In ordinary linear regression, the yi values are estimated from the xi values with error ɛi. In Deming regression, it is assumed that also the xi values are estimated with error.
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Reference
NCSS (2016)Â Deming regression
https://www.ncss.com/wp-content/themes/ncss/pdf/Procedures/PASS/Deming_Regression.pdf
Dear Dr. Zaiontz,
Hello again.
Is it possible to calculate prediction intervals and curves for the Deming Regression, using your tool?
I know I have to find a t value considering 95% confidence level and the degree of freedom related to my data, and also have to determine the standard errors of the prediction values.
Hello Waldemar,
See the following webpage for details about how to obtain predicted values, along with their standard error and 95% confidence interval.
https://www.real-statistics.com/regression/deming-regression/deming-regression-predictions/
Charles
Thank you very much Charles! I’ll have a look!
Waldemar
Dr. Zaiontz,
Good evening.
First of all, thank you very for the help put available in your website, specially the resource pack. I’m starting to use it to calculate and learn Deming Regression.
My questions is: should I have always two columns or more for X and Y? I tried to use the add-in entering just one column for X (mean of 3 replicates for each sample) values and one column for Y (mean of 3 replicates) and it did not work. Only when I entered all the values (3 columns 61 rows for X, 3 columns 61 rows for Y) I got the results. It also complained about one the cells being blank.
Regards,
Waldemar
Waldemar,
You can have one or more columns for X as well as for y. The case where there is one column for each is shown in Example 1, while the case for more than one column for X and Y is shown in Example 2.
If you email me an Excel file with your data and test results, I will try to figure out why it didn’t work in the case of one column for X and one column for Y. I can also see where there was a blank.
Charles
Dear Dr. Zaiontz,
Thank you for answering. I sent you a Excel file with Xi and Yi values(3 columns for the replicates each), as well as another two columns with the averages.
In the email I explain my objectives.
Thank you!
Waldemar
Dear Waldemar,
Thanks for sending this to me. I am just finishing up the next release of the Real Statistics software and will respond shortly after I issue the release.
Charles
Dear Charles,
Ok. I apreciate.
Thank you.
Waldemar
Dr, good evening, in Deming regression, in the case of two or more dependent variables (y), both must be the same type of response ?, or it is possible that based on the independent variables (x), two different answers (and), in which case we treat the model as a Deming regression?
Thank you very much
Gerardo,
I am not familiar with Deming regression with two or more dependent variables and so I am unable to answer your question.
Charles
Doc, thank you very much for your answer, I ask the question, because what happens is that I see in example 2, you use two dependent variables
Gerardo,
Yes, you are correct. I forgot about this case. I will answer your original question shortly.
Charles
Gerardo,
I am sure that you can perform Deming regression when the two types of responses are different, but I don’t know what this means for the interpretation of the results.
Charles
Ah, Ok Doc thank you very much
Weighted or unweighted Deming regression should I use if the variable X and Y are measured with either constant error nor proportional error? It only measured with random error.
Thank for your kind reply
All types of regression that I am familiar with are based on random error.
Charles
Very valuable site for Excel users. But I have a comment about the Deming regression formulas.
It seems that the variances in the x and y values (s^2 and t^2) should be written in terms of relative error, not absolute error. Otherwise, the Deming lambda is not dimensionless. Thus it would be possible to change the value of lambda merely by changing units of the x or y from, say, g to kg.
Mark,
Thanks for this insight. Do you have an easily available source that explains how to perform Deming regression in the manner that you are suggesting? Also how do you measure relative error? Are you referring to normalizing (i.e. standardizing) the data first?
Charles