Quadratic least squares equation

In summary, the conversation is discussing finding the quadratic least squares approximating function g for the function f(x) = –3√x with a domain of 1 ≤ x ≤ 4. The goal is to minimize the integral of (f(x) - g(x))^2 using the function g(x) = a0 + a1x + a2x^2. The person is asking for help understanding how to minimize with respect to a0, a1, and a2 using partial derivatives.
  • #1
tza5021
5
0
f(x) = –3√x, 1 ≤ x ≤ 4
(a) Find the quadratic least squares approximating function g for the function f.

g(x)=?
 
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  • #2
The best fit function is clearly g(x)=-3/sqrt(x). But I'm guessing you trying to fit a function that's doesn't have that form. What kind of function are you trying to fit and what's the definition of 'least squares fit'?
 
  • #3
Using g(x)= a0+a1x+a2x^2 when 1<x<4
using intergral(f(x)-g(x)dx)
 
  • #4
If you could help that would be very much appreciated as I do not knw how to punch and chug that in an intergral.
 
  • #5
tza5021 said:
If you could help that would be very much appreciated as I do not knw how to punch and chug that in an intergral.

I think you want to minimize the integral of (f(x)-g(x))^2 don't you? Put in your f(x) and your g(x). It's not a hard integral. Just square it out. It's just powers of x. Then try to minimize with respect to a0, a1 and a2.
 
  • #6
How do I minimize the a0,a1 and a2 I do not get that part
 
  • #7
tza5021 said:
How do I minimize the a0,a1 and a2 I do not get that part

Use partial derivatives with respect to a0, a1 and a2. What should they be at a minimum? Didn't they teach you that part?
 
Last edited:
  • #8
Yes, but I missed the class. So could you tell me how to do that
 
  • #9
tza5021 said:
Yes, but I missed the class. So could you tell me how to do that

What should the partial derivatives be at a minimum? Missing the class means i) you could try to find the method yourself by looking it up or reading a book or even better, ii) thinking about it yourself.
 

1. What is a quadratic least squares equation?

A quadratic least squares equation is a mathematical formula used to find the best fit line through a set of data points. It is used to minimize the sum of the squares of the differences between the actual data points and the predicted values on the line.

2. When is a quadratic least squares equation used?

A quadratic least squares equation is used when the relationship between two variables is expected to be quadratic, meaning the data points form a curved shape rather than a straight line. It is commonly used in regression analysis and curve fitting.

3. How is a quadratic least squares equation calculated?

The equation is calculated by finding the coefficients that minimize the sum of the squared differences between the actual data points and the predicted values on the line. This is usually done using a computer program or calculator, using a process called the method of least squares.

4. What is the significance of the least squares method?

The least squares method is significant because it allows us to find the best fit line through a set of data points, providing a mathematical model to describe the relationship between the variables. This can be useful for making predictions and understanding the underlying patterns in the data.

5. What are the limitations of using a quadratic least squares equation?

A quadratic least squares equation assumes that the relationship between the variables is quadratic, which may not always be the case. Additionally, it may not accurately predict data points that fall outside of the range of the original data used to calculate the equation. It is also important to consider other factors and potential confounding variables when interpreting the results of a quadratic least squares equation.

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