Solve How does Linest calculate the error?

October 07, 2020 by Logan Oppen

 

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If the ranges of x and y values ​​overlap, the LINEST worksheet function generates incorrect values ​​in all result cells. Statistical normal probability prevents overlapping (duplication) of x and y range values. You can use the regression tool instead of the LINEST worksheet function.

 

 

Introduction

Linearity uncertainty (or linearity error or nonlinearity) is a source of uncertainty that should be included in most uncertainty budgets. This is a general specification published in the manufacturer's specifications for various types of measuring devices. However, I don't see this as often as I should in Uncertainty Budgets.



If you have a test or measurement function that spans a range of values, you may want to include linearity in your uncertainty analysis. For this reason, I thought it would be a good idea to develop a guide that shows you how to estimate linearity uncertainty step by step using Microsoft Excel.

What Is Linearity Uncertainty?

When you think about how meters work, you are probably assuming that the measurement efficiency is linear over the entire measurement range.

The measurement functions of most devices are non-linear. Instead, they are largely linear. So we try to fix them with coefficients and linear or Polynomial equations to make their performance more predictable.

Non-linear behavior is most commonly seen in many mechanical devices and physical materials. For example, here is a list of devices typically rated for linearity:

Whichever type of equipment you use, be sure to include linearity in your uncertainty analysis unless it is negligible or inadequate.

Why Is Linearity Uncertainty Important?

Linearity uncertainty is important because it allows for the effects of non-linear behavior in the measurement function. When using an equation to estimate uncertainty over a measuring range, you may need to consider estimating the uncertainty of linearity.

I often hear people say that linearity is not important or that it should not be included in the uncertainty budget. I say check it out and let the results speak for themselves.

If the result is small or insignificant, so much the better! You now have objective evidence to back up your argument.However, I would go on to add it to your uncertainty budget to prove that you are thinking.

If you cannot calculate linearity, read the manufacturer's manuals and specifications to determine if they are included in the specifications.

When Should Linearity Error Be Included?

If you plan to predict the measurement uncertainty of a given measurement range using a linear equation, you should include linearity in your uncertainty analysis.



When you estimate the uncertainty of a measurement over a measuring range, you usually estimate the uncertainty at the control points close to the minimum and maximum of the measuring range. Since your uncertainty analysis does not estimate the uncertainty at the points between the minimum and maximum values, you must consider the nonlinearity of the function.

In addition, many meters exhibit non-linear behavior below 10% of the measuring range. If you estimate the uncertainty for values ​​less than 10% of the measuring range, the more you will see non-linear behavior.the closer you get to zero.

Linearity Uncertainty Methods

Method 1: Maximum Deviation From Linearity

Method 2: Standard Error Due To Linearity

Standard error is the typical deviation from the linear behavior of a fitted row prediction equation (eg, regression, interpolation, B.F.S.L.).



Both methods assess deviation from linearity. The difference between the two methods is that one method evaluates the worst-case scenario and the other the most likely or most likely scenario.

Which Error Should Be Used: Maximum Or Standard

Maximum deviation method - most widely used Th method for assessing the uncertainty of linearity. Moreover, this is the most recommended method. If you decide to do some research, you are more likely to find information on the maximum deviation method.

When estimating linearity uncertainty, I prefer the standard error method. I think this is more applicable to uncertainty analysis and the development of the CMC uncertainty prediction equation, especially if I have already accounted for any bias or errors in my uncertainty analysis.


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When using the maximum deviation for linearity, be careful not to falsify results or overestimate the measurement uncertainty.


How does the Linest function work in Excel?

Description. LINEST calculates statistics for a string, using the least squares method to calculate the straight string that best fits your data, and then returns an array describing the string.


If you include bias or errors in your uncertainty analysis, you are more likely to overestimate your uncertainty using the maximum deviation method. Moreover, maximum deflection and preload can be the same result!

If you choose the standard error method, you are more likely to underestimate the measurement uncertainty ifand don't include bias in your uncertainty budget.

If you include bias in your uncertainty analysis, you are more likely to get a more accurate estimate of the measurement uncertainty by using the standard error for linearity uncertainty.

So use whichever method you like best. At the very least, if someone asks you a question, you should know what options are available to you and why you chose the method you chose.

Calculating Linearity Error

To calculate the linearity error, I will show you how to perform regression analysis in Microsoft Excel and find the maximum deviation and standard error.

Determine Linearity Uncertainty Using The Data Analysis Toolkit

This section shows you how to use a data analysis tool to determine the linearity uncertainty by following these four steps:



To calculate the linearity uncertainty, you need to perform regression analysis. To do this, you need to install Data Analysis Tool Pack on Microsoft Excel.

Since this add-in is built into Microsoft Excel, all you have to do is activate it. Follow these steps to activate the Data Analysis Toolkit:


and. Click on the "File" tab




b. Click Options (left)




vs. A new window will open. Click Add-Ins.




re. Use the drop-down menu at the bottom of the screen to select Excel Add-ins, and then click the Go button.

how does linest calculate error

 

 

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