lack of fit
tancho
I have made a calibration curve and I have determined the lack of fit
with excel.
Can someone check this file because Fcal > Ftab and I have doubts.
Thx
Xt
Can you explain more clearly what you did?
xt
Phil Sherrod
--
Phil Sherrod
http://www.dtreg.com -- Neural networks, SVM, Decision trees
tancho
Can I attach the file ?
tancho
> OK, post the data you want calibrated.
>
> --
X Y1 Y2 Y3
64,99468998 0,88796 0,88799 0,88799
68,00154953 0,88037 0,88039 0,88043
68,98511957 0,87776 0,87781 0,87785
69,9900 0,87519 0,87517 0,87528
70,9924937 0,87270 0,87269 0,87270
71,99872723 0,87006 0,87007 0,87008
75,00927914 0,86218 0,86218 0,86221
SS df MS
Fcal Ftab
Lack of fit 8,78176E-08 5 1,75635E-08 17,23522221 2,96
Pure error 1,42667E-08 14 1,01905E-09
Multiple R 0,999957355
R Square 0,999914712
Adjusted R Square 0,999910223
Standard Error 7,32998E-05
Observations 21
df SS MS F
Significance F
Regression 1 0,001196828 0,001196828 222754,6437 3,98402E-40
Residual 19 1,02084E-07 5,37285E-09
Total 20 0,00119693
Coefficients Standard Error t Stat P-value Lower
95% Upper 95% Lower 95,0% Upper 95,0%
Intercept 1,055415349 0,000382186 2761,520407 1,05483E-54
1,054615424 1,056215274 1,054615424 1,056215274
X Variable 1 -0,002574763 5,45537E-06 -471,9689012
3,98402E-40 -0,002586181 -0,002563345 -0,002586181 -0,002563345
Xt
> On 3 nov, 02:03, "Phil Sherrod" <PhilSher...@NOSPAMcomcast.net> wrote:
>
> > OK, post the data you want calibrated.
>
> > --
This is what I get -
ANOVA df SS MS F Significance F
Regression 1 0.001196832 0.001196832 232100.987 2.69623E-40
Residual 19 9.79738E-08 5.15652E-09
Lack of Fit 5 9.08405E-08 1.81681E-08 35.65700203 1.74966E-07
Error 14 7.13333E-09 5.09524E-10
Total 20 0.00119693
which differs from yours because the SS residual is a bit different.
However, the conclusion is the same - there is a lack of fit. The
line looks straight, but the points are so accurate the means are off
the line more than would be exoected just by chance.
xt
tancho
> On Nov 4, 2:54 am, tancho <tanch...@hotmail.com> wrote:
>
>
>
>
>
> > On 3 nov, 02:03, "Phil Sherrod" <PhilSher...@NOSPAMcomcast.net> wrote:
>
> > > OK, post the data you want calibrated.
>
> > > --
>
> > X Y1 Y2 Y3
> > 64,99468998 0,88796 0,88799 0,88799
> > 68,00154953 0,88037 0,88039 0,88043
> > 68,98511957 0,87776 0,87781 0,87785
> > 69,9900 0,87519 0,87517 0,87528
> > 70,9924937 0,87270 0,87269 0,87270
> > 71,99872723 0,87006 0,87007 0,87008
> > 75,00927914 0,86218 0,86218 0,86221
>
> > SS df MS
> > Fcal Ftab
> > Pure error 1,42667E-08 14 1,01905E-09
>
> > Multiple R 0,999957355
> > R Square 0,999914712
> > Adjusted R Square 0,999910223
> > Standard Error 7,32998E-05
> > Observations 21
>
> > df SS MS F
> > Significance F
> > Regression 1 0,001196828 0,001196828 222754,6437 3,98402E-40
> > Residual 19 1,02084E-07 5,37285E-09
> > Total 20 0,00119693
>
> > Coefficients Standard Error t Stat P-value Lower
> > 95% Upper 95% Lower 95,0% Upper 95,0%
> > Intercept 1,055415349 0,000382186 2761,520407 1,05483E-54
> > 1,054615424 1,056215274 1,054615424 1,056215274
> > X Variable 1 -0,002574763 5,45537E-06 -471,9689012
> > 3,98402E-40 -0,002586181 -0,002563345 -0,002586181 -0,002563345
>
> This is what I get -
> ANOVA df SS MS F Significance F
> Regression 1 0.001196832 0.001196832 232100.987 2.69623E-40
> Error 14 7.13333E-09 5.09524E-10
> Total 20 0.00119693
>
> which differs from yours because the SS residual is a bit different.
> line looks straight, but the points are so accurate the means are off
> the line more than would be exoected just by chance.
>
> xt
OK, Thx
Can I accept this calibration or do I change the regression into Y =a
+ bx + cx² ?
I'm validating this method & all other methods that I have validated
the lack of fit was not significant.
Which software do you use to calculate Lack of fit ?
I have also another question, I don't want to de the calibration befor
each measurement but I just want to verifie with
tancho
> Which software do you use to calculate Lackoffit?
> each measurement but I just want to verifie it with a standard solution.
What is max. allowed deviation (statistically calculated) of obtained
value compared to the real value of this standard solution to declare
that the calibration is still ok
Xt
>
> - Show quoted text -
In this instance, I just used Excel regression from the Analysis
Toolpack and then split the residual error up into pure error and lack
of fit error by hand. The small differences in our results may be due
to something in the process of getting the data from your spreadsheet
to this posting and over to my spreadsheet. You use commas, for a
start where I use decimal points.
As to whether to use the quadratic version, this depends on whether or
not the linear version is accurate enough for your purposes and this
is a practical question, not a statistical one. The values you give
are remarkably accurate. Are you really measuring things like
64.99468998 to 10 sig figs and is it important to have this accuracy
in your final results?
cheers
xt
tancho
> to something in the process of getting the data from your spreadsheet
> to this posting and over to my spreadsheet. You use commas, for a
> start where I use decimal points.
>
> As to whether to use the quadratic version, this depends on whether or
> not the linear version is accurate enough for your purposes and this
> is a practical question, not a statistical one. The values you give
> are remarkably accurate. Are you really measuring things like
> 64.99468998 to 10 sig figs and is it important to have this accuracy
> in your final results?
>
> cheers
>
> xt
You are right, X values % V/V are calculated values from %W/W 2
figures after the digit.
64,99
64,99
64,99
68
68
68
68,99
68,99
68,99
69,99
69,99
69,99
70,99
70,99
70,99
72
72
72
75,01
75,01
75,01
If I determin the lack of fit on the quadatric version , the pure
error & df of pure error rest the same I think but what about df of
lack of fit ?
Xt
>
> - Show quoted text -
The pure error is calculated from the replicates alone. You have 7
points with three replicates each. Each point estimates the pure
error with 3-1 = 2 df so yes, the pure error has 7x2=14 df. The SS
pure error is also the same as before. You can get these by getting
the variance and df for each point, multiply the variance by the df to
get the SS for that point, then add to get the SS pure error. This
will work for unequal reps too. The regression has one more df for
the quadratic term, so that will now be 2 df and the lack of fit df
will be one less, at 4 df to give a grand total of 21-1 = 20. So, do
the quadratic regression on the 21 points and get the residual SS and
18 df. Split the SS residual and its df into two by lack of fit =
residual - pure. Do the F test by comparing the lack of fit with the
pure with 4 and 14 df.
This is all a bit quick because I'm assuming that you have a
reasonable knowledge of regression and its connection to anova. If
you want me to slow down, just say.
cheers
xt
tancho
> > error & df of pure error rest the same I think but what about df of
>
> > - Show quoted text -
>
> The pure error is calculated from the replicates alone. You have 7
> points with three replicates each. Each point estimates the pure
> error with 3-1 = 2 df so yes, the pure error has 7x2=14 df. The SS
> pure error is also the same as before. You can get these by getting
> the variance and df for each point, multiply the variance by the df to
> get the SS for that point, then add to get the SS pure error. This
> will work for unequal reps too. The regression has one more df for
> the quadratic term, so that will now be 2 df and thelackoffitdf
> will be one less, at 4 df to give a grand total of 21-1 = 20. So, do
> the quadratic regression on the 21 points and get the residual SS and
> 18 df. Split the SS residual and its df into two bylackoffit=
> pure with 4 and 14 df.
>
> This is all a bit quick because I'm assuming that you have a
> reasonable knowledge of regression and its connection to anova. If
> you want me to slow down, just say.
>
> cheers
>
> xt
Xt
>
> - Show quoted text -
Sure. Let me know if my "Reply to author" doesn't arrive.