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What are the conditions for error to be minimum in least squares approximation?
Wiki User
∙ 12y ago
Let's start with a first degree polynomial equation:
This is a line with slope a. We know that a line will connect any two points. So, a first degree polynomial equation is an exact fit through any two points with distinct x coordinates.
If we increase the order of the equation to a second degree polynomial, we get:
This will exactly fit a simple curve to three points.
If we increase the order of the equation to a third degree polynomial, we get:
This will exactly fit four points.
if we have more than n + 1 constraints (n being the degree of the polynomial), we can still run the polynomial curve through those constraints. An exact fit to all constraints is not certain (but might happen, for example, in the case of a first degree polynomial exactly fitting three collinear points). In general, however, some method is then needed to evaluate each approximation. The least squares method is one way to compare the deviations.
Wiki User
∙ 12y ago
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What is the error propagation in numerical methods?
Error propagation in numerical analysis is just calculating the uncertainty or error of an approximation against the actual value it is trying to approximate. This error is usually shown as either an absolute error, which shows how far away the approximation is as a number value, or as a relative error, which shows how far away the approximation is as a percentage value.
Why is lower percentage error better?
I would have thought this blindingly obvious but no matter, a lower percentage error is better because it means your approximation to a solution is closer to the real answer than an approximation with a higher error.
Why is the residual sum of squares bigger then total sum of squares when there isn't a constant?
There is a calculation error.
Which statistic estimates the error in a regression solution?
The mean sum of squares due to error: this is the sum of the squares of the differences between the observed values and the predicted values divided by the number of observations.
Define error relative error and absolute error give examples of each?
Error is the term for the amount of difference between a value and it's approximation, and is represented by either an upper or lower case epsilon (E or ε)Eabs, absolute error, is |x-x*| where x* is the approximate of x, and gives a value that shows how far away the approximate is as a numerical valueErel, relative error, is |x-x*| / |x| and gives a value that shows how far away the approximate is as a decimal percentage i.e. if you times the relative error by 100 you get the percentage error of the approximation.
What is approximation error?
An approximation error is the discrepancy between an exact value and the approximation to it. This occurs when the measurement of something is not precise.
What is the error propagation in numerical methods?
Error propagation in numerical analysis is just calculating the uncertainty or error of an approximation against the actual value it is trying to approximate. This error is usually shown as either an absolute error, which shows how far away the approximation is as a number value, or as a relative error, which shows how far away the approximation is as a percentage value.
Why is lower percentage error better?
I would have thought this blindingly obvious but no matter, a lower percentage error is better because it means your approximation to a solution is closer to the real answer than an approximation with a higher error.
Why is the residual sum of squares bigger then total sum of squares when there isn't a constant?
There is a calculation error.
Which statistic estimates the error in a regression solution?
The mean sum of squares due to error: this is the sum of the squares of the differences between the observed values and the predicted values divided by the number of observations.
Define error relative error and absolute error give examples of each?
Error is the term for the amount of difference between a value and it's approximation, and is represented by either an upper or lower case epsilon (E or ε)Eabs, absolute error, is |x-x*| where x* is the approximate of x, and gives a value that shows how far away the approximate is as a numerical valueErel, relative error, is |x-x*| / |x| and gives a value that shows how far away the approximate is as a decimal percentage i.e. if you times the relative error by 100 you get the percentage error of the approximation.
What is compound error and what are sources of it?
A compounded error is an error caused by something which is unforeseen, such as extreme weather conditions.
Calculate pi using two whole numbers?
333/106 is a good approximation. The error is less than 0.003%
When will the unexplained variation or error sum of squares be equal to 0?
When all the data points are the same.
Is it possible for you to use trial and error method or the X-method to factor the difference of two squares?
No it is not. At least, not sensibly.
What is the minimum hamming distance if t-error correcting code?
2t+1
What is the minimum Hamming distance if a code t error corrrecting?
2T + 1
