Binary regression analysis based on analysis of fire data

Papers to write Net: Abstract: According to the 2003-2007 fire-related statistics, regression analysis to study the economic losses caused by fire and the fire burned in the wounding of the number and the relationship between the construction area, the establishment of binary linear regression model, the accuracy of the equation correlation test.

Keywords: fire, binary linear regression analysis, correlation test


Fire is unexpected injuries, the frequency of the current society of a higher and more harmful disasters, especially in recent years of more than Qunsiqunshang unexpected injuries in fires account for a proportion of annual will result in casualties and huge economic losses. In view of this, the paper's direct economic losses caused by fire related factors were studied, and relevant statistical data regression analysis.

In real life, for a correlation between the variables, we often can not be found as a function between them as the exact expression, but through a large number of trials (observational data, can be found between them there is a certain statistical regularity, mathematical statistics study of a random variable (the dependent variable and the other one or several common variables (independent variables change in the relationship between an effective way to regression analysis by the regression equation derived, called the regression equation regression equation for the line of as linear regression or a non-linear regression Linear regression is regression analysis of the basic model, a number of complex cases can be processed into a linear regression, for example, [1] discussion of the statistical understand and solve the problem of the importance of fire, the literature [2-3] using the linear regression model of the related fires.

Paper, for the 2003-2007 national fire-related statistics, the cost of damage caused by fire and the number of fires and burning buildings in the area of ??wounding analysis of the relationship between the establishment of a binary linear regression model.

A linear regression model

1 to collect data in Table 1 China's 2003-2007 fire wounding the number of burned area and direct economic losses of construction statistics.
2 Set the regression equation by qualitative analysis shows that the number of fire injuries in the more burning building, the more so the greater the economic losses caused, and if no one burns a fire, the house is not burned, there is no economy can be considered loss, therefore, can be installed binary linear regression analysis of the regression equation

= B1x1 + b2x2 (1

Where: - the dependent variable (direct loss costs; x1 - the independent variable (the number of injuries, x2 - the independent variable (burn building area, b1, b2 - the regression coefficients.

3 to determine the regression coefficients would be given data set into the regression equation, and the least square method (see [4] to calculate the regression coefficient to determine the regression equation specific steps are as follows: Table 1 is known from 2003 to 2007, there were five data sets:
(X11, x12, y1, (x21, x22, y2, ..., (x51, x52, y5

Let the remaining sum of squares for the

Q = (yi-i2 = (yi-bixi1-b2xi22

Where: yi - 1 page table on the first set of data of the dependent variable, xik - the i-th group of data of the k independent variables (k = 1,2.
Calculated through the knowledge of calculus minimum value of Q, and even if the regression coefficients of Q on each partial derivative equal to zero, then the two simultaneous equations = 0, = 0 can solve for the regression coefficient b1 = 49.0119, b2 = 0.0033. Therefore, the return equation
= 49.0119x1 +0.0033 x2 (2

Second, the correlation test

Correlation test is the regression equation have been identified to represent the independent variable and dependent variable relationship between the reliability of testing and only after testing by correlation to the regression equation as a basis for analysis and forecasting. General use R test and F test other methods. Here we use the R test method. so

Syy = (yi-i2 = (i-y2 = Q + U

Where: y - Table 1 on page 5 the average of the dependent variable yi, i - xi1 and xi2 values ??into (2 type from value.
r = is a test of the correlation coefficient R, the more it is close to 1, it shows the regression equation the independent variables and the dependent variable in the linear approximation of the higher, the smaller the error of the equation by calculating the availability of r = 0.9988 Therefore, equation (2 passed the relevant test, quantitative description of fire it can slander the number of burned area and direct economic losses of building relationships.

In addition, from the regression equation can also be seen, the number of fire injuries in front of the partial regression coefficient, mainly because statistics in burned building area of ??the higher numbers, and did not consider other aspects such as material losses in the fire , the economic losses. For the same dimension more than three variables, we can take the form, so

zi = yi / y, ti1 = xi1/xi1, ti2 = xi2/xi2, (3

Where: y - Table 1 on page 5 the average of the dependent variable yi, tik - Table 1 on page 5 from the average of the variable xik (k = 1,2.

By (3-type data obtained using the above methods will get the regression equation:

= 0.8264x1 +0.177 x2
Correlation coefficient r = 0.9990, also passed the correlation test. Links to free download


The regression equation shows the economic losses caused by fire and the fire burned the building number and slander area were positively correlated with our qualitative analysis consistent with the quantitative relationship, in the absence of statistics of economic losses caused by fire before We can then fire and burned down the number of injuries in the construction area of ??economic loss to the general forecast, or if you want to fire the next year, economic losses caused by the restriction to a certain amount, then we can according to the regression equation given the number of fire injuries and burning building area cap.

In order to reduce the losses and casualties caused by fire, we must focus on eliminating fire hazards, the proposed risk factors for the fire to take comprehensive preventive measures to strengthen urban public fire-fighting facilities and fire organizations, to increase fire safety publicity to raise people's awareness of fire safety and fire self-help knowledge and skills.


[1] LIU Dong-hai, Ji Tao, etc. Problems of fire statistics [J]. Fire Technology and Products, 2005, (5) :35-37.

[2] Zhou Chongmin. Statistics on fires and fire monitoring [J]. Armed Police Institute, 2002, (2) :28-29.

[3] Cao Wenjuan Statistical models in applied statistics in the fire [J]. Armed Police Institute, 2006, (2) :23-25.

[4] Sheng sudden, Shyh-thousand, etc. Probability and Mathematical Statistics (Zhejiang Fourth Edition) [M]. Beijing: Higher Education Press, 2008. Links to free download http://www.hi138. com

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