Conditions for Straight Line Regression Analysis, Regression Straight Line Formula?

The formula is b=(n xiyi- xi· yi) [n xi2-( xi) 2],a=[(xi 2) yi- xi· xiyi] [n xi 2-( xi) 2], where xi and yi represent known observations.

There is another kind of "simple" to find a and b, and its formula is: b=(n xy- x· y), the regression straight line method is based on the historical data of the volume of business and capital occupation in several periods, and uses the principle of the least flat method to calculate the constant capital a and the variable capital b required for unit production and sales.

A regression straight line equation is a straight line that best reflects the deficit between x and y in a set of correlated variables (x and y).

The geometric significance of the dispersion is the difference between the ordinate y of the regression line corresponding to xi and the observed value yi, and its geometric significance can be described by the distance between the point and its projection in the vertical direction of the regression line. Mathematical expression: yi-y = yi-a-bxi

The total dispersion cannot be expressed as the sum of n dispersions, it is usually calculated as the sum of the squares of the dispersions, i.e., (yi-a-bxi) 2.

The formula for calculating the regression straight line method a,b is b=(n xiyi- xi· yi) [n xi2-( xi) 2],a=[(xi 2) yi- xi· xiyi] [n xi 2-( xi) 2], where xi and yi represent known observations.

There is another "simple" way to find a and b, and its formula is: b=(n xy- x· y), and the regression straight line method is based on the historical data of several periods of business volume and asset and auction money occupation, using the least flat method.

Principle: Calculate the constant capital A and the variable capital B required for unit production and sales.

Overview Analysis:

The regression straight-line method is based on a series of historical cost data, using the principle of the mathematical minimum talk about the hidden envy method, to calculate the straight-line intercept that can represent the average cost level.

and slope, which is used as a fixed cost.

and unit variable cost.

The regression straight line method is theoretically sound and the calculation results are accurate, but the calculation process is cumbersome. If you use a computer's regression analysis program to calculate the regression coefficients.

This shortcoming can be better overcome.

Regression analysis is an analytical method to study the relationship between the quantitative changes between the independent variable and the dependent variable, which is mainly through the dependent variable y and the independent variable xi(i1,2,3...).) to measure the ability of the independent variable xi to affect the dependent variable y, which can then be used to develop the dependent variable y.

Regression analysis includes: linear regression and nonlinear regression.

Linearity: The relationship between two variables is a one-time function - the image is a straight line, and the highest order term of each self-variation is 1

Linear regression is further divided into: univariate linear regression and multiple linear regression (the difference in the number of independent variables x).

2 Linear regression.

Conditions for linear regression.

Linear regression is a regression problem.

The opposite of regression is a classification problem, where the output set of variables y is finite, and the value can only be one within a finite set. When the output set of the variable y to be ** is infinite and continuous, we call it regression. For example, whether it will rain tomorrow is a matter of categorization; How much rain will fall tomorrow is a regression question.

There is a linear relationship between the variables.

Linearity usually refers to the fact that variables maintain equal proportions between them, graphically the shape between the variables is a straight line, and the slope is a constant. This is a very strong assumption that the distribution of data points presents complex curves that cannot be modeled using linear regression.

The error obeys a normal distribution with a mean of zero.

Error can be expressed as Error = Actual Value - **Value. This assumption can be understood in this way: linear regression allows for an error between the ** value and the true value, and the average error of these data is 0 as the amount of data increases; Graphically, the true values can be above or below a line, and when there is enough data, the data cancels each other out.

If the error does not follow a normal distribution with a mean of zero, then it is likely that some outliers have occurred.

Question: I can't remember the formula for finding a and b by the regression straight line method, can you give a good way to summarize it?

The formulas of A and B given in the textbook are too complex and really difficult to remember, so I will introduce you to the methods of easy memorization:

by y=a+bx:

Add y=a+bx n times at the same time to get y=na b x; Multiply y=a+bx by x at the same time to get xy ax bx2, and then add both sides of this equation n times at the same time to get xy a x b x2.

So let's make a system of equations:

y=na b x Qimeng xy a x b x2 When we do the problem, we first calculate the values of x, y, x2, xy, and then list the above equations, and solve the equations to know the group to find the values of a and b, so there is no need to memorize the formulas in the textbook. Quietly old.

Least Squares:

The total dispersion cannot be the sum of the n dispersions of Hongzhaoxiao.

to denote it, usually in terms of the sum of the squares of the dispersion, ie.

As the total dispersion, and make it to the minimum, so that the regression line is the one where q takes the minimum value of all straight lines, this method of making the "sum of squares of the dispersion minimum" is called the most shielded small squares:

Since the absolute value makes the calculation constant, in practical applications people prefer to use: q=(y1-bx1-a) +y2-bx-a )+yn-bxn-a).

In this way, the problem boils down to the fact that when a and b take what value q is the smallest, that is, the "overall distance guess file" of the straight line y=bx+a to the point is the smallest.

To find a,b in a regression linear equation using least squares, there is the following formula:

Regression to the method of finding a straight line.

Least Squares:

The total dispersion cannot be the sum of the n dispersions of Hongzhaoxiao.

to denote it, usually in terms of the sum of the squares of the dispersion, ie.

As the total dispersion, and make it to the minimum, so that the regression line is the one where q takes the minimum value of all straight lines, this method of making the "sum of squares of the dispersion minimum" is called the most shielded small squares:

Since the absolute value makes the calculation constant, in practical applications people prefer to use: q=(y1-bx1-a) +y2-bx-a )+yn-bxn-a).

In this way, the problem boils down to the fact that when a and b take what value q is the smallest, that is, the "overall distance guess file" of the straight line y=bx+a to the point is the smallest.

To find a,b in a regression linear equation using least squares, there is the following formula: