How to program least squares in C for calculation methods

The least squares formula is a mathematical formula, which is called curve fitting in mathematics, and the least squares method mentioned here refers specifically to the linear regression equation! The formula for least squares is b=y(average)-a*x(average).

Calculation method: y = ax + b: a = sigma[(yi-y mean)*(xi-x mean)] sigma[(xi-x mean)]; b = y-means - a*x-mean.

The derivation process of the regression linear equation by the least squares method.

This is to distinguish the actual value of y (the actual value here is the true value of the statistic, which we call the observed value), when x takes the value (i=1,2,3......n), y is an approximate value (or the corresponding ordinate).

Its equation is called the regression linear equation of y vs. x, and b is called the regression coefficient. To determine the regression linear equation, we only need to determine a and the regression coefficient b.

Let the set of observations for x,y be:

i = 1，2，3……n

The regression linear equation is:

When x is taken as Lingqiao (i=1,2,3......n), the observed value of y is wide, and the difference depicts the degree of deviation between the actual observed value and the ordinate of the corresponding point on the regression line, as shown in the figure below

In fact, we want the total dispersion of these n dispersions to be as small as possible, so that the line can be closest to the known point. In other words, the process of finding the equation of the regression line is actually the process of finding the minimum value of the dispersion.

A natural idea is to add up the individual dispersions as the total dispersion. However, since the dispersion is positive and negative, the direct addition will cancel each other out, so it cannot reflect the closeness of these data, that is, this total dispersion cannot be expressed as the sum of n dispersions, as shown in the figure below

The general practice is that we use the sum of squares of the dispersion, i.e

as the total dispersion and make it to a minimum. In this way, the regression line is the one with the lowest value of q among all the lines. Since the square is also called the square, this method of making the sum of squares of the dispersion the smallest is called the least squares method.

The formula for finding a and b in a regressive linear equation using least squares is as follows:

where , is the mean of the sum, and the addition of " " above a and b indicates that it is an estimate obtained by the least squares method of the observed values, and after a and b are obtained, the regression linear equation is established.

Of course, we must not be satisfied with getting the formula directly, we can only remember it and use it well if we understand how the formula came about, so it is more important to give the derivation process of the above two formulas. Before giving the derivation process of the above formula, we first give the derivation process of the two key deformation formulas used in the derivation process. First of all, the first formula:

This is followed by the second formula:

Now that the basic deformation formula is ready, we can begin the derivation of the formula for the regression linear equation by least squares:

At this point, the deformation part of the formula <> ends, and we can see the last two terms from the final formula.

It has nothing to do with a and b, it is a constant term, and we only need it.

to get the smallest q value, thus:

The formula for least double multiplication is a y (averaging) b x (averaging).

Bai is studying the relationship between two variables (dux, y).

Usually you can get a series of pairs of data (x1, y1), (x2, y2)...xm，ym）；Plot these data in a Cartesian coordinate system of x y, and if you find that these points are near a straight line, you can make the equation for this straight line such as a y (average) b x (average). Where:

a, b are arbitrary real numbers.

The least squares formula is a mathematical formula in.

Du mathematically called curve fitting, and the least squares method mentioned here refers specifically to the linear back-attribution equation! The formula for least squares is b=y(average)-a*x(average).

Curve fitting, commonly known as pull curve, is a way to represent existing data into a number formula through mathematical methods. Scientific and engineering problems can obtain a number of discrete data by methods such as sampling, experiments, etc., and based on these data, we often want to get a continuous function (i.e., a curve) or a more dense discrete equation that matches the known data, a process called fitting.

The smallest multiplication formula of 111 gives 112 gets two, which should be one two gets two.

a=(n xy- x y) (n x 2-( x) 2)b=y(average)-a*x(average).

b is the intercept.

a is the slope.

I don't know, I'm sorry I couldn't help you, I hope a teacher can solve it for you.

Summary. Hello dear, the formula for least squares is a=y(average)-b*x(average). Least Squares (also known as least square) is a mathematical optimization technique.

It looks for the best function match for the data by minimizing the sum of squares of the error. Unknown data can be easily obtained by using the least squares method, and the sum of squares of the errors between these calculated data and the actual data is minimized.

Hello dear, the formula for least squares is a=y(average)-b*x(average). Least Squares (also known as least square) is a mathematical optimization technique. It looks for the best functional match for the data by minimizing the sum of the squares of the chain error.

The least squares method can be used to easily obtain the unknown data, and the sum of the squares of the errors between the obtained data and the actual data is the minimum barrage beam.

Extension: The manuscript segment of the ordinary least squares estimator has the above three characteristics: 1. Linear characteristics:

The so-called linear characteristic refers to the linear function of the estimated value of the sample observation, that is, the linear combination of the estimated value and the observed value. 2. Unbiased: Unbiased means that the expected value of the parameter estimator is equal to the overall real parameters.

3. Minimum variance: The so-called minimum variance refers to the smallest variance of the estimator compared with the estimator obtained by other methods, that is, the best. Minimal variance is also known as validity.

This property is known as the Gauss-Markov theorem. This theorem clarifies that ordinary least squares estimation of the divine quantity is optimal compared to any linear unbiased estimator obtained by other methods.

The formula for least squares is a y (average) b x (average).

When studying the interrelationship between two variables (x,y), it is common to obtain a series of pairs of data (x1,y1),(x2,y2)...xm，ym）；Plot these data in a Cartesian coordinate system of x y, and if you find that these points are near a straight line, you can make the equation for this straight line such as a y (average) b x (average). Where:

A and b are arbitrary real collapse numbers.