To determine the regression linear equation ①, only a and regression coefficient b need to be determined, and the regression line is usually solved by the least square method: the deviation is the difference between the ordinate y of the regression line corresponding to xi and the observed value yi, and its geometric meaning can be described by the distance between a point and its projection in the vertical direction of the regression line. Mathematical expression: yi-y = yi-a-bxi. The total deviation cannot be expressed by the sum of n deviations, but is usually calculated by the sum of squares of deviations, that is, (yi-a-bxi) 2.
That is, as the total deviation, and minimize it, so that the regression straight line is the one that removes the minimum value from all the straight lines. This method of minimizing the sum of squares of deviations is called least square method. The formulas shown in Figure 1 and Figure 2 can be used for reference to find A and B in the regression linear equation by the least square method. Where sum is shown as the center of the sampling point.
Extended data:
The expression of linear equation:
1: The general formula: Ax+By+C=0(A and B are not 0 at the same time) is applicable to all straight lines.
,?
A1/a2 = b1/b2 ≠ c1/c2 ←→ Two straight lines are parallel.
A1/a2 = b1/B2 = c1/C2 ←→ Two straight lines coincide.
Cross intercept a=-C/A
Longitudinal intercept b=-C/B
2. Point skew: y-y0=k(x-x0) is suitable for straight lines that are not perpendicular to the X axis.
Represents a straight line with a slope of k and passing through (x0, y0).
3. Interception formula: x/a+y/b= 1 is applicable to straight lines that are not perpendicular to the origin or the X and Y axes.
Represents a straight line intersecting the X axis and the Y axis, with the X axis intercept a and the Y axis intercept b..
4. Oblique tangent formula: y=kx+b is suitable for straight lines that are not perpendicular to the X axis.
Represents a straight line with a slope of k and a y-axis intercept of b.
References:
Baidu Encyclopedia-Regression Linear Equation