What are the similarities and differences between goodness of fit and modified goodness of fit?

Goodness of fit. goodness of fit) refers to the degree to which the regression line fits the observations. The statistic that measures goodness-of-fit is the coefficient of determination (also known as the coefficient of certainty), and the range of values r is [0,1].

The closer the value of r 2 is to 1, the better the regression line fits the observations. Conversely, the closer the value of r 2 is to 0, the worse the regression line fits the observed value.

r measures the fit of the regression equation as a whole and is the expression of the dependent variable.

with all independent variables.

the overall relationship between them. r is equal to the ratio of the sum of squares of the regression to the sum of the total squares, i.e., the percentage of variability of the dependent variable that the regression equation can explain. Actual vs. average.

In the total error, the regression error and the residual error are the trade-off relationship. Therefore, the regression error determines the goodness-of-fit of the linear model from the front, and the remaining error determines the goodness-of-fit of the linear model from the negative side.

Statistically defines the residual error divided by degrees of freedom.

The square root of the quotient obtained by n 2.

It is an estimation of standard error. In order to judge and evaluate the goodness of fit of the regression model, the estimation standard error is obviously not as good as the judgment coefficient is dimensionless coefficient, and there is a definite value range (0-1), which is convenient for comparing the goodness of fit of different data regression models. However, the estimation of standard error has a unit of measurement, and there is no definite range of values, which is not convenient for comparing the goodness of fit of different data regression models.

Applications and Interpretations of Finance:

Goodness-of-fit is a statistical term that measures the difference between the expected value of a financial model and the actual value obtained.

It is a statistical method applied to areas such as finance and is based on the observations obtained. In other words, it's a measure of how the actual observed values are simulated. [1]

Adjust goodness-of-fit: Sometimes you don't need to pay much attention to goodness-of-fit, and the economic implications of econometric equations are far more important than statistical significance. As long as the economic implication is correct, we still think that a low goodness-of-fit is telling.

Of course, you can also correct for heteroskedasticity, autocorrelation, or logarithms.

and other ways to improve the model.

It is also important to note that variables should not be added to the econometric analysis, as the adjusted goodness-of-fit may decrease while the adjusted goodness-of-fit may occur, and multi-collinear problems may occur.

The correction is to put the variance in the calculation.

The lost degrees of freedom are excluded.

The correction is to exclude the degrees of freedom lost in calculating the variance.

Goodness of fit. The formula for calculating r2 is r2=1-"regression to the ratio of the sum of squares to the total sum of squares;

The closer the value of r 2 is to 1, the better the regression line fits the observations. Conversely, the smaller the value of r, the worse the regression line fits the observations. Refers to the degree to which the regression line fits the observation. The statistic that measures goodness-of-fit is the coefficient of determination (also known as the coefficient of certainty) r.

r The maximum value is 1.

The goodness-of-fit test is for the whole model, taking the model y=10m+2n as an example, the goodness-of-fit test has the statistics r of the real value (or experimental value) y and the calculated value of the model y* (using the model y=10m+2n, input (m,n) to obtain the calculated value of the model y*) to estimate the degree of fit between the whole model and the actual situation. To put it simply, it is to compare the real value and the calculated value to see if the whole model is good.

The t test is to see whether the single parameter is significant, that is to say, whether it is 0, taking the model y=10m+2n as an example, through the coefficients of m and n, here is the t-test statistics of 10 and 2 are calculated, if it is significant, it means 10, or 2, not 0, if it is not significant, it means that 10 or 2 may be 0, so that one variable of the model may be problematic, for example, 10 may be 0, then m may be removed from the model.

1. The goodness-of-fit test is a test of the overall degree of fit of the regression results, and the higher the goodness-of-fit, the more consistent the relationship between the independent variable and the dependent variable described by the regression equation is with the actual situation.

2. The significance test of the variable refers to the t-test of the coefficients of the independent variables of the equation within a certain confidence range after obtaining the regression equation, if the test result is within the confidence range, the coefficient is considered credible and can be used to describe the relationship between the independent variable and the dependent variable, otherwise it is not significant.

"Goodness-of-fit" meaning: It is used in regression analysis to test the density of sample data points gathered around the regression line, and is used to evaluate the degree to which the regression equation fits the sample observations.

1. Origin of goodness of fit:

1. When British statisticians studied the relationship between the height of the father and the height of his adult son, he found a straight line running through it from the scatter plot of a large number of sample observations, which can describe the relationship between the height of the father and the adult son. This phenomenon is called a "regression", and the line that runs through the data points is called a "regression line".

2. Of course, it was also found that even if the fathers were all the same height, their adult sons were not the same height. This is to say: the difference in the height of an adult son is affected by two factors: one is the influence of his father's height; The other is the influence of other random factors.

3. Then, we can understand that the difference between the slips of the observed values of the explanatory variable y in the "regression equation" is also caused by two reasons: one is caused by the different values of the explanatory variable x; The second is caused by other random factors.

2. Understanding of goodness of fit.

1. The goodness-of-fit test of the regression equation is essentially a descriptive characterization, which does not involve the inference of the overall relationship between the explanatory variable and the explanatory variable.

2. Then, for models with different signals, the greater the goodness of fit, the better. But, on the other hand, how acceptable is the goodness of fit? This different discipline often has different conventions and standards, some say that it is almost common in sociology, and some say that the goodness of fit is as high as above at every turn, which makes people questionable; Moreover, different sample observations will also get different values, and in terms of goodness of fit for regression analysis, the same model can achieve it, but it can only be achieved by itself.

However, in general, if the goodness-of-fit is exceeded, then there should be no need to worry too much, because we should not simply use the goodness-of-fit as the criterion for judging the quality of the model, but should pay more attention to the rationality of the model setting.