How to calculate the deviation of points from a curve?

In summary, the speaker is seeking advice on how to calculate the closeness of points to a curve in order to compare different types of curves. They mention using the root mean square distance and a chi-square test as potential methods.
  • #1
MelanieBrett
7
0
Hi,
I'm working on some coursework for which I have been modelling a curve to a set of points, and for the final section I am wanting to calculate how close each point is to the curve as a method of comparison between the curves I have calculated. Some of the curves are quadratic, and others are the Cartesian form of some Polar equations. If anyone could offer any help or advice, it would be much appreciated :)
 
Mathematics news on Phys.org
  • #2
You could try calculating the average distance of each set of points from the curve - perhaps better to look at the root mean square distance. Essentialy the standard deviation of the points from the curve.
 

1. What is the formula for calculating the deviation of points from a curve?

The formula for calculating the deviation of points from a curve is: d = y - f(x), where d represents the deviation, y is the actual value of the point, and f(x) is the corresponding value on the curve.

2. How do you interpret the deviation of points from a curve?

The deviation of points from a curve represents the difference between the actual value of a point and the value predicted by the curve. A positive deviation indicates that the point is above the curve, while a negative deviation means that the point is below the curve.

3. Can the deviation of points from a curve be negative?

Yes, the deviation of points from a curve can be negative. This means that the point is below the curve, and the actual value is less than the predicted value by the curve.

4. How do you find the average deviation of points from a curve?

The average deviation of points from a curve can be found by summing up all the individual deviations and then dividing by the total number of points. This gives an overall measure of how far the points are from the curve on average.

5. Are there any other methods for calculating the deviation of points from a curve?

Yes, there are other methods such as the root mean square deviation, which takes into account the magnitude of the deviations. Additionally, statistical methods like regression analysis can also be used to calculate the deviation of points from a curve and determine the relationship between the variables.

Similar threads

I Central Limit Theorem and fitting data
    • General Math
Replies
22
Views
3K
Analyzing Hysteresis Curve Fitting: Overfitting or Not?
    • MATLAB, Maple, Mathematica, LaTeX
Replies
9
Views
1K
I Best fit to an oscillating function
    • General Math
Replies
9
Views
1K
B Conversion of parametric form to polar for the rose curve
    • General Math
Replies
3
Views
2K
B Best fit curve associated with the combination formula
    • General Math
Replies
1
Views
942
B Reprise: Calculate the distance between two points without using a coordinate system
    • General Math
Replies
1
Views
235
A The abc conjecture and Virasoro algebra
    • General Math
Replies
1
Views
1K
B How can we accurately model data using curve fitting techniques?
    • General Math
Replies
4
Views
1K
Curve Matching Techniques for Rotated Curves in Geometric Analysis
    • General Math
Replies
1
Views
922
I Average of prime factors growth
    • General Math
Replies
12
Views
966

Hot Threads

Recent Insights

Back
Top