
Korean: 
제가 자료를 몇개 가져왔는데요
상관계수 직관에 대한 칸 아카데미의 연습 문제입니다
우리에게는 몇 가지 상관계수가 주어져있고
그것들을 문제에 주어져있는
다양한 산포도에 대응시켜야 합니다
이것을 테이블에서 드래그해서
다른 산포도에 대응시킬 수 있는
작은 인터페이스가 있습니다
핵심은 얼마나 정확히 계산하는지를 보는 것이 아닙니다
이건 나중에 할 일입니다
우리가 측정해보려는 것에 대한 
직관을 얻는 것이 중요합니다
핵심 아이디어는 상관계수가
선형모델이 두 변수 사이의 관계를 얼마나 잘 나타내는지를
측정하려고 시도한다는 것입니다.
예를 들어
좌표축이 이렇게 있다고 합시다.
이것을 한 변수로 하고
이것을 y 변수라고 합시다
그리고 이것을 x 변수라고 합시다
x가 작을 때 y가 작다고 하고
x가 조금 커지면, y도 조금 커지고
x가 좀 더 커지면, y도 커지고

Thai: 
ผมถ่ายภาพหน้าจอจาก
แบบฝึกหัดคานอะคาเดมี่เรื่องสัญชาตญาณ
สัมประสิทธิ์สหสัมพันธ์
เขาให้สัมประสิทธิ์สหสัมพันธ์มา
และเราต้องจับคู่มันกับ
พลอตแบบกระจายต่างๆ ในแบบฝึกหัดนั้น
มันมีส่วนที่คุณลากไปมา
ในตารางเพื่อจับคู่พวกมัน
กับพลอตแบบกระจายต่างๆ ได้
ประเด็นไม่ใช่หาว่าวิธี
คำนวณค่าเหล่านี้ เราจะทำต่อไปในอนาคต
แต่ตอนนี้เราอยากได้สัญชาตญาณว่า
เรากำลังวัดอะไร
แนวคิดหลักคือว่า สัมประสิทธิ์สหสัมพันธ์
คือการพยายามวัดว่าแบบจำลองเชิงเส้น
สามารถบรรยายความสัมพันธ์ระหว่าง
ตัวแปรสองตัวได้ดีแค่ไหน
ตัวอย่างเช่น
ขอผมวาดแกนพิกัดตรงนี้นะ
สมมุติว่านั่นคือหนึ่งตัวแปร
สมมุติว่านั่นคือตัวแปร y ของผม
และสมมุติว่านั่นคือตัวแปร x
สมมุติว่าเมื่อ x ต่ำ y ก็ต่ำ
เมื่อ x สูงขึ้นหน่อย y ก็สูงขึ้นหน่อย
เมื่อ x สูงขึ้นอีก y ก็สูงขึ้น

Bulgarian: 
Заснех няколко упражнения от
Кан Академия, свързани с разглеждането
на корелационния коефициент.
Дадени са ни няколко 
корелационни коефициента
и ние трябва да ги свържем с различните
точкови диаграми в упражнението.
Има възможност да ги местим
наоколо в таблица, за да ги свържем
с различните точкови диаграми.
Целта не е да намерим как точно
да ги изчислим, ще правим
това по-нататък,
а всъщност да добием представа за това
какво се опитваме да измерим.
Основната идея е, че 
корелационните коефициенти
се опитват да измерят
колко добре един линеен модел
може да опише зависимостта
между две променливи.
Например, ако имам...
ще начертая тук координатни оси.
Нека кажем, че това е едната 
променлива.
Това е променливата у
и нека кажем, че това е 
променливата х.
Нека кажем, че когато х е разположено
ниско, у също е ниско.
Когато х е малко по-високо, 
у е също малко по-високо.
Когато х е още малко по-високо,
у е също по-високо.

English: 
- I took some screen captures from the
Khan Academy exercise on
correlation coefficient intuition.
They've given us some
correlation coefficients
and we have to match them to the various
scatterplots on that exercise.
There's a little interface
where we can drag
these around in a table to match them
to the different scatterplots.
The point isn't to figure out how exactly
to calculate these, we'll
do that in the future,
but really to get an intuition
of we are trying to measure.
The main idea is that
correlation coefficients
are trying to measure
how well a linear model
can describe the relationship
between two variables.
For example,
let me do some coordinate axes here.
Let's say that's one variable.
Say that's my y variable
and let's say that is my x variable.
Let's say when x is low, y is low.
When x is a little higher,
y is a little higher.
When x is a little bit
higher, y is higher.

Thai: 
เมื่อ x สูงมาก y ก็สูงมาก
แบบจำลองเชิงเส้นจะบรรยายมันได้ดีมาก
มันลากเส้นตรง
ผ่านจุดเหล่านี้ได้ง่ายมาก
อะไรแบบนี้จะมีค่า r เป็น 1
r เท่ากับ 1
แบบจำลองเชิงเส้นบรรยายมันได้โดยสมบูรณ์
และมันเป็นสัมพันธ์ร่วมแบบบวก
เมื่อตัวหนึ่งเพิ่มขึ้น เมื่อตัวแปรหนึ่งโตขึ้น
แล้วตัวแปรอีกตัวจะโตขึ้น
เมื่อตัวแปรหนึ่งเล็กลง ตัวแปรอีกตัว
ก็ลดลงด้วย และในทางกลับกัน
ทีนี้ r เท่ากับลบ 1 จะเป็นอย่างไร?
เหมือนเดิม มันคือกรณี
ที่แบบจำลองเชิงเส้นใช้ได้ดีมาก
แต่เมื่อตัวแปรหนึ่งเพิ่มขึ้น
อีกตัวจะลดลง และในทางกลับกัน
ขอผมวาดแกนพิกัดนะ
แกนพิกัดของผม
ผมพยายามวาดชุดข้อมูลที่
r เท่ากับลบ 1
บางทีเมื่อ y สูง y จะต่ำมาก
เมื่อ y ต่ำลงหน่อย x จะเพิ่มขึ้นหน่อย
เมื่อ y ต่ำลงอีก

Bulgarian: 
Когато х е наистина високо, 
у е дори по-високо.
Един линеен модел би описал
това много, много добре.
Много е лесно да начертаем права,
която да минава през тези точки.
Така че нещо подобно
би имало коефициент r = 1.
Един линеен модел 
идеално го описва
и имаме положителна корелация.
Когато едното нараства, когато
едната променлива става по-голяма,
тогава и другата променлива
е по-голяма.
Когато едната променлива е по-малка, 
тогава и другата променлива
е по-малка и обратното.
Как би изглеждало r от –1.
Отново това ще бъде ситуация,
при която един линеен модел 
ще свърши доста добра работа,
но когато едната променлива
отива нагоре,
другата се придвижва надолу
и обратното.
Нека начертая
отново координатните оси.
Ще се опитам да начертая 
множество от данни, при които
r ще бъде –1.
Може би когато у е високо, 
х ще бъде много ниско.
Когато у става по-ниско, 
х става по-високо.
Когато у става доста по-ниско,

English: 
When x is really high, y is even higher.
A linear model would
describe it very, very well.
It's quite easy to draw a line
that essentially goes
through those points.
So something like this
would have an r of 1,
r is equal to one.
A linear model perfectly describes it
and it's a positive correlation.
When one increases, when
one variable gets larger,
then the other variable is larger.
When one variable is
smaller then other variable
is smaller and vice versa.
Now what would an r of
negative one look like?
Well, that would once again be a situation
where a linear model works really well
but when one variable moves up,
the other one moves down and vice versa.
Let me draw my coordinates,
my coordinate axes again.
I'm gonna try to draw a dataset where the
r would be negative one.
Maybe when y is high, x is very low.
When y becomes lower, x become higher.
When y becomes a good bit lower,

Korean: 
x가 아주 크면, y도 아주 크다고 합시다
선형 모델은 이걸 매우, 매우 잘 나타냅니다
선을 긋는 건 꽤 쉽습니다
이 점들을 지나도록 말입니다
이런 것들은 1인 r을 가지고 있고
r은 1과 같습니다
선형 모델은 이것을 완벽하게 나타내고
이것은 양의 상관관계입니다
하나의 변수가 증가하면
다른 변수도 증가합니다
반대로 한 변수가 감소하면
다른 변수도 감소합니다
그렇다면,  r이 1이면 어떻게 생겼을까요?
이 상황에서도
선형 모델은 아주 잘 작동합니다
하지만, 한 변수가 올라가면
다른 변수는 내려가고, 반대의 경우도 마찬가지입니다
좌표를 잡아봅시다
좌표축을 다시 그려봅시다
데이터들을 그려봅시다
r이 -1이 되도록 말이죠
y가 크면, x는 아주 작을 것이고
y가 작아지면, x는 커질 겁니다
y가 조금 낮아지면

Korean: 
x는 조금 커질겁니다
다시 짚어보면, y가 감소하면 x가 증가하거나
x가 증가하면 y는 감소합니다
서로 반대 방향으로 움직이기는 하지만
여러분은 쉽게 알맞은 선을 그릴 수 있습니다
선은 이런 식으로 그어집니다
이건 r=1을 가지고 있습니다
그리고 r이 0인 경우는
데이터들에 알맞은 선을
전혀 그을 수 없습니다
작게 한번 그려보겠습니다
여백이 부족하네요
r이 0인 경우는
이렇게 나타납니다
데이터를 나타내는 점이 여기 하나
저기 하나
여기도 하나
여기, 여기도
이렇게 규칙적일 필요는 없지만
감을 잡을 수 있을 겁니다
여기는 어떻게 선을 그어야 할까요?
여러분은 선을 이렇게 그을 수도 있고
아니면 이렇게 긋거나

English: 
x becomes a good bit higher.
Once again, when y decreases,
x increases or as x
increases, y decreases.
They're moving in opposite directions
but you can fit a line
very easily to this.
The line would look something like this.
This would have an r of negative one,
and r of zero, r is equal to zero,
would be a dataset which a line
doesn't really fit very well at all.
I'll do that one really small,
since I don't have much space here.
An r of zero might look
something like this.
Maybe I'll have a data point here,
maybe have a data point here,
maybe I have one there.
There, there.
And it wouldn't necessarily
be this well organized
but this gives you a sense of things.
How would you actually
try to fit a line here?
You could equally justify
a line that looks like that
or a line that looks like that,

Bulgarian: 
х става доста по-високо.
Още веднъж, когато у намалява,
х нараства или когато
х нараства, у намалява.
Те се движат в противоположни посоки,
но тук можеш много лесно
да начертаеш права.
Правата ще изглежда 
по подобен начин.
Ще имаме r от –1,
а при r равно на 0
ще имаме данни, при които
една права
няма изобщо да съвпада добре.
Ще го направя наистина малко,
тъй като няма много място тук.
r от 0 може да изглежда
по подобен начин.
Може би имам точка с данни тук,
може би имам точка с данни тук
и може би имам една там.
Там, там.
Като това няма непременно да бъде 
толкова добре организирано,
но ще ти даде представа за нещата.
Как всъщност ще се опиташ 
да начертаеш права тук?
Можеш да нагодиш дадена права,
която да изглежда ето така
или права, която изглежда
 по този начин,

Thai: 
x ก็เพิ่มขึ้นอีก
ย้ำอีกครั้ง เมื่อ y ลดลง
x เพิ่งขึ้นหรือเมื่อ x เพิ่มขึ้น y จะลดลง
พวกมันไปในทิศตรงกันข้าม
แต่คุณลากเส้นตรงแทนข้อมูลได้ง่าย
เส้นตรงจะเป็นแบบนี้
อันนี้จะมี r เท่ากับลบ 1
และ r เป็น 0, r เท่ากับ 0
จะเป็นชุดข้อมูลที่เส้นตรง
ไม่เข้ากับข้อมูลนัก
ผมจะวาดเล็กๆ นะ
เพราะผมไม่มีที่ว่างมากนัก
r เป็น 0 อาจเป็น
แบบนี้
บางที ผมอาจมีจุดข้อมูลตรงนี้
บางทีจุดข้อมูลตรงนี้
บางทีผมมีอันนี้ตรงนี้
ตรงนี้ ตรงนี้
และมันไม่จำเป็นต้องเรียงดีอย่างนี้
แต่มันพอทำให้คุณเข้าใจ
แล้วคุณจะลากเส้นตรงแทนข้อมูลได้อย่างไร?
คุณลากเส้นตรงที่เป็นแบบนี้
หรือเส้นตรงที่เป็นแบบนั้น

Korean: 
이렇게 그을 수도 있습니다
선형모델은 두 변수 사이의 관계를
잘 나타내지 못합니다
여기 보듯이 말입니다
이걸 시작점으로 합시다
우리가 이 산포도를 처리할 수 있는지 봅시다
제가 할 것은
선형 모델이 어떻게 생겼는지 살펴보는 것입니다
불완전한 데이터 집합에
선형 모델을 맞추는 몇 가지 방법들이 있습니다
저는 적어도 r이 -1이거나 r이 1인 경우에는
완벽한 선을 그었지만
하지만 이것이 실제 세상이 어떤지를 나타냅니다
아주 드물게만 완벽하게 선 위에 있을 것입니다
산포도 A의 경우, 제가 선을 맞추려고 한다면
이런 식으로 생길 것입니다
제가 선에서 점까지의 거리를 최소화하려 한다면
저는 일반적인 추세를 볼 것입니다
여기 있는 데이터 점들을 보면
y가 크면, x는 작습니다
x가 커지면 y는 작아집니다
r이 0보다 작을 것으로 보이고
0보다 약간 작습니다

Bulgarian: 
или права която изглежда
ето така.
Един линеен модел наистина
не описва
зависимостта между двете променливи 
толкова добре,
ето тук.
Това тук е пример.
Нека видим, дали можем да се справим
с тези точкови диаграми.
Начинът, по който ще го направя, е
да се опитам да преценя на око как може 
да изглежда даден линеен модел.
Има различни методи да се опитаме
да нагодим един линеен модел
към множество от данни, 
което не е идеално.
Начертал съм доста идеални 
случаи, поне за r = –1 и r = 1,
защото точно така всъщност 
изглежда реалността.
Много рядко нещата ще се намират
 точно на една права.
При точкова диаграма А, ако се опитам
да начертая права,
тя ще изглежда по подобен начин.
Ако се опитам да минимизирам
разстоянията от
точките до правата, ще видя 
основната тенденция,
ако разгледам тези точки
с данни ето тук,
когато у е високо, х е ниско.
Когато х е по-голямо, у е по-малко.
Изглежда, че r ще бъде 
по-малко от 0
и достатъчно малко по-малко от 0.

Thai: 
หรือเส้นตรงที่เป็นแบบนั้นก็ได้
แบบจำลองเชิงเส้นไม่ได้บรรยาย
ความสัมพันธ์ระหว่างตัวแปรสองตัวนี้ได้ดีนัก
ตรงนั้น
นั่นคือบทเริ่มต้น
ลองดูว่าเราจัดการพลอตกระจายพวกนี้ได้ไหม
วิธีที่ผมจทำ คือผมจะ
พยายามกะด้วยสายตาว่าแบบจำลองเชิงเส้น
จะเป็นอย่างไร
มนมีวิธีหาแบบจำลองเชิงเส้นที่เข้ากับข้อมูล
มากที่สุดได้หลายวิธี 
โดยเฉพาะข้อมูลที่ไม่สมบูรณ์แบบ
ผมวาดอันที่สมบูรณ์แบบมาก อย่างน้อยก็
สำหรับ r เท่ากับลบ 1 กับ r เท่ากับ 1
แต่นี่คือหน้าตาของข้อมูลในโลกความจริง
น้อยครั้งที่คุณจะได้ทุกอย่างอยู่บนเส้นตรงสมบูรณ์
สำหรับพลอตแบบกระจาย A 
ถ้าผมพยายามลากเส้นตรง
มันจะเป็นแบบนั้น
ถ้าผมพยายามทำให้ระยะห่างระหว่าง
จุดกับเส้นตรงน้อยที่สุด ผมจะเห็นแนวโน้มทั่วไป
ถ้าเราดูจุดข้อมูลเหล่านี้ตรงนี้
เมื่อ y สูง, x จะต่ำ
เมื่อ x เพิ่มขึ้น, y จะเล็กลง
ดูเหมือนว่า r จะน้อยกว่า 0
และมันน้อยกว่า 0 พอสมควร

English: 
or a line that looks like that.
A linear model really does not describe
the relationship between
the two variables that well,
right over here.
So with that, is a primer.
Let's see if we can
tackle these scatterplots.
The way I'm gonna do it is I'm just gonna
try to eyeball what a linear
model might look like.
There's different methods of
trying to fit a linear model
to a dataset, an imperfect dataset.
I drew very perfect ones, at least for the
r equals negative one and r equals one
but these are what the real
world actually looks like.
Very few times will things
perfectly sit on a line.
For scatterplot A, if I
were to try to fit a line,
it would look something like that.
If I were to try to
minimize distances from
the points to the line,
I do see a general trend
if we look at these data points over here,
when y is high, x is low.
When x is larger, y is smaller.
Looks like r is going
to be less than zero,
and a reasonable bit less than zero.

Thai: 
จะเข้าใกล้อันนี้ตรงนี้
ถ้าเราดูตัวเลือกของเรา
มันจะไม่ใช่ r เท่ากับ 0.65
พวกนี้เป็นบวก ผมจึงไม่เลือกอันนั้นหรืออันนั้น
และอันนี้แทบไม่มีสหสัมพันธ์เลย
r เท่ากับลบ 0.02 มันใกล้กับ 0 มาก
ผมพอใจกับ r เท่ากับลบ 0.72
ผมอยากบอกให้ชัด ถ้าผมไม่มีตัวเลือกเหล่านี้
ผมจะบอกไม่ได้ว่า
ถ้าดูแค่จุดข้อมูลเหล่านี้โดยไม่ได้
คิดคำนวณ
ผมบอกไม่ได้ว่า r จะเท่ากับลบ 0.72
ผมแค่บอกจากสัญชาตญาณว่ามันมี
สหสัมพันธ์เป็นลบ มันค่อนข้างชัดเจน
รูปแบบโผล่ขึ้นมาให้เห็น
ว่าเมื่อ y มาก x จะน้อย
เมื่อ x มาก y จะน้อย
ผมจึงชอบอันที่เข้าหา
r เท่ากับลบ 1
ผมใช้อันนี้ไปแล้ว
ทีนี้พลอตแบบกระจาย B 
ถ้าผมพยายามกะด้วยสายตา
เหมือนเดิม อันนี้ไม่สมบูรณ์แบบ
แต่แนวนอน ถ้าผมพยายามลากเส้นตรง
มันจะเป็นแบบนั้น
มันดูเหมือนว่าเส้นตรงเข้ากับข้อมูลได้ดีทีเดียว
มันมีจุดที่ยังเข้ากับเส้นตรงยาก
มันยังไกลจากเส้นตรงนั้น

Bulgarian: 
То ще клони към това нещо тук.
Ако разгледам отговорите,
няма да имаме r  = 0,65.
Тези са положителни, така че няма да използвам
този или този коефициент.
А тук нямаме почти никаква 
корелация.
r = –0,02 е доста близо до нулата.
Чувствам се уверен в r  = –0,72.
Искам да съм ясен. Ако 
нямах тези отговори тук,
нямаше да мога просто
така да кажа,
само като гледам тези точки с данни,
без да мога да направя 
някакви изчисления,
че r е равно на –0,72.
Основавам се само на логиката, че
имаме отрицателна корелация,
която изглежда доста силна.
Зависимостта един вид просто
ти изниква насреща,
че когато у е голямо, х е малко.
Когато х е голямо, у е малко.
Така че ми трябва нещо,
което клони към r = –1.
Вече използвах този коефициент.
Сега при точкова диаграма В, ако трябваше
просто да я преценя на око,
това отново ще бъде неточно.
Но тенденцията, ако трябваше
да се опитам да начертая права,
тя би изглеждала по подобен начин.
Щеше да изглежда, че
една права пасва доста добре.
Има няколко точки, които
ще бъде трудно да паснат.
Те ще са доста далеч от правата.

Korean: 
여기 이것에 접근할 것입니다
우리의 선택을 보면
r은 0.65가 아닐 것입니다
이것들은 양수이고, 따라서 저는
 이것과 이것을 사용하지 않을 것입니다
그리고 이것은 거의 상관관계가 없는 것입니다
r은 -0.02이고, 이것은 0에 상당히 가깝습니다
r이 -0.72인 것이 그럴듯해 보입니다
저는 분명히 하고 싶은데, 제게 선택지가 없었다면
저는 말할 수 없었을 것입니다
아무런 계산을 하지 않고
단지 데이터 점들만을 보고는
r이 -0.72라는 것을 말이죠
저는 음의 상관관계라는 직관에 기반하고 있고
그것은 꽤 적합해 보입니다
여러분에게 보이는 패턴은
y가 크면 x가 작습니다
x가 크면, y가 작습니다
따라서 저는 r이 -1에 가까워지는 것이
좋습니다
저는 이것을 이미 사용했습니다
이제 산포도 B를 보면, 한번 살펴보면
이것도 완벽하지 않을 것입니다
하지만 추세는, 선을 맞추려 하면
이런 식으로 생길 것입니다
선이 상당히 잘 맞는 것으로 보입니다
몇 개의 점은 여전히 맞추기 힘듭니다
그것들은 여전히 선에서 꽤 멀리 떨어져 있습니다

English: 
It's going to approach this thing here.
If we look at our choices,
it wouldn't be r equals 0.65.
These are positive so I wouldn't
use that one or that one.
And this one is almost no correlation.
R equals negative 0.02, this
is pretty close to zero.
I feel good with r is
equal to negative 0.72.
I wanna be clear, if I didn't
have these choices here,
I wouldn't just be able to say,
just looking at these data points without
being able to do a calculation,
that r is equals to negative 0.72.
I'm just basing it on
the intuition that it is
a negative correlation,
it seems pretty strong.
The pattern kind of jumps out at you,
that when y is large, x is small.
When x is large, y is small.
So I like something that's approaching
r equals negative one.
I've used this one up already.
Now scatterplot B, if I were
to just try to eyeball it,
once again this is gonna be imperfect.
But the trend, if I were
to try to fit a line,
it looks something like that.
It looks like a line
fits in reasonably well.
There's some points that
would still be hard to fit.
They're still pretty far from the line.

English: 
It looks like it's a positive correlation.
When y is small, x is
relatively small and vice versa.
As x grows, y grows and
when y grows, x grows.
This ones going to be positive
and it looks like it would
be reasonably positive.
I have two choices here.
I don't know which of
these it's going to be.
It's either going to be r is equal to 0.65
or r is equal to 0.84.
I also got scatterplot C,
this ones all over the place.
It kinda looks like what we did over here.
What does a line look like?
You could almost imagine anything.
Does it look like that?
Does a line look like that?
There's not a direction
that you could say,
"Well, as x increases, maybe
y increases or decreases."
There's no rhyme or reason here,
so this looks very non-correlated.
So this one is pretty close to zero.
I feel pretty good that this is the
r is equal to negative .02.
In fact, if we tried
probably the best line
that could be fit, would be one with
a slight negative slope.

Bulgarian: 
Но изглежда, че имаме 
положителна корелация.
Когато у е малко, х е относително
малко и обратното.
Когато х расте, у расте и когато
у расте, х расте.
Това ще бъде положителна 
корелация
и изглежда, че ще бъде доста
положителна.
Тук имам два отговора.
Не знам кой от тях ще бъде.
Ще имаме или r = 0,65
или r = 0,84.
Имам също и точкова диаграма С, 
тази с точки навсякъде.
Тя прилича на това, което
направихме тук.
Как ще изглежда правата?
Можеш да си представиш
почти всичко.
Ще изглежда ли така?
Ще изглежда ли правата
по този начин?
Няма никаква посока, за която
може да кажеш:
"Когато х нараства, може би
у нараства или намалява."
Тук няма никаква логика,
така че изглежда много
некорелативно.
Така че това е доста близо до 0.
Сигурен съм, че това е r = –0,02.
Всъщност, ако пробваме с възможно
най-добрата права,
това щеше да съвпада, 
щеше да бъде тази с
малък отрицателен наклон.

Thai: 
มันดูเหมือนว่ามีสหสัมพันธ์แบบบวก
เมื่อ y น้อย x จะน้อย และในทางกลับกัน
เมื่อ x โตขึ้น y จะโตขึ้น และ
เมื่อ y โตขึ้น x จะโตขึ้น
อันนี้จะเป็นบวก
และมันดูเหมือนว่าเป็นบวกพอสมควร
ผมมีตัวเลือกสองตัวตรงนี้
ผมไม่รู้ว่าอันไหนจะใช่
มันจะเป็น r เท่ากับ 0.65
หรือไม่ก็ r เท่ากับ 0.84
ผมยังมีพลอตแบบกระจาย C 
อันนี้กระจายทั่วไปหมด
มันดูเหมือนสิ่งที่เราทำไปตรงนี้
เส้นตรงจะเป็นอย่างไร?
คุณคงคิดว่าเป็นอะไรก็ได้
มันดูเป็นอย่างนั้นหรือเปล่า?
เส้นตรงเป็นอย่างไร?
มันไม่มีทิศทางที่คุณบอกได้
ว่าเมื่อ x เพิ่มขึ้น y จะเพิ่มขึ้นหรือลดลง
มันไม่มีรูปแบบหรือเหตุผลอะไรตรงนี้
อันนี้ดูไม่เข้ากันมากๆ
อันนี้จึงใกล้กับ 0
ผมรู้สึกมั่นใจว่าอันนี้
คือ r เท่ากับลบ 0.02
ที่จริง ถ้าเราลองหาเส้นตรงที่เข้ากับ
ข้อมูลได้ดีที่สุด มันจะเป็นเส้น
ที่ความชันเป็นลบนิดหน่อย

Korean: 
양의 상관관계가 있는 것으로 보입니다
y가 작으면, x는 상대적으로 작고 반대도 마찬가지입니다
x가 증가하면 y가 증가하고,
 y가 증가하면 x가 증가합니다
이것은 양이 될 것이고
합리적으로 양수인 것으로 보입니다
여기 두 가지 선택지가 있습니다
저는 어떤 것이 될지 모릅니다
r은 0.65가 될 수도 있고
r은 0.84가 될 수도 있습니다
저는 완전히 퍼져있는 산포도 C도 있습니다
우리가 여기서 했던것과 비슷합니다
선이 어떻게 생겼나요?
여러분은 거의 아무렇게나 상상할 수 있습니다
이렇게 생겼나요?
선이 이렇게 생겼나요?
여러분이 
"음, x가 증가함에 따라 y가 증가하거나 감소하네요"
라고 말할 수 있는 방향성이 없습니다
여기에는 어떠한 규칙도 없고
따라서 거의 상관관계가 없는 것으로 보입니다
그러므로 이것은 거의 0에 가깝습니다
r이 -0.02라고 하는 것이 좋겠습니다
r이 -0.02라고 하는 것이 좋겠습니다
사실, 우리가
딱 맞는 선을 그으려 한다면
약간의 음의 기울기를 가질 것입니다

Thai: 
มันอาจเป็นแบบนี้
และสังเกตดู ถึงแม้เราจะลากเส้นตรงที่ดีที่สุด
มันก็ยังมีจุดมากมายที่ห่างจากเส้นตรงมาก
แบบจำลองเชิงเส้นจึงไม่ได้เข้ากับข้อมูลนัก
r เท่ากับลบ 0.02
เราจะใช้อันนั้น
ทีนี้เรามีพลอตแบบกระจาย D
มันจะใช้ค่าสหสัมพันธ์ที่เป็นบวกอีกตัว
มันดูเหมือนว่ามีความสัมพันธ์ร่วมเป็นบวกอยู่
เมื่อ y ต่ำ, x จะต่ำ
เมื่อ x สูง, y จะสูง และในทางกลับกัน
เราลองหาเส้นแทนข้อมูลที่
เป็นอย่างนั้นได้
แต่มันยังไม่ดีเท่ากับอันนั้น
คุณเห็นจุดที่เราพยายามลากเส้นได้
ยังมีหลายจุดที่ห่างออกไป
จากแบบจำลองของเรา
แบบจำลองไม่ได้เข้ากับข้อมูลนัก
ผมจึงบอกว่าพลอตแบบกระจาย B แทนข้อมูลดีกว่า
แบบจำลองเชิงเส้นใช้แทนข้อมูลได้ดีกว่าสำหรับ
พลอตแบบกระจาย B
มากกว่าพลอตแบบกระจาย D
ผมจะให้ค่า r ตัวมากกับ
พลอตแบบกระจาย B
และ r ตัวน้อย r เท่ากับ 0.65 
ให้กับพลอตแบบกระจาย D

Bulgarian: 
Може да изглежда по подобен начин.
И забележи, че дори ако
се опитаме да начертаем права,
има всякакви видове точи, които
се намират на разстояние от правата.
Така че линейният модел
не пасва толкова добре.
r е равно на –0,02.
Така че ще използваме този отговор.
Сега имаме точкова диаграма D.
Ще използваме една от
другите положителни корелации,
като наистина изглежда, че тук
имаме положителна корелация.
Когато у е ниско, х е ниско.
Когато х е високо, у е високо
и обратното.
Можем да опитаме да нагодим
права, която изглежда
по подобен начин.
Но няма да е добра
колкото тази.
Можеш да видиш от точките,
които се опитваме да обхванем,
че има няколко точки, които
са доста далеч от модела.
Моделът не съвпада толкова добре,
така че бих казал, че точкова
диаграма В съвпада по-добре.
Един линеен модел пасва повече
на точкова диаграма В,
отколкото на точкова диаграма D.
Ще дам по-голямото
r на точкова диаграма В
и по-малкото r или r = 0,65 на
точкова диаграма D.

English: 
It might look something like this.
And notice, even when
we try to fit a line,
there's all sorts of points
that are way off the line.
So the linear model did
not fit it that well.
R is equal to negative 0.02,
So we'll use that one.
Now we have scatterplot D.
That's gonna use one of the
other positive correlations
and it does look like there
is a positive correlation.
When y is low, x is low.
When x is high, y is high and vice versa.
We could try to fit something that looks
something like that.
But it's still not as good as that one.
You can see the points
that we're trying to fit,
there's several points that
are still pretty far away
from our model.
The model is not fitting it that well,
so I would say scatterplot
B is a better fit.
A linear model works
better for scatterplot B
than it works for scatterplot D.
I would give the higher r to scatterplot B
and the lower r, r equals
0.65, to scatterplot D.

Korean: 
아마 이렇게 생길 것입니다
우리가 선을 맞추려고 해도
선에서 벗어난 모든 종류의 점들이 있습니다
따라서 선형 모델은 그다지 잘 맞춰지지 않습니다
r은 -0.02이고
우리는 이것을 사용할 것입니다
이제 산포도 D를 봅시다
이것은 다른 양의 상관계수를 사용해야 할 것이고
양의 상관관계가 있는 것으로 보입니다
y가 작으면, x가 작습니다
x가 크면 y도 크고, 반대도 마찬가지입니다
우리는 이렇게 보이는 것
이런 것에 맞추는 것을 시도할 수 있습니다
그러나 여전히 그만큼 좋지는 않습니다
여러분이 우리가 맞추려고 하는 것을 보면
우리의 모델로부터 여전히 꽤 멀리 떨어진 점들이
몇 개 있습니다
모델은 그렇게 잘 맞지 않고
따라서 저는 산포도 B가 더 적합하다고 할 것입니다
선형 모델은 산포도 D보다
산포도 B에서 더 적합합니다
저는 산포도 B에 더 높은 r을 부여할 것이고
산포도 D에는 더 낮은 r=0.65를 부여할 것입니다

English: 
R is equal to 0.65.
Once again that's because
with a linear model
it looks like there's a
trend but there's several
more data points are way off the line
in scatterplot D than in
the case of scatterplot B.
There's a few that are
still way off the line
but these are even more
off of the line in D.

Thai: 
r เท่ากับ 0.65
ย้ำอีกครั้ง นั่นเป็นเพราะจากแบบจำลองเชิงเส้น
มันดูเหมือนจะมีแนวโน้มแต่มันมี
หลายจุดที่ห่างจากเส้นตรงในพลอต
แบบกระจาย D มากกว่าในกรณีของ
พลอตแบบกระจาย B
มีหลายจุดที่ยังห่างจากเส้นตรง
แต่มันยิ่งมากไปใหญ่สำหรับเส้นตรงใน D

Bulgarian: 
r е равно на 0,65.
Още веднъж, това е така, защото
с даден линеен модел
изглежда, че тук имаме някаква
тенденция, но има няколко
точки, които са на по-голямо
разстояние от правата
при точкова диаграма D, отколкото
в случая с точкова диаграма В.
Има няколко, които са все още
на разстояние от правата,
но тези са много по-отдалечени
от правата при D.

Korean: 
r은 0.65입니다
선형 모델을 사용하면
추세가 있는 것처럼 보이지만
산포도 B보다 산포도 D에서
더 많은 점들이 선에서 벗어나 있습니다
여전히 선에서 벗어난 몇몇이 있지만
D에서는 더 많이 벗어나 있습니다
