YAN Zheng-ren ; WEI Yu-rui ; LIU Qi-shan

（South China Normal University, Guangdong Province, Guangzhou 510007,China）

Study of Application of Coach Evaluation

YAN Zheng-ren ; WEI Yu-rui ; LIU Qi-shan

（South China Normal University, Guangdong Province, Guangzhou 510007,China）

We built a models to deal with the problems, including how to select the best coach, how to build a reasonable evaluation system, and how to make our model applied in any situation. The name of model is Stepwise Regression. We need to do the normalization processing of data and then through the step-by-step calculation only several factors were left. We find six factors to evaluate the basketball coaches, and we select two factors are important. Finally, we built an expression to calculate. By calculate the two factors data on the expression, we can rank these coaches, find the best basketball coach.

Coach; Evaluation; Stepwise Regression;

1 Introduction

To ranking of some coaches of one sport, we build 2 models. One is Stepwise Regression, another is Grey Relational Analysis Method. We input some data about some coaches of NCAA into 2 models to find the best coach of NCAA.

1.1 The Data

By accessing to relevant information[1], wegain some data about some coaches of NCAA. In Table 1, we assume that “S” is salary(million),“W” is victory, “L” is lose, “PCT” is Winning percentage, “C” is career and “P” is prizes.

And then, we do the normalization processing of data.

Where:

is the jth index of the ith coach in Table 1. By using the Matlab program, we do the the normalization processing of the data. And then we gain the new data(Table 1)

Table 1. The data of some coaches of NCAA after the normalization processing.

2 Model 1:Stepwise Regression

2.1 Introduction

Stepwise regression is to choose the variables which have significant effects on Y to build a regression equation from some Y(dependent variable)-related variables, i. e. , it should try the best to use more Y-related variables, while highlighting some of the major factors.

2.2 Build the Model[2-6]

To build this model, there are generally the following steps:

(1)Calculate simple correlation coefficient matrices of the variables, and then analyze the correlation of between these variables. Observe that if there has the phenomenon of multicollinearity.

(2)Use the least-squares to build multiple linear regression equation, and then test the equation with the goodness of fit test.

(3)If the goodness of the linear regression equation is better, calculate the t-statistic of each regression parameter, and do the significant test for each parameter. Eliminate the insignificant factors in a significant level of a.

(4)After eliminating the insignificant factors, rebuild the linear regression equation with the remaining variables, and then do the significant test for each parameter until every factor is significant in the given significant level of a. After all, we have build the multivariate linear regression model with the high quality.

With the above steps, we can draw the the mind map of model(Figure 1).

Figure 1. The mind map of model 1: Fs are all of the evaluation factors , and then through the some calculation of our model , several important factors(F’) will be selected to regarded as main element of our simplified(m will much less than n)evaluation system.

After learning the above steps, we assume that X1 is victory, X2 is lose, X3 is Winning percentage, X4 is career, X5 is prizes and Y is salary(million). And then, we a input the data of Table 1 into the Matlab program, and then we can gain the result(Figure 1)

Figure 1. The calculated result of Table 1

From Figure 2, we can learned X1 and X5 have significant effects on Y, so we can gain the final linear regression equation. It is:

Y=-0. 382224X1+0. 946496X5+0. 3301.

Supplementary Explanation of the Final Linear Regression Equation

Here is the correlation coefficient matrices:

From the last row, we can see X1(0. 394), X3(0. 511) and X5(0. 838) all have close correlation with Y. but why can not X3 be selected in our model? Because it has close correlation with X1 and X5, through (0. 391) and (0. 511) , by compared with others. On the other word, X3 is odd.

2.3 The Best College Coach

By inputting the data of Table 2 into the equation(i. e. , Y=-0. 382224X1+0. 946496X5), we can get the top 5 coaches of NCAA(Table 2).

Table 2. the ranking of the coaches of NCAAFrom Table 2, we can learn that the best coach is Mike Krzyzewski who comes from Duke University.

[1]qingyanbailang. 2013. introduct NCAA basketball coach salaries of the top 25, http://bbs. hupu. com/8234131. html

[2]sports reference. Pro-Football-Reference. com. http://www. pro-football-reference. com/coaches/

[3]wikipedia. http://en. wikipedia. org/wiki/List_ of_college_men's_ice_hockey_coaches_with_350_wins. http://en. wikipedia. org/wiki/List_of_college_ women％27s_soccer_coaches_with_250_wins

[4]QiYuan Jiang. JinXing Xie. Jun Ye. 2011. Shuxue Moxing. Gaodeng Jiaoyue Press. (in Chinese)

[5]XueJun Wu. Kai Zhou. JunQuan Song. 2009. Shuxu ejianmojingsaifudaojiaocheng. Zhenjiang University Press. (in Chinese)

[6]Liu Yongjuan, Cao Jianjun. Research of Model of the Evaluation for Teaching Quality Base on Stepwise. 2007(in Chinese)

TS951.7+3

A

1009-5624-（2016）02-0091-03