Determine dispersion from fitting equation

In summary, dispersion in the context of fitting equations refers to the degree of variation or spread of data points around the fitted curve or line. It is determined by calculating the difference between the actual data points and the predicted values from the fitted equation, and is used to assess the overall fit of the equation to the data. A lower dispersion indicates a better fit and a higher level of confidence in the results obtained from the equation. Dispersion can also be used as a measure of error in fitting equations and can be minimized by choosing an appropriate fitting method, adjusting parameters, and identifying and addressing any outliers in the data.
  • #1
mufc4ever
5
0
1. Homework Statement

Determine the dispersion (dn/d lambda) at a wavelength of 800 nm from fitting equation.


2. Homework Equations

Fitting equation from graph of n vs 1/lambda^2

y = 7e-15 x + 1.60


3. The Attempt at a Solution

Since it is a plot of n vs 1/lambda^2 I thought that x would be 1/lambda^2 so I took the derivative of that to get -2/lambda^3 and then put in the number. However I did not get a correct answer consistent with earlier findings.

What am I doing wrong?
 
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  • #2
You forgot the coefficient of x.
 

Related to Determine dispersion from fitting equation

1. What is dispersion in the context of fitting equations?

Dispersion in the context of fitting equations refers to the degree of variation or spread of data points around the fitted curve or line. It measures how well the fitted equation represents the data and how closely the data points cluster around the line.

2. How is dispersion determined from a fitting equation?

Dispersion is determined by calculating the difference between the actual data points and the predicted values from the fitted equation. This difference is known as the residual and is used to assess the overall fit of the equation to the data.

3. What is the significance of dispersion in fitting equations?

The dispersion of data points around the fitted equation indicates the accuracy and precision of the equation in representing the data. A lower dispersion indicates a better fit and a higher level of confidence in the results obtained from the equation.

4. Can dispersion be used as a measure of error in fitting equations?

Yes, dispersion can be used as a measure of error in fitting equations. It is commonly used to calculate the sum of squared errors (SSE) which is then used to determine the goodness of fit of the equation to the data.

5. How can dispersion be minimized in fitting equations?

Dispersion can be minimized by choosing an appropriate fitting method and adjusting the parameters of the equation to improve its fit to the data. Additionally, it is important to carefully select and examine the data to identify any outliers that may be contributing to the dispersion and consider removing or adjusting these data points.

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