.1,7}} -> ->Out[1]= ->{{2.1, 3}, {2.1, 4}, {2.1, 5}, {2.1, 6}, {2.1, 7}} -> ->In[2]:= ->ft=Fit[ls,{1,x},x] -> ->Out[2]= ->0.924214 + 1.94085 x -> ->Obviously, this equation does not "fit" the data I have given. The ->equation x=2.1 would. Can anyone explain this very unusual behavior. The equation x=2.1 is not a linear model in x, which is what you requested. You are asking for "the" linear function of x which minimizes total squared error at the data points. Since all data points have the same abscissa (2.1), any linear function whose value at x=2.1 is 5 ties for least squared error. Note that the function coughed up by Fit qualifies (it evaluates to 5 at x=2.1). It happens that there are uncountably many possible OLS fits to this data. Why Fit chose that one is a mystery to me, but it is in fact a correct answer. Paul ************************************************************************** * 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