How to Calculate Uncertainty in Polynomial Fit Parameters Using Excel?

In summary, James is asking how to get the uncertainty in the resulting parameters of a polynomial fit using EXCEL. They mention that the R^2 correlation coefficient can be used to determine the accuracy of the equation and can be outputted in EXCEL by selecting certain options in the "INSERT TRENDLINE" dialog box. They also warn that increasing the number of decimal places in the equation may improve the correlation between the regression and data. They then ask about performing a fit to data that should follow [csc(theta/2)]^4 and wonder if this is covered in a numerical methods book.
  • #1
JamesJames
205
0
I performed a fit, using EXCEL, to data and the fit gave me a polynomial. How do I get the uncertainty in the resulting parameters. For example the least squares fit gives y = Ax+B and there are equations to give the uncertainties in A and B. IS there a program that does this for non linear fits?

James
 
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  • #2
You'll want to output the R^2 correlation coefficient. The closer R^2 is to 1, the more accurate the equation is. I know excel can output it, but I'm not sure exactly how since I haven't used excel in a long time.
 
  • #3
In the "INSERT TRENDLINE" dialog box, there is a tab for options. At the bottom of the dialog box you will see three check boxes. "SET INTERCEPT TO 0," "DISPLAY EQUATION ON CHART" and "DISPLAY R^2 ON CHART." Select the ones you want.

Word of warning, if you check the equation output, you may have to increase the number of decimal places shown in the equation to get better correlation between your regression and the data.
 
  • #4
How about performing a fit to data that should obey [csc(theta/2)]^4. Would this be out of a numerical methods book or something?

James
 

What is polynomial fit using EXCEL?

Polynomial fit using EXCEL is a statistical method used to find the best-fit curve for a set of data points. It involves using the polynomial regression function in EXCEL to create a mathematical model that represents the relationship between the independent and dependent variables.

How do I perform a polynomial fit using EXCEL?

To perform a polynomial fit using EXCEL, you need to first organize your data into two columns, with the independent variable in one column and the dependent variable in the other. Then, select the data and go to the "Insert" tab, click on "Recommended Charts", and choose the "Scatter" chart type. Right-click on any data point in the chart and select "Add Trendline". From the options, choose "Polynomial" and enter the desired order for your polynomial fit.

What is the purpose of polynomial fit using EXCEL?

The purpose of polynomial fit using EXCEL is to find the best-fit curve for a set of data points. This curve can then be used to make predictions and analyze the relationship between the variables. It is often used in scientific research and data analysis to understand and model complex relationships between variables.

What is the difference between linear and polynomial fit using EXCEL?

The main difference between linear and polynomial fit using EXCEL is the type of curve that is fitted to the data. Linear fit uses a straight line, while polynomial fit uses a curved line. In general, a polynomial fit can capture more complex relationships between variables compared to a linear fit.

What is the degree of a polynomial fit using EXCEL?

The degree of a polynomial fit using EXCEL refers to the highest power of the independent variable in the polynomial equation. For example, a second-degree polynomial has a degree of 2, while a third-degree polynomial has a degree of 3. The degree of the polynomial fit can affect the accuracy of the model and should be chosen based on the complexity of the data and the desired level of accuracy.

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