Error of slope taking into account error of the data points

[cer144]

Hi!
I need to find the error of the slope of the line of best fit taking into
account the error of the individual data points. I have a fixed value for the
error of the points that I have figured out independently. (It's about .8 for
every point)
I have the error bars on, but excel isn't taking the error of the points
into account when determining the error of the slope! So...how do I solve
this? I don't necessarily need an excel function to do it for me, a formula
would be fine.
Thanks!

 

[Pete_UK]

The slope of a line is given by the change in y values divided by the
change in corresponding x values, i.e.:

slope = (y2 - y1) / (x2 - x1)

where x2,y2 is at one end of the line and x1,y1 is at the other end.
In your case the errors in the y values are plus or minus 0.8, so in
the worst two cases y2 may be +0.8 with y1 being -0.8, or y2 may be
-0.8 and y1 may be +0.8, so you could work out the two extremes from
this.

Hope this helps.

Pete

 

[cer144]

Thanks!! I'll try that, see if it's good enough for the boss lol.

 

[cer144]

Didn't work lol! It just changed the y-intercept!! Still need some help on
this one.

 

[Pete_UK]

Another thing about errors is that if you combine two (or more) values
with addition or subtraction to get a result, then the error in the
result is the sum of the errors in the two (or more) components.

However, if you combine using multiplication or division, then the
%age errors are added to give the cumulative error in the result.

Hope ths helps.

Pete

 

[Pete_UK]

What do you mean "it didn't work"? - I didn't tell you to do anything
in Excel. You have a (value for the) slope, so choose two points on
this line to give you the x1,y1 and x2,y2 values. Then using the
(mathematical) formula that I gave, you can work out a value for the
slope for one extreme, and then a value for the slope for the other
extreme - these represent the range in values that the slope can take,
and you can express that as an error range for the value of the slope
that you start with.

Hope this helps.

Pete