Why does goodness of fit have a negative value?

I read it for 20 minutes, and I still don't understand it.

"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.

Summary. Goodness-of-fit (also known as coefficient of determination or r-squared) is a metric that evaluates the degree of fit of a regression model and can range from 0 to 1. It represents the proportion of variance of the dependent variable explained by the model.

Ideally, goodness-of-fit should be greater than or equal to 0, and closer to 1 the better. If the goodness-of-fit is less than 0, it means that the model fits the observed data worse than the simple average. However, in practice goodness-of-fit less than 0 is very rare and usually occurs when the model does not fit the data or the wrong regression formula is used.

If you encounter a goodness-of-fit of less than 0 in your application, you may need to re-check the model methodology, the validity of the data, or other relevant factors.

Can you elaborate on that a little bit more?

Pro, the degree of fit optimum imitation (also known as the coefficient of determination or the square of the paratonic fiber r) is an index to evaluate the degree of fit of the regression model, and its value ranges from 0 to 1. It represents the proportion of variance of the dependent variable explained by the model. Ideally, goodness-of-fit should be greater than or equal to 0, and closer to 1 the better.

If the goodness-of-fit is less than 0, it means that the model fits the observed data worse than the simple average. However, in practice goodness-of-fit less than 0 is very rare and usually occurs when the model does not fit the data or the wrong regression formula is used. If you encounter a goodness-of-fit score of less than 0 in your practical application, you may need to re-check the model construction method, the validity of the data, or other relevant factors.

Goodness-of-fit is one of the important indicators to evaluate the fitting degree of linear regression model, which reflects the best ability of the model. When calculating goodness-of-fit, we introduced the mean of y as a reference. This is because, in regression, we need to compare the actual value to the value, and the average of y can be used as a benchmark.

By comparing each actual value to the mean of y, we can calculate the sum of squares of the errors and use it to assess how well the model fits.

On the other hand, the flat mean of y can also help us understand the distribution of the data. If each actual value is equal to the average of y, then the data is completely randomly distributed. In real life, data is often not completely randomly distributed, but there is some kind of trend or pattern.

By calculating the sum of squares of errors, we can model this trend or law and use the model to generate future data.

When calculating goodness-of-fit, we also need to consider the number of degrees of freedom. Degrees of freedom refers to the number of parts of an independent variable that can be freely changed. **In sexual regression, the degrees of freedom are equal to the sample size minus 1.

By introducing the average of y, we can reduce one degree of freedom and thus more accurately assess how well the model fits.

Introducing the mean of y is a necessary step in calculating goodness-of-fit. Not only can it serve as a benchmark for the sum of squares of errors, but it also helps us understand the distribution of the data and also helps to accurately assess how well the model fits.

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.

Summary. Goodness-of-fit refers to the degree of difference between the fitting result and the actual data, it is a numerical value, the value range is from 0 to 1, the larger the value, the smaller the difference between the fitting result and the actual data, and the more accurate the fitting result. When the goodness-of-fit degree is, it indicates that the difference between the fitting result and the actual data is large, and the fitting result is not accurate enough, and the fitting method needs to be further improved to improve the goodness-of-fitting.

Goodness-of-fit refers to the degree of difference between the fitting result and the actual data, it is a numerical value, the value range is from 0 to 1, the larger the value, the smaller the difference between the fitting result and the real hole leakage data, the more accurate the fitting result. When the goodness-of-fit degree is large, it indicates that the difference between the fitting result and the actual data is large, and the fitting result is not accurate enough, and the fitting method needs to be further improved to improve the goodness-of-fit.

Fellow, I really didn't understand, I can be more specific.

Goodness-of-fit refers to the degree of difference between the fitting result and the actual data, which indicates that the difference between the fitting result and the actual data is large, and the fitting effect is not very reasonable. This can happen because the parameters of the fitting model are not set properly, or the fitting model itself is not accurate enough, or the actual data itself is noisy, etc. The workaround is:

First of all, you should check whether the parameters of the fitting model are set correctly, if not, you can try to adjust the parameters to get a better fitting effect; Secondly, you can try to use a more accurate fitting model to get a better fitting effect; Finally, you can try to denoise the actual data to get a better fit. Personal tip: When fitting the oak acacia, you should carefully check the parameter settings of the fitting model, try to use a more accurate spine fitting model, and try to reduce the noise of the actual data to get a better fitting effect.