|Disclaimer: The information on this page has not been checked by an independent person. Use this information at your own risk.|
Click arrows to page adverts
In an experiment it is normal to obtain a number of data points (x,y) on a graph.
It is generally required to find a line that best fits these points and thus resulting
in a nice rule that can be reasonably applied to the experimental results. This
is most often done by simply drawing a line on the graph paper by eye using judgement.
To achieve this with a little more precision a statistical process called linear regression is used.
Consider a set of n data point (xi ,yi) ). In general the best fit line will not intersect a data point and the following relationship applies.
y i = m xi + b + e i
Where e i = y i - y. This makes a reasonable assumption that x = x i i.e there is no error on the x value.
The sum of the deviations is
To obtain the best fit line involves minimising ε requiring
On calculating a best fit line it is useful to determine if the line is a corrleation with the points . If the points are scattered all over the xy plane then the correlelation is poor. If the points are all located along the best fit line then the correlation is good. The equation for the correlation r =
sx and sy are the standard deviations of the x and y sample points.
Useful Related Links
Send Comments to Roy Beardmore
Last Updated 19/04/2008