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

content: Simple Linear Regressionas an example of the actual processes descriptionResearch workPavel Shevchenko

content: GoalsTo 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.

content: PreambleThe 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.

content: 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.рекламапродажаExample of a graph of the linear regressionFormulas for finding the coefficientsregression equation:

content: Relationship of Human's Anxiety Leveland Amount of Time,Spending in Computer Games

content: №Surname, name, class, ageQuantity of hours (in a week)Anxiety laevel1Анпилов Александр, 10-А, 15 лет25,532,2752Гайдаш Екатерина, 10-А, 15 лет16,31,5253Иванников Виталий, 10-А, 16 лет32,33,1254Клименко Дмитрий, 10-А, 14 лет22,322,0755Команчи Дмитрий, 10-А, 15 лет29,872,756Короткова Лилия, 10-А, 15 лет21,781,6757Куприн Кирилл, 10-А, 15 лет33,73,0258Мартиросян Арам, 10-А, 15 лет21,621,8759Хлопов Артём, 10-А, 14 лет26,852,2510Якуба Александр, 10-А, 15 років37,433,05№хіуіхі2хіуіуі р(уі р – у)2(уі – у)2125,532,275651,7858,082,2550,01110,01229,872,75892,2282,142,6320,07410,15332,33,1251043,29100,942,8440,23380,59422,322,075498,1846,311,9750,14790,08521,781,675474,3736,481,9280,18630,47616,31,525265,6924,861,4520,82510,70721,621,875467,4240,541,9140,19850,24833,73,0251135,69101,942,9650,36640,44926,852,25720,9260,412,3690,00010,011037,433,051401,00114,163,2900,86460,48267,723,6257550,57665,872,913,16Summary table of dataThe auxiliary table for calculation of coefficients of regression

content: 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:iinnRegression StatisticsR-square0,920855Observation10CoefficientsY-interacting0,033684independent X0,086993;

content: Anxiety LevelsThe second (low):Third (satisfactory):Fourth (unsatisfactory):The Fifth(High):The First (minimum):The Sixth(extreme):More than 40 hours

content: Dependence of a GPA of progressand estimates in the chosen subject

content: Укр. языкУкр. ЛитАнгл. Яз.Франц/ НемецРус. Яз.Литер.Истор. Укр.Всем. Истор.ПравоАлгебрГеометр.Биологгеограф.физикахимияхуд. Культ.трудыинформ.черчен.О.Б.Ж.Анпилов910991011101010881288889989Бабич54445565844456558746Бирюкова85510888884456548109810Бородина99810101110101010109989121181210Воропай5647677864466637107510Гаврилов784878886766765779610Герда43556444543443358948Иваников787697987878987891079Клименко53455654344443258645Команчи43435456333433238813Кононенко745678777445654610947Коржова778789998987107891110710Короткова99881099108888879891189Кретинин52344455533443247559Кулиш64446567645554459856Куприн7978898871010871087810810Лашина86678888744666679769Мартиросян99971010897101097910991079Мишин978899999987876899410Овчаренко768676887897798791079Приймак7797888910766865891069Ревуцкий87579877744685479959Савина633576795544456610859Семенько111110101111101010101010109101010111011Сенюк886679889646756910879Тарасенко53456466344434348844Хлопов44546454433443248764Шевченко А.73387876544565479938Шевченко П.1112101210111010101212101010111011111011Якуба42436456544642338855

content: №SubjectRegression equationR21.Ukrainian-0,056427Х+0,4607540,0171922.Ukrainian Literature0,410689Х-3,6745090,3616943.English0,018284Х-1,0702150,0009854.French/German-0,011133Х-0,1655610,0003145.Russian-0,131005Х+1,5649190,0990266.Russian Literature0,138371Х-0,4161910,0711317.Ukrainian History0,132193Х-0,3719580,0735618.World History-0,137436Х+1,6436890,0782219.Government-0,049057Х+0,3051990,00629910.Algebra0,301833Х-2,8515950,19764911.Geometry0,265489Х-2,8496420,13576312.Biology0,003642Х-0,6180850,00004913.Geography0,015582Х-0,559930,00123814.Physical Science0,061598Х-1,439930,01289715.Chemistry0,3185131Х-3,5727110,24736616.Esthetical Science0,0470855Х-0,31964680,01036217.Трудовое обучение-0,665022Х+6,7386020,70087118.Computers-0,463331Х+5,0342620,43532319.Technical Drawing-0,028611Х-0,6760690,00162320.Life Science-0,12703Х+2,3061560,028974

content: iinnThe regression equation for algebraLet's calculate coefficients of linear regression on the given formulas:Thus, required regression dependence looks like:Let's find determination coefficient on a formula:

content: Let's carry out the regression analysis in the MS Excel Regression mode. Work with the program is presented ​​ in the following drawings:

content: Let's generate results on regression statistics are necessary and we will present them in the table:Регресійна статистикаR-квадрат0,1976Спостереження30КоэффициентыY-пересечение-2,851595Переменная X0,301833Proceeding from calculations, we can write down the regression equation as follows:;.

content: Let's generate results on regression statistics are necessary and we will present them in the table:Регресійна статистикаR-квадрат0,1976Спостереження30КоэффициентыY-пересечение-2,851595Переменная X0,301833Proceeding from calculations, we can write down the regression equation as follows:;.

content: iinnThe regression equation for labor ScienceLet's calculate coefficients of linear regression on the given formulas:Thus, required regression dependence looks like:Let's find determination coefficient on a formula:

content: Let's carry out the regression analysis in the MS Excel Regression mode for confirmation of settlement data.Регрессионная статистикаR-квадрат0,700865Наблюдения30КоэффициентыY-пересечение6,738609Переменная X-0,665023Proceeding from calculations, we can write down the regression equation as follows:;.

content: Finding of the main factor of receiving by the pupil of a high GPA of estimation№Family nameGPANumber of AbsencesTime for hw(IQ)1Анпилов9,218415,51262Бабич5,22397863Бирюкова7,11459,521014Бородина9,81618,481295Воропай6,22037,44896Гаврилов7,0748,971077Герда4,81114,65838Иваников7,916816,361119Клименко4,5585,638410Команчи3,919848311Кононенко6,16717,699012Коржова8,428023,5411513Короткова8,714816,5212214Критинин4,31373,857815Кулиш5,4506,4892№Family nameGPAAbsencesTime for hw(IQ)16Куприн8,43021,4611717Лашина6,84713,2810018Мартиросян8,918117,8712819Мишин8,110816,0111420Овчаренко7,712419,3211321Приймак7,729818,6311022Ревуцкий6,88417,510123Савина5,912715,29824Семенько10,320214,4213125Сенюк7,36518,5110726Тарасенко4,62878,38427Хлопов4,41694,988828Шевченко А.5,95711,379529Шевченко П.10,711612,8713630Якуба4,62835,6389

content: Factor No. 1: Visit of lessonsRegression 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.

content: Factor No. 2: Time of homeworkRegression 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.

content: 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.

content: ConclusionResearch 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.