plotting confidence bands

[Mike]

Hi,

I conducted a number of fatigue tests on some steel specimens and am
in the process of plotting the data out on stress vs cycles to failure
curves.
I need to fit 95% confidence bands to the results after i had done
regression analysis to draw a least squares fit on the data...

As an example I have been looking at Example 1 in ASTM E739 on their
strain-life diagrams and fitting confidence bands to that...
The data they use in their example is pasted below..

strain cycles
0.01636 168
0.01609 200
0.00675 1000
0.00682 1180
0.00179 4730
0.0016 8035
0.00165 5254
0.00053 28617
0.00054 32650

The data needs to be plotted on log-log curve with strain on the Y and
cycles on the X.

The equation is of the form log N = A + B log e , where N is the
cycles to failure and S is the strain, since the life is dependant on
the strain.

My question is this, I can get the line of best fit, but how do I get
the upper and lower confidence bands...

From the above data Ahat=-0.24474 and Bhat=-1.45144
I can get confidence intervals for A and B of -0.6435<A<0.154 and
-1.6054<B<-1.2974 but I dunno what to do with these...
Firstly, I want to know at a strain of 0.01, how to work out the value
to add and subtract to Yhat so that I can work out the variance in the
number of cycles, and then how to get the rest of the values too.

Man that was long winded, and I apologise, but it's kind of urgent :/
If anyone has an idea please help Trying to plot it out in excel,
so that's why I asked in this group.

Cheers,
Mike.

 

[dvt]

I need to fit 95% confidence bands to the results after i had done
regression analysis to draw a least squares fit on the data...

Does this page help?

http://www.stfx.ca/people/bliengme/ExcelTips/RegressionAnalysisConfidence3.h
tm

Dave
dvt at psu dot edu

 

[Jerry W. Lewis]

Bernard is looking at calibration, which is a bit different. In his 2nd
formula, lose the |m| and the 1/k to get the confidence bound for the
fitted regession line. This should be centered on the fitted line, with
the critical t statistic given by =TINV(alpha,df) for a 2-sided 1-alpha
confidence interval.

Jerry

 

[Mike]

Bernard is looking at calibration, which is a bit different. In his 2nd
formula, lose the |m| and the 1/k to get the confidence bound for the
fitted regession line. This should be centered on the fitted line, with
the critical t statistic given by =TINV(alpha,df) for a 2-sided 1-alpha
confidence interval.

Jerry

Thanks to the both of you for your quick responses, it helped me to
work out what I needed, hopefully I've done it correctly in any case
:/ Haven't had much sleep lately, trying to get this thesis done, it's
overdue already

Mike.