Modul 5 Correlation Regression

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CORRELATION &

REGRESSION

STATISTIKA TEKNIK

LNK2016


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Correlation is a statistical method used to determine whether a

relationship between variables exists.

Regression is a statistical method used to describe the nature of

the relationship between variables, that is, positive or negative,

linear or nonlinear.

The purpose of this chapter is to answer these questionsstatistically:

1. Are two or more variables related?

2. If so, what is the strength of the relationship?

3. What type of relationship exists?

4. What kind of predictions can be made from the

relationship?


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correlation coefficient : a measure that REPRESENTS strength of the

relationship between or among the variables.

There are two types of relationships:

simple and multiple.

In a simple relationship, there are two variables

—an independent variable, also called an explanatory variable or a predictor

variable, and

-- a dependent variable, also called a response variable.

A simple relationship analysis is called simple regression, and there is one

independent variable that is used to predict the dependent variable.

In a multiple relationship, called multiple regression, two or more independent

variables are used to predict one dependent variable. This type of study involves

several variables.


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Simple relationships can also be positive or negative.

A positive relationship exists when both variables increase ordecrease at the same time.

For instance, a person’s height and weight are related; and the

relationship is positive, since the taller a person is, generally, themore the person weighs.

In a negative relationship, as one variable increases, the

other variable decreases, and vice versa.

For example, if you measure the strength of people over 60 years ofage, you will find that as age increases, strength generally decreases.

The word generally is used here because there are exceptions.


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Some predictions are more accurate than others, due to

the strength of the relationship.

That is, the stronger the relationship is between

variables, the more accurate the prediction is.


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Scatter Plots and Correlation

The possibilities include a positive linear relationship, a

negative linear relationship, a curvilinear relationship, or nodiscernible relationship.


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examples

POSITIVE

RELATION-

SHIPTEND TO

LINEAR


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E

x a m p l e 2

NEGATIVERELATION-

SHIP

TEND TO

LINEAR


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E

x a m p l e 3

NO PATTERN

NO SPECIFICRELATIONSHIP


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" !*,P/0,2 !*+,-./0# 959+.2 /,:,+.=. 59.489:92;.2 .24.+. 69.


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STRONG POSITIF LINEAR RELATIONSHIP $ 0 TO +1

NO LINEAR RELATIONSHIP $ = 0STRONG NEGATIVE LINEAR RELATIONSHIP $ 0 TO -1


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COEFFICIENT

CORRELATION


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!*+,-./0 K,.+/*2


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TARAF SIGNIFIKANSI :

• Adalah suatu formasi yang ditetapkan oleh peneliti/penulis.

• Disimbolkan dengan :α

• Disesuaikan dengan isu/topik kajian dan tuntutan akurasi

data

•

Sesuai alasan pertimbangan yang rasional;

• Untuk bidang eksakta/teknik ! = 5% = 0,05

:(%& K#"B&(%(J&' Y ! (< 5%) MAKA H0 DITOLAKDAN HA diterima

012 32*456,2,


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POSITIVE

STRONG

RELATIONSHIP


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NEGATIVE

STRONG

RELATIONSHIP


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POSITIVE

WEAK

RELATIONSHIP


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78,89 !6*050,8: 012

!496;8,2


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REGRESSION

If the value of the correlation coefficient is significant,

the next step is to determine the equation of the

regression line, which is the data’s line of best fit.

(Note: Determining the regression line when r is notsignificant and then making predictions using the

regression line are meaningless.)

The purpose of the regression line is to enable the

researcher to see the trend and make predictions on

the basis of the data.


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• Regresi # alat ukur yang juga digunakan untuk

mengukur ada atau tidaknya korelasi antar

variabelnya.

• Istilah regresi itu sendiri berarti ramalan atau

taksiran.

•

Persamaan yang digunakan untuk mendapatkan garisregresi pada data diagram pencar disebut persamaan

regresi.

• Untuk menempatkan garis regresi pada data yang

diperoleh maka digunakan metode kuadrat terkecil,sehingga bentuk persamaan regresi adalah sebagai

berikut: Y’ = a + b X


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PERSAMAAN REGRESI


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DARI PERSAMAAN REGRESI Y’ = a + b X

• Nilai konstan (a)$ nilai nol untuk variable observasi x

(negatif or positif)

•

Bilai nilai x jauh dari 0 maka nilai tersebut hanyamerupakan ekstrapolasi (penaksiran diluar jangkauan)

• Nilai (b) merupakan koefisien regresi, nilai tersebut

menunjukkan kemiringan garis lurus yang ditemukan.

•

Makna nilai b, setiap x bertambah satu satuan,maka yakan bertambah menjadi b kali satuan pengukuran


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• Kesamaan di antara garis regresi dan garis trend tidak

dapat berakhir dengan persamaan garis lurus.

•

Garis regresi (seperti garis trend dan nilai tengaharitmatika) memiliki dua sifat matematis berikut :

!(Y – Y’) = 0 dan !(Y – Y’)2 = nilai terkecil atau

terendah.

•

Dengan perkataan lain, garis regresi akanditempatkan pada data dalam diagram sedemikian

rupa sehingga penyimpangan (perbedaan) positif titik-

titik terhadap titik-titik pencar di atas garis akan

mengimbangi penyimpangan negatif titik-titik pencar

yang terletak di bawah garis, sehingga hasil

penyimpangan keseluruhan titik-titik terhadap garis

lurus adalah nol.


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KOEFISIEN DETERMINASI$ R 2 = R *

R


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F a A"%GH$ K$EXG&%&EK#"DG!

TENTUKAN

A. Nilai korelasi dan determinasi

B. Persamaan Regresi Sederhana

C. Analisis dan Kesmpulan


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Given a scatter plot, you must be able to draw the line of best fit.

Best fit means that the sum of the squares of the vertical distancesfrom each point to the line is at a minimum.

The reason you need a line of best fit is that the values of y will bepredicted from the values of x; hence, the closer the points are to theline, the better the fit and the prediction will be.


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Modul 5 Correlation Regression

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