Kul 5 Korelasi Dan Regresi2012I1

7/29/2019 Kul 5 Korelasi Dan Regresi2012I1

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Correlationlinear pattern of relationshipbetween one variable (x) and anothervariable (y) an association betweentwo variables

relative position of one variablecorrelates with relative distribution ofanother variable

graphical representation of the

relationship between two variablesWarning:

No proof of causality

Cannot assume x causes y


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A new sort of test : Perbedaan t-

test, chi square, correlasi

One qualitative and one quantitative variable

= t-test

Two qualitative variables = chi square

What if you have two quantitative variables,

and you want to know how much they go

together? E.g., study time and grades

correlation


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3

Overview of Correlation and Regression

Correlation seeks to establish whether a relationship exists betweentwo variables

Regression seeks to use one variable to predict another variable

Both measure the extent of a linear relationship between two variables

Statistical tests are used to determine the strength of the relationship

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Koefisien Korelasir

A measure of the strength and direction of a linear relationship between twovariables

The range ofris from 1 to 1.

Ifris close to 1

there is a strongpositive

correlation.

Ifris close to 1 there

is a strong negativecorrelation.

Ifris close to 0

there is no linearcorrelation.

1 0 1


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r indicates strength of relationship (strong, weak, or none)

direction of relationship

positive (direct) variables move in same direction

negative (inverse) variables move in opposite directions

r ranges in value from

1.0 to +1.0

Pearsons Correlation Coefficient

Strong Negative No Rel. Strong Positive

-1.0 0.0 +1.0


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Examples of positive and negative relationships. (a) Beer sales are positively

related to temperature. (b) Coffee sales are negatively related to temperature.

Contoh: Positive vs Negative


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Examples of relationships that are not linear: (a) relationship between

reaction time and age; (b) relationship between mood and drug dose.

Contoh: non-linear relationships


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Correlations:

0.0

6.7

13.3

20.0

0.0 4.0 8.0 12.0

C1 vs C2

C1

C2

0.0

40.0

80.0

120.0

0.0 83.3 166.7 250.0

C1 vs C2

C1

C2

Positive

Large values of X associated

with large values of Y,small values of X associatedwith small values of Y.

e.g. IQ and SAT

Large values of X associated

with small values of Y& vice versa

e.g. SPEED and ACCURACY

Negative


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x y

8 78

2 925 90

12 58

15 43

9 746 81

AbsencesFinalGrade

Application

959085807570656055

45

40

50

0 2 4 6 8 10 12 14 16

FinalGrad

e

X

Absences


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6084

8464

8100

33641849

5476

6561

624

184

450

696645

666

48657 516 3751 579 39898

1 8 78

2 2 92

3 5 90

4 12 58

5 15 43

6 9 74

7 6 81

64

4

25

144225

81

36

xy x2

y2

Computation ofr

x y


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Coefficient of Determination,

r 2

To understand the strength of the

relationship between two variables

The correlation coefficient, r, issquared

r 2 shows how much of the variationin one measure (say, fecal energy) isaccounted for by knowing the value

of the other measure (fecal lipid loss)


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Linear Regression Used when the goal is to predict the value of one

characteristic from knowledge of another Assumes a straight-line, or linear, relationship between two

variables

when term simpleis used with regression, it refers tosituation where one explanatory (independent) variable is

used to predict another Multipleregression is used for more than one explanatory

variable

If the point at which the line intercepts or crosses the Y-axis is a

and the slope of the line is denoted as b, then Y =1X + 0

Like y = mx + b

The slope is a measure of how much Y changes for a one-unit

change in X


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Regression: Correlation + Prediction

predicting y based on x

Regression equation

formula that specifies a line

y = bx + a

plug in a x value (distance from target) andpredict y (points)

note y= actual value of a score

y= predict value

Regression


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Simple Linear Regression

The regression line is the best fit through the data. Best fit is defined asthe average line the one that minimises the distance between the data

points and the line. It is the best description of the data

Y=bX + a Y is the dependent variable b is the slope of the line -

the rate at which Y willchange when X changes byone unit of X

a is the intercept that value

of Y when X is equal to zero


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The equation of a line may be written as y = mx + bwhere m is the slope of the line and b is the y-intercept.

The line of regression is:

The slope m is:

The y-intercept is:

Regression indicates the degree to which the variation in one variable X, is related to or can

be explained by the variation in another variable Y

Once you know there is a significant linear correlation, you can write an equation describing

the relationship between the xand yvariables. This equation is called the line of regression

or least squares line.

The Line of Regression


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Calculate m and b.

Write the equation of the

line of regression with

x= number of absencesand y= final grade.

The line of regression is: = 3.924x+ 105.667

6084

8464

81003364

1849

5476

6561

624

184

450696

645

666

486

57 516 3751 579 39898

1 8 78

2 2 92

3 5 904 12 58

5 15 43

6 9 74

7 6 81

64

4

25144

225

81

36

xy x2 y2x y


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0 2 4 6 8 10 12 14 16

4045

50556065707580

859095

Absences

Final

Grad

e

m = 3.924 and b = 105.667

The line of regression is:

Note that the point = (8.143, 73.714) is on the line.

The Line of Regression


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Kul 5 Korelasi Dan Regresi2012I1