Презентація на тему «Simple Linear Regression as an example of the actual processes description»

Simple Linear Regression
as an example of the actual processes description
Research work
Pavel Shevchenko
Goals
To confirm hypothesis: the anxiety level of computer addict is in direct proportion to the amount of time he spent on computer games;
 To predict the dependency between the average score of for assessment and evaluation of of the selected object;
 Find a major factor getting a high average score on the example of students from 9-A grade in public institution Dneprorudnenskaya High  School "Sofia" in the 2011-2012 school year.
Preamble
 The Method of Regression analysis has a big popularity nowadays. It has been successfully applied in the analysis of experimental data in the various fields of science: psychology, economics, sociology, physics, chemistry, geology, automation and others.
       For example, in the economy of these methods can be used to find the relationship between the cost of advertising a product and generate revenue from sales.
This example will start a conversation about Simple Linear Regression, which can be used to describe the actual processes.
General Ideas and Conceptions 
 

Regression  - functional relationship      between independent      variables   and      conditional mathematical expectation (average mean)  response variable (regressand) . 
 
Simple Linear Regression expressed by a linear function:
у=bx+a+e. 
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Example of a graph of the linear regression
Formulas for finding the coefficients
regression equation:


Relationship of Human’s Anxiety Level 
and Amount of Time, 
Spending  in Computer Games
 
Summary table of data
The auxiliary table for calculation of coefficients of regression
Let's calculate coefficients of linear regression on the given formulas:
Thus, required regression dependence looks like:
Let's find determination coefficient on a formula:
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Anxiety Levels
 
The  second (low):

 
 
Third (satisfactory):


  
Fourth (unsatisfactory):

 
 
 
 
The Fifth(High): 

The First (minimum):
The Sixth(extreme): 
More than 40 hours
Dependence of a GPA of progress 
and estimates in the chosen subject 








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The regression equation for algebra
Let's calculate coefficients of linear regression on the given formulas:
Thus, required regression dependence looks like:
Let's find determination coefficient on a formula:
Let's carry out the regression analysis in the MS Excel Regression mode. Work with the program is presented ​​ in the following drawings:
Let's generate results on regression statistics are necessary and we will present them in the table:
Proceeding from calculations, we can write down the regression equation as follows:

;

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The regression equation for labor Science
Let's calculate coefficients of linear regression on the given formulas:
Thus, required regression dependence looks like:
Let's find determination coefficient on a formula:
Let's carry out the regression analysis in the MS Excel Regression mode for confirmation of settlement data.
Proceeding from calculations, we can write down the regression equation as follows:

;

.
Finding of the main factor of receiving by the pupil of a high GPA of estimation
Factor No. 1: Visit of lessons
Regression Equation —
Determination Coefficient  —
The schedule and the chart of dispersion visually prove lack of linear dependence. The theoretical line of regression passes almost parallel to abscissa axis, and it states lack of linear dependence between variables x and at. That is it is possible to interpret that attendance of lessons isn't the main factor of receiving a GPA of training. Then we will review the following examples.
Factor No. 2: Time of homework
 Regression Equation  —
 
 Determination Coefficient     —
 
About a half of points are at a straight line, as confirms determination coefficient. That is if diligence, persistence and definiteness in achievement of the purpose also isn't the main factor for receiving an appreciation, precisely is a component of this process.
Factor No. 3: Level of intelligence (IQ))
 
Regression Equation —
Determination coefficient —
Summing up this section it is necessary to tell the following: from the mathematical point of view it is proved that the main factor in training is erudition and intelligence, but also it is necessary to consider that all the same study - compound process it is possible to achieve which highest success only in that case when all considered factors are considered.
Conclusion
Research objective of real processes are attempts to give the idea of possible ways of further succession of events, to predict this or that situation, to expect the future of values of influencing factors, to specify instruments of studying of a situation in the desirable direction. 
So, for example, in this work use of pair linear regression for forecasting of various examples of the description of a picture of training of pupils of one (local) class was considered. Are also found negatively and positively influencing factors on further process. Practical value of this work also consists in it.