刘忠青

（山东科技大学电气信息系，济南 250031）

1 Introduction

The World Association of Sleep Medicine has set March 21 as World Sleep Day every year since 2001 so as to draw attention to the importance and quality of sleep.The mental state of a whole day depends on the sleep quality last night,and high sleep quality naturally ensures people to be energetic.According to statistics,however,the rate of insomnia in Chinese adults is as high as 38.2%,and the rate of insomnia in adolescents is rising meanwhile.In general,it belongs to the category of insomnia if the time to fall asleep is more than 30 minutes,so we believe many participants are also the insomniac.Long-term insomnia makes people feel tired,lack of energy in the whole day,and cannot concentrate attentions,so the efficiency of working and study is accordingly low.Severe insomnia even will cause autonomic nerve function disorder,resulting in imbalance and various problems of various systems in the body.

Many factors affect insomnia,and they can generally be divided into objective and subjective factors.Objective factors are environmental changes,tea or coffee before going to bed,and so on,and subjective factors are generally the pressure of life,emotional loss,mental excitement and other spiritual factors.However,the brains of young people in the period of growth and development are extremely prone to fatigue due to learning and work stress.Therefore,they must pay special attention to bed rest to ensure a good and healthy body.Human body's sleep quality and data of various indicators possibly affecting the sleep quality are given in Annex I.（Source and test number are not indicators）

The relevant scores for sleep conditions are given in Annex II（"0"for good,"1"for normal,"2"for poor,and"3"for very poor）,the higher the score,the worse the sleep condition.

（1）Analyze the relationship between the indicators given and the quality of sleep according to the data in Annex I,if there is no correlation between one or several indicators and sleep quality,find it or them out and delete.

（2）Analyze the relationship between the diagnosis results and sleep.

（3）Assuming you are a doctor,what diagnosis would you make to the patient based on the data in Annex III?Give your diagnosis result.

2 Model hypothesis

（1）Assume that the reliability in Annex I represents the reliability of the diagnosis.

（2）Assume that records with a reliability below 30 do not have a reference value,they are not real and objective.

（3）Assume that the diagnostic result is not affected by the scoring of each index,that is,the scores are independent of each other.

（4）Assume that the sleep indicators have the same effect on the diagnosis.

3 Model establishment and solution

Question 1 asks whether Annex I contains irrelevant indicators that affect the quality of sleep and by analyzing the indicators to analyze the relationship between indicators and quality of sleep[1].This question sets out the requirements for the analysis of the indicators given in Annex I and the quality of sleep,which is answered in the following two steps：

Step1：Through simple correlation analysis,identify the main indicators of sleep quality.

Step2：According to the above main indicators to find the relationship between sleep quality and each indicator.

（1）Data preprocessing

Assuming that the magnitude of the Reliability value in Annex I represents the reliability of the diagnosis,we assume that the diagnostic record with an Reliability value of less than 30 has no effect on this issue[2],so 669 diagnostic records with an Reliability value of less than 30 are excluded.

（2）Bivariate Correlation Analysis

The correlation coefficient obtained from the bivariate correlation analysis is a statistic that describes the degree and direction of the correlation between the two variables and is calculated as follows[3]：

Where：x,yare the two variables with analysis respectively;xˉ,yˉare the mean of the variables to be analyzed;ris the Pearson correlation coefficient,the dimension is 1 and the value is-1≤r≤1;whenr＞0,Positive correlation between the two variables,whenr＜0means that the two variables negative correlation,r=1is completely related,r=1,said irrelevant.

（3）Analysis results and the main indicators to determine

Correlation coefficient and significance level between each index and Sleep quality were obtained by SPSS bivariate correlation analysis,as shown in Table I.

Table I Correlation analysis between sleep quality and bivariate variables

Among all the indicators,Age has the highest correlation coefficient.There are four indicators（Age,Sex,Psychoticim,Nervousness）significantly correlated with Sleep quality at 0.01 level（bilateral）,and Sex is negatively correlated with Sleep quality and positive with Sleep quality Related.Because Reliability,Character significance are greater than 0.05,does not meet p＜0.05,Age,Psychoticim,Nervousness then Reliability,Character and Sleep quality has nothing to do,then remove the Reliability,Character indicators in Annex I.

Finally we come to the main indicators affecting Sleep quality：Age,Sex,Psychoticim,Nervousness.Character,Reliability is irrelevant index.

（4）Solution of Multivariate Linear Regression

First of all,the quality of Sleep,Age,Sex,Psychot-icim,and Nervousness was sampled with the help of MATLAB using MATLAB software（see appendix table test set sample）[5].Then using the index values of these 3000 samples,the SPSS software was used to solve the five-element linear regression equation of Sleep quality and Age,Sex,Psychoticim and Nervousness：

Among them,the main indicators that affect Sleep quality Psychoticim,Nervousness,Age,Sex.

（5）Solution of Multivariate nonlinear Regression

Question 2 requires analysis of the relationship between Diagnosis and sleep quality,Sleep latency,Sleep time,Sleep efficiency,Sleep disorder,Hypnagogue,Daytime dyfunction.Since there are 299 different types of diagnoses in Annex II,this question is answered in the following three steps for a better degree of fit[6]：

Step1：Perform data preprocessing first,delete data that is not normal,invalid and noisy,and then standardize the data.

Step2：Based on the first step,re-numberkdiseases according to some classification rules on the data in Annex II.

Step3：Taking the average of each index of each disease as the independent variable and the disease number as the dependent variable to establish the multivariate nonlinear regression model.

（6）Divide the disease types and renumber them

Twenty-four diseases were classified according to the same disease or the same disease in Annex II,meanwhile the corresponding indexes and average values of each disease and the average of each index were obtained.According to each index and the average value of each disease,it is sorted in ascending order,and new disease numbers from 0～23 are obtained.The larger the disease type number,the more serious the diagnosis result is.Data processing results in the following table：

Table II Division of Disease Outcomes

（7）Establish multiple nonlinear regression models

Using the corresponding numbers of each disease obtained in step two and the average value of each index of each disease as data sources,24 data were imported into MATLAB to obtain the multivariate nonlinear regression model(M model)as follows：

Among them,the dependent variable is the diagnosis result,and the independent variables are Sleep quality,Sleep latency,Sleep time,Sleep efficiency,Sleep disorder,Hypnagogue,Daytime Dyfunction.

（8）Regression model significance test

We use statistical software SPSS to solve the sevenelement nonlinear regression model Significance test,the result is as follows[7]：

①Judgment coefficient

Table III Model Summary

②Significance Test of Regression Equation

Table IV Analysis of variance table

We can gotfrom the above tableF =37.57371,F＞F0.05(5,3)=2.51 regression equation was significant,that is,there is a clear functional relationship between independent variables and dependent variables.

③Result analysis

In summary,there is a close relationship between Diagnosis and Sleep indicators,Sleep latency,Sleep time,Sleep efficiency,Sleep disorder,Hypnagogue,Daytime dyfunction.The relationship is as follows：

（9）Into the model of the second question

The data in Annex 3 is substituted into formula(3),and the diagnosis result is obtained.The calculation process is shown in the following table V：

Table V Data obtained from the process of solving

：

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