Difference between revisions of "SumSquaredErrors Command"

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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|statistics}}
 
<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|statistics}}
;SumSquaredErrors[ &lt;List of Points>, <Function> ]
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;SumSquaredErrors[ <List of Points>, <Function> ]
 
:Calculates the sum of squared errors, SSE, between the y-values of the points in the list and the function values of the x-values in the list.
 
:Calculates the sum of squared errors, SSE, between the y-values of the points in the list and the function values of the x-values in the list.
:{{example|1= If we have a list of points: L={A,B,C,D,E}  and have calculated for example: <code>f(x)=FitPoly[L,1]</code> and <code>g(x)=FitPoly[L,2]</code>, then it is possible to decide which of the two functions offers the best fit, in the sense of the least sum of squared errors (Gauss), by comparing: <code>sse_f=SumSquaredErrors[L,f]</code> and <code>sse_g=SumSquaredErrors[L,g]</code>.}}
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:{{example|1= If we have a list of points <code><nowiki>L={(1, 2), (3, 5),(2, 2), (5, 2), (5, 5)}</nowiki></code> and have calculated for example: <code>f(x)=FitPoly[L,1]</code> and <code>g(x)=FitPoly[L,2]</code>. <code>SumSquaredErrors[L,f]</code> yields ''9'' and <code>SumSquaredErrors[L,g]</code> yields ''6.99'', and therefore we can see, that ''g(x)'' offers the best fit, in the sense of the least sum of squared errors (Gauss).}}

Revision as of 08:18, 24 August 2015


SumSquaredErrors[ <List of Points>, <Function> ]
Calculates the sum of squared errors, SSE, between the y-values of the points in the list and the function values of the x-values in the list.
Example: If we have a list of points L={(1, 2), (3, 5),(2, 2), (5, 2), (5, 5)} and have calculated for example: f(x)=FitPoly[L,1] and g(x)=FitPoly[L,2]. SumSquaredErrors[L,f] yields 9 and SumSquaredErrors[L,g] yields 6.99, and therefore we can see, that g(x) offers the best fit, in the sense of the least sum of squared errors (Gauss).
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