Re: Can straight line est fit with error measure be made in single pass?

It would be nice if one could make do with a non-copyable forward
iterator for the (x,y) data points, without storing the points.

However, my current code requires the ability to iterate a second time,
from a copy of the start iterator.

Any suggestions for how to avoid the second iteration, or should I
perhaps just forget it (I only need this to check algorithm complexity
in unit test, so it's not a current problem, just "not ideal" code...)?

[code]
#pragma once
// Copyright (c) 2013 Alf P. Steinbach

// <url:
http://terpconnect.umd.edu/~toh/spectrum/CurveFitting.html#MathDetails>
// n = number of x,y data points
// sumx = ??x
// sumy = ??y
// sumxy = ??x*y
// sumx2 = ??x*x
// meanx = sumx / n
// meany = sumy / n
// slope = (n*sumxy - sumx*sumy) / (n*sumx2 - sumx*sumx)
// intercept = meany-(slope*meanx)
// ssy = ??(y-meany)^2
// ssr = ??(y-intercept-slope*x)^2
// R2 = 1-(ssr/ssy)
// Standard deviation of the slope = SQRT(ssr/(n-2))*SQRT(n/(n*sumx2 -
sumx*sumx))
// Standard deviation of the intercept =
SQRT(ssr/(n-2))*SQRT(sumx2/(n*sumx2 - sumx*sumx))
//
// Also, <url: http://mathworld.wolfram.com/LeastSquaresFitting.html>

#include <rfc/cppx/calc/Statistics.h> // cppx::calc::Statistics

namespace cppx{ namespace calc{

     class Best_line_fit
         : private Statistics
     {
     private:
         double intercept_;
         double slope_;
         double ssy_; // Sum of squares of y-expressions
         double ssr_; // Sum of squares of residue expressions

     public:
         auto stats() const -> Statistics const& { return *this; }

         auto slope() const -> double { return slope_; }
         auto intercept() const -> double { return intercept_; }

         auto ssy() const -> double { return ssy_; }
         auto ssr() const -> double { return ssr_; }
         auto r_squared() const -> double { return (ssr_ == 0 || ssy_
== 0? 1.0 : 1.0 - ssr_/ssy_); }
         auto r() const -> double { return sqrt( r_squared()
); }

         template< class It >
         Best_line_fit( It const first, It const end )
             : Statistics( first, end )
             , ssy_( 0.0 )
             , ssr_( 0.0 )
         {
             slope_ = (n()*sum_xy() - sum_x()*sum_y()) / (n()*sum_xx() -
square( sum_x() ));
             intercept_ = mean_y() - slope_*mean_x();

             for( It it = first; it != end; ++it )
             {
                 double const x = x_of( *it );
                 double const y = y_of( *it );

                 //ssy_ += square( y - mean_y() );
                 ssr_ += square( y - (slope_*x + intercept_) );
             }
             ssy_ = sum_yy() - 2*sum_y()*mean_y() + n()*square( mean_y() );
         }
     };

} } // namespace cppx::calc
[/code]

Disclaimer 1: I do not KNOW that the code is correct, in particular the
r_squared() implementation.

Disclaimer 2: In the mathworld reference I do not understand eq. 17.