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Дата загрузки 13 Декабрь 2024
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Раздел Презентации
Предмет Информатика и ИТ

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Bohodir Jalolov

O’zaro bog’lanishlarni statistik o’rganish – correlatsion va regression tahlil

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zO’zaro bog’lanishlarni statistik o’rganish – correlatsion va regression tahlil z O’zaro bog’lanishlarni statistic o’rganish – correlatsion va regression tahlil z Types of relations / bog’lanish turlari  Funksional bog`lanish - bu shunday to`liq bog`lanishki, unda bir belgi yoki belgilar o`zgarish qiymatiga har doim natijaning ma`lum me`yorda o`zgarishi mos keladi.  Masalan, uchburchakning sathi (S) uning asosi (a) bilan balandligiga (h) bog`liq bo`lib, bu bog`lanish formula orqali hisoblanadi. S = ½ a h  Functional connection is such a complete connection in which a sign or signs always correspond to the result in a certain way.  For example, the level of a triangle (S) depends on its base (a) and experience (h), and this connection is made through the formula. S = ½ a h z Types of relations / bog’lanish turlari  Korrelyatsion bog`lanish - bu shunday to`liqsiz bog`lanishki, unda omillarning har bir qiymatiga turli zamon va makon sharoitlarida natijaning har xil qiymatlari mos keladi. Bu holda omillar to`liq soni noma`lumdir.  Korrelyatsiya so`zi lotincha correlation so`zidan olingan bo`lib, o`zaro munosabat, muvofiqlik, bog`liqlik degan lug`aviy ma`noga ega.  Correlation is an incomplete connection in which each value of the factors corresponds to different values of the result in different time and space conditions. In this case, the full number of factors is unknown.  The word &#34;correlation&#34; is derived from the Latin word &#34;correlation&#34; and has the dictionary meaning of &#34;reciprocity, compatibility, connection&#34;. z Types of relations / bog’lanish turlari  Analitik ifodalarining ko`rinishiga qarab bog`lanishlar to`g`ri chiziqli (yoki umuman chiziqli) va egri chiziqli (yoki chiziqsiz) bo`ladi.  Depending on the form of analytical expressions, connections are linear (or completely linear) and curved (or non-linear). z Regression va korrelyatsion tahlil vazifalari va bosqichlari  Korrelyatsion tahlil korrelyatsiya koeffitsiyentlarini aniqlash va ularning muhimligini, ishonchliligini baholashga asoslanadi.  Korrelyatsiya koeffitsiyenti (r) -1 dan 1 chegarasida yotadi, agar r=0 bog`lanish yo`q, 0 < r < 1bo`lsa, to`g`ri bog`lanish mavjud -1 < r < 0 teskari bog`lanish mavjud. Funksional bog`lanish mavjud r =1  Correlation analysis is based on determining correlation coefficients and evaluating their importance and reliability.  The correlation coefficient (r) ranges from - 1 to 1, if r=0 there is no correlation, if 0 < r < 1 then there is a positive correlation -1 < r < 0 inverse correlation there is. There is a functional connection r =1 z Juft korrelyatsiya  Ikki hodisa yoki omil va natijaviy belgilar orasidagi bog`lanish juft korrelyatsiya deb ataladi. Tahliliy jihatdan u turli, masalan, to`g`ri chiziqli, parabola, giperbola va boshqa shaklli regressiya tenglamalari orqali tasvirlanadi.   The connection between two events or factors and the resulting signs is called pairwise correlation. Analytically, it is described by various, for example, straight line, parabola, hyperbola and other regression equations. z Juft korrelyatsiya / Pair correlation z z z  A correlation coefficient (from co - and relation ) is a numerical assessment of the strength of relationship between the x and y values in a set of ( x , y ) pairs.  Korrelyatsiya koeffitsienti (ko- va munosabatdan) - (x, y) juftliklar to&#39;plamidagi x va y qiymatlari o&#39;rtasidagi munosabatlar kuchini raqamli baholash. z z Pearson’s Sample Correlation Coefficient / Pearsonning namunaviy korrelyatsiya koeffitsienti z z Example: Graduation Rates and Student-Related Expenditures z z the strength of a linear relationship / chiziqli munosabatlarning darajasi z Properties of r  The value of r does not depend on the unit of measurement for either variable . For example, if x is height, the corresponding z score is the same whether height is expressed in inches, meters, or miles, and thus the value of the correlation coefficient is not affected. The correlation coefficient measures the inherent strength of the linear relationship between two numerical variables.  R ning qiymati har ikkala o&#39;zgaruvchining o&#39;lchov birligiga bog&#39;liq emas. Misol uchun, agar x balandlik bo&#39;lsa, mos keladigan z ball balandlik dyuym, metr yoki milyada ifodalanganidan qat&#39;i nazar, bir xil bo&#39;ladi va shuning uchun korrelyatsiya koeffitsienti qiymatiga ta&#39;sir qilmaydi. Korrelyatsiya koeffitsienti ikkita raqamli o&#39;zgaruvchi o&#39;rtasidagi z Properties of r  The value of r does not depend on which of the two variables is considered x . Thus, if we had let x = graduation rate and y= student related expenditure in Example 5.1, the same value, r = 0.05, would have resulted.  R qiymati ikki o&#39;zgaruvchidan qaysi biri x deb hisoblanishiga bog&#39;liq emas. Shunday qilib, agar biz 5.1-misolda x = bitiruv darajasi va y = talaba bilan bog&#39;liq xarajatlarni qo&#39;yganimizda, bir xil qiymat, r = 0,05 bo&#39;lar edi. z Properties of r  The value of r is between - 1 and +1. A value near the upper limit, +1, indicates a substantial positive relationship, whereas an r close to the lower limit, -1, suggests a substantial negative relationship. Figure 5.4 shows a useful way to describe the strength of relationship based on r . It may seem surprising that a value of r as extreme as -.5 or .5 should be in the weak category; an explanation for this is given later in the chapter. Even a weak correlation can indicate a meaningful relationship.  r qiymati -1 va +1 orasida. Yuqori chegaraga yaqin bo&#39;lgan qiymat, +1, sezilarli ijobiy munosabatni ko&#39;rsatadi, pastki chegaraga yaqin r, -1 esa sezilarli salbiy munosabatni bildiradi. 5.4-rasmda r ga asoslangan munosabatlarning mustahkamligini tavsiflashning fo z Properties of r  The correlation coefficient r =1 only when all the points in a scatterplot of the data lie exactly on a straight line that slopes upward. Similarly, r =-1 only when all the points lie exactly on a downward-sloping line . Only when there is a perfect linear relationship between x and y in the sample does r take on one of its two possible extreme values.  Korrelyatsiya koeffitsienti r =1 faqat ma&#39;lumotlarning tarqalish diagrammasidagi barcha nuqtalar yuqoriga qiyshaygan to&#39;g&#39;ri chiziqda to&#39;liq yotsa. Xuddi shunday, r=-1 faqat barcha nuqtalar pastga qiya chiziqda to&#39;liq yotsa. Namunadagi x va y o&#39;rtasida mukammal chiziqli munosabatlar mavjud bo&#39;lgandagina r uning ikkita mumkin bo&#39;lgan ekstremal qiymatlaridan birini qabul qiladi. z Properties of r  The value of r is a measure of the extent to which x and y are linearly related —that is, the extent to which the points in the scatterplot fall close to a straight line. A value of r close to 0 does not rule out any strong relationship between x and y ; there could still be a strong relationship but one that is not linear.  r ning qiymati x va y ning chiziqli bog&#39;lanish darajasining o&#39;lchovidir, ya&#39;ni tarqalish chizig&#39;idagi nuqtalarning to&#39;g&#39;ri chiziqqa qanchalik yaqin tushishi. r ning 0 ga yaqinligi x va y o‘rtasidagi kuchli bog‘lanishni istisno etmaydi; Hali ham kuchli munosabatlar bo&#39;lishi mumkin, ammo bu chiziqli emas. z z z z Outliers z z The page intentionally left blank z Linear Regression: Fitting a Line to Bivariate Data / Chiziqli regressiya: ikki o&#39;zgaruvchan ma&#39;lumotlarga chiziq o&#39;rnatish zLinear Regression: Fitting a Line to Bivariate Data / Chiziqli regressiya: ikki o&#39;zgaruvchan ma&#39;lumotlarga chiziq o&#39;rnatish zLinear Regression: Fitting a Line to Bivariate Data / Chiziqli regressiya: ikki o&#39;zgaruvchan ma&#39;lumotlarga chiziq o&#39;rnatish z zLinear Regression: Fitting a Line to Bivariate Data / Chiziqli regressiya: ikki o&#39;zgaruvchan ma&#39;lumotlarga chiziq o&#39;rnatish  The objective of regression analysis is to use information about one variable, x, to draw some sort of conclusion concerning a second variable, y.  Regressiya tahlilining maqsadi bitta o&#39;zgaruvchi, x, ikkinchi o&#39;zgaruvchi, y haqida qandaydir xulosa chiqarish uchun ma&#39;lumotlardan foydalanishdir. zLinear Regression: Fitting a Line to Bivariate Data / Chiziqli regressiya: ikki o&#39;zgaruvchan ma&#39;lumotlarga chiziq o&#39;rnatish  Scatterplots frequently exhibit a linear pattern.  It is natural in such cases to summarize the relationship between the variables by finding a line that is as close as possible to the points in the plot.  Bunday hollarda syujetdagi nuqtalarga imkon qadar yaqin bo‘lgan chiziqni topib, o‘zgaruvchilar orasidagi bog‘lanishni umumlashtirish tabiiydir. z The least-squares line is often called the sample regression line . z z z z z z z z z z Assessing the Fit of a Line / Chiziqning mosligini baholash z z 0 z z z z Coefficient of Determination z z z z z z The page intentionally left blank z Nonlinear Relationships and Transformations/ Nochiziqli aloqalar va transformatsiyalar  Polynomial Regression  Transformations  Logistic Regression z Polynomial Regression z r 2 = 0.001 se = 56.9439 z z z z z Transformations z z z z z Tortilla Chips: Relationship Between Frying Time and Moisture Content z z z z Logistic Regression z z z z z z z
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