Trent Introductory Physics Lab
Slope and intercept uncertainty
Slope and intercept uncertainty in Excel, OpenOffice Calc and Apple Numbers
Microsoft Excel and OpenOffice Calc have a built in formula called Line Statistics which calculates slope,
intercept, uncertainty in the slope and uncertainty in the intercept.
Enter the X axis data in one column and the corresponding Y axis data in an
adjacent column
Here, 9 pairs of (X,Y) data points are entered in columns A and B.
We will be using the LINEST formula which is an array output formula. That is, the results span several
cells.
Move to an empty cell and enter the LINEST formula
=LINEST(known Y value cells, known X value cells, 1, true)
For this example the known Y value cells are B1:B9 and the known X value cells are A1:A9. You can type
the ranges in or use the cursor to highlight the cells.
The “1” forces the intercept to be calculated normally and the “true” forces full statistics reporting.
For this example then the formula entered in cell A11 will be
for Excel = LINEST (B1:B9,A1:A9,1,TRUE)
for OpenOffice = LINEST (B1:B9;A1:A9;1;TRUE) semicolons instead of commas
Now press
for Excel <ENTER>
for OpenOffice press <CTRL>+<SHIFT>+<ENTER>
Line slope and intercept
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Trent Introductory Physics Lab
Slope and intercept uncertainty
for Excel only: After entering this formula cell A11 contains only the slope value.
In order to see the full statistics, a 2x5 cell area must be selected for the formula
output.
Select a 2x5 cell area starting with the formula cell by clicking the left mouse
button and dragging from cell A11 (the formula cell) to cell B15.
Press F2, and then press <CTRL>+<SHIFT>+<ENTER>
The values of interest
are in the top 4 cells
Here the slope is 9.977099  0.464593 and the intercept is 0.782443  2.629275
Reformatted correctly (one significant digit in the uncertainty and rounding the value to match the
accuracy of the uncertainty), the slope is 10.0  0.5 and the intercept is 1  3
for Excel:
If the cell [=LINEST …] is edited and you want to refresh the calculation, press
<CTRL>+<SHIFT>+<ENTER> after editing (i.e. do not just press <ENTER>).
for OpenOffice:
In order to edit the =LINEST… formula you must select the 2x5 cell area of the formula output. Then,
press <CTRL>+<SHIFT>+<ENTER> after editing (i.e. do not just press <ENTER>).
Apple Numbers
The LINEST function in Numbers from Apple is an array function and each element in the array is
accessed with the “INDEX” function.
If the X values are in cells A21:A30 and the Y values are in cells B21:B30 then the slope value is accessed
with:
=INDEX(LINEST(B21:B30, A21:A30, 1, TRUE), 1, 1)
Line slope and intercept
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Trent Introductory Physics Lab
Slope and intercept uncertainty
Similarly, the error or uncertainty in the slope value (±δslope) is accessed with:
=INDEX(LINEST(B21:B30, A21:A30, 1, TRUE), 2, 1)
More help can be found at:
http:// http://help.apple.com/functions/mac/3.0/#ffa5a58341
Thanks to Joel Fifield for researching this.
Line slope and intercept
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