The 'Box' method is a fast and simple way of determining the uncertainty or error in the slope and intercept of a linear plot. When a plot is made of several points, under experimental conditions in the laboratory, usually there is some amount of scattering. The scattering is usually about some best straight line, drawn so that there is equal (as best as possible) scatter on both sides of it.

For the above plot, which has six (6) points, the best straight line is shown by the line

At this point it would be good to note that if one or two points seem to be very far off the best straight line then it may be possible to 'exclude' them. Tests on significance can be run to determine whether these points, called 'outliers', can be legitamately ignored.

The next step is to find the gradient of the lines forming the diagonals of the 'box'. The line

If the slope of the best straight line has a value of

Similarly, if the value of the intercept is

n = number of points enclosed in the 'box'.

The fractional error in the slope is given by

If you are using

- Enter the X and Y values for which you wish to do the analysis
- Highlight a range for the output of the analysis (This should be 2 columns wide and 4 rows deep and away from your X,Y points)
- enter the formula for LINEST.

For example, =LINEST(b2.b12,a2.a12,TRUE,TRUE)

then hit the Control,Shift,Enter keys simultaneously - the slope and intercept are in the first row of the output and the error in the slope and the intercept are in the second row of the output. The correlation coefficient is in the third row.

The output will show only the slope and intercept and not the errors or correlation coefficient.

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Copyright © 2006 by Robert John Lancashire, all rights reserved.

Created and maintained by Prof. Robert J. Lancashire,The Department of Chemistry, University of the West Indies,

Mona Campus, Kingston 7, Jamaica. Created Nov 2002. Links checked and/or last modified 14th March 2006.