confidence interval - delta slope

[nitad54448]

Hi

I need to confirm something.  What is the output for the Ni_AALPro.lvlib:confidence interval (linear).vi as delta slope ? It is the calculated interval (based on the confidence level value, e.g.  +/- 3 ESD/sqr(N) for the 68 % confidence level) ? Thanks

N

[Steve__M. · Accepted solution]

Hi,

I'm not familiar with those VIs but after some research and if I understand well, I found a post that may answer your question : « The delta slope and delta intercept are all related to the confidence levels. The Linear Fit Intervals.vi when used in the 'Confidence' polymorphic setting will compute the confidence interval for the data provided.  This mean that it is going to calculate a range in which 95% of the data-set will fall within the range provided.

Normally when the Linear Fit Intervals VI is used for this, an original slope and intercept will be provided as inputs.  This is for y = m*x + b form equation of the line that 'best' matches the data (which can be acquired by the 'Linear Fit.vi' (not intervals).

The 'delta' slope and intercept give the values +/- from the original slope and intercept provided that will create this 'window' in which 95% of the data will reside.

For example, if the data was all over the place (a scatter plot, for example) and the 'Linear Fit.vi' was used for it, it will come up with some sort of line graph that will be 'closest' to all of the data.  This equation will have a y-intercept, and a slope.  For example purposes, lets say the equation is:  Y = 6x+3.  This means that the slope is 6 and it crosses the Y axis (X=0) at 3.  This will line up the 'best' with the data provided.  But, we are wanting to compute the Confidence Interval, which is the range in which 95% of the data will reside.  If the 'delta slope' was 1.4, and the 'delta intercept' was .6 then the resulting 'range' will essentially be:

Y = 6 (+/- 1.4) * x + 3 (+/-) .6

Which would yield in a graph which would look similar to the following:

 

Where the 'Black' line is the 'Linear Fit' for the data (scatter plot) and the two 'Blue' curved lines make up the 'range' or the Confidence Interval for the data.

This data is acquired by some fairly intense mathematics, and here are a few references with some equations:

http://faculty.cns.uni.edu/~campbell/stat/inf1.html

http://stattrek.com/AP-Statistics-4/Estimate-Slope.aspx?Tutorial=Stat

http://zone.ni.com/reference/en-XX/help/371361F-01/lvanlsconcepts/conf_pred_intervals/

http://zone.ni.com/devzone/cda/tut/p/id/6954 

http://zone.ni.com/devzone/cda/epd/p/id/1335  »

If this doesn't answer your request, please reformulate your question. 

Regards,

Message Edité par Steve M. le 29-10-2009 10:21 AM

[nitad54448]

hi

thanks for the answer. i understand the point about the confidence interval but my question is in the output of the delta slope or delta intercept. The confidence interval calculated (given a certain value 90%, 95% etc) is related to the standard deviation (and erf function) for a given confidence. As such the delta slope can also be expressed as the standard deviation of the slope; I want to be sure of what is the output...

I think my best bet is to get 4-5 pairs of points, calculate everything by hand and then compare with the output of the vi.

regards

N

[RipRock99]

Hi all,

I have been trying to figure out the answer to this question as well.  I think I understand what the NI routine is doing, but am unsure how to interpret the number it returns.  Specifically, many other linear fitting routines return the standard deviation of the slope, not the "delta slope".  For my data sets, I have been noticing that the delta slope for any given confidence level appears to be twice as big as my IDL LINFIT routines standard deviation. So I am assuming delta slope is the full width of the assumed gaussian distribution, not the half width usually defined (I think) as the standard deviation.  In short:

STDDEV = Delta Slope / 2

Does anyone know if this is correct?

Many thanks,

S- 

[nitad54448]

hi,

I don't know if delta means two times std dev, but you ,ay need to post a new thread since this one is markes as solved. For my case I just wrote a subvi doing all the calculations by myself.

regards