2

1. Simple Regression and
Correlation Analysis

2. Pendahuluan
• Regression and correlation often prove vital in identifying
the nature of the relationship among the business and
economic variables that decision makers work with on a
daily basis or in engineering to make a decision.
• Regression and correlation analysis recognize that there
may be a determinable and quantifiable relationship
between two or more variables.
• Regression analysis was first developed by the English
scientist Sir Francis Galton (1822-1911)
 XfY   nXXXfY ,, 21 

3. Pendahuluan
• Y disebut sebagai variable dependent (terikat, tak
bebas), regressand variable, explained variable.
• X disebut sebagai variabel independent (variabel bebas),
regressor variable, explanatory variable.
• Regression and correlation are actually two different but
closely related concepts.
• Regression is a quantitative expression of the basic
nature of the relationship between the dependent and
independent variable.
• Correlation, on the other hand, determines the strength
of the relationship.

4. The Basic Objective of Regression Analysis
• Relationships between variables are either deterministic
or stochastic (random).
• Deterministic relationship can be expressed by a
mathematical model and there is no error.
• Model diatas menyatakan hubungan secara populasi
antara variabel X dan Y.
  XY 10
deterministic
component
random
component

5. The Basic Objective of Regression Analysis
• When estimating the true, but unknown, population
regression line with our sample regression
line , we are trying to find that line which
passes through the means of the various distributions of
Y-values for each X-value.
• Dalam menaksir paramater-parameternya, terdapat
beberapa asumsi (asumsi dalam OLS) :
– The error term is a random variable and is normally distributed.
– Any two errors are independent of each other.
– All error have the same variance.
– The means of Y-values all lie on a straight line.
XY 10  
XY 10
ˆˆˆ  

6. • Metode yang digunakan yaitu OLS (Ordinary Least
Square), yaitu meminimumkan error yang terjadi.
• Nilai dan diperoleh dari :
XY 10   XY ˆˆˆˆ
10  
xy 10
ˆˆ  
n
x
x
n
yx
yx
n
i
in
i
i
n
i
n
i
i
n
i
i
ii
2
1
1
2
1
11
1
ˆ

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











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
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








0
ˆ 1
ˆ
The Basic Objective of Regression Analysis

7. Hydrocarbon Level (X) in % Purity (Y) in %
0.99 90.01
1.02 89.05
1.15 91.43
1.29 93.74
1.46 96.73
1.36 94.45
0.87 87.59
1.23 91.77
1.55 99.42
1.40 93.65
1.19 93.54
1.15 92.52
0.98 90.56
1.01 89.54
1.11 89.85
1.20 90.39
Contoh :

8. Advertising (X) in $1000 Passengers (Y) in 1000
10 15
12 17
8 13
17 23
10 16
15 21
10 14
14 20
19 24
10 17
11 16
13 18
16 23
10 15
12 16
Contoh :

9. • Notasi-notasi :
The Basic Objective of Regression Analysis
n
x
xS
n
i
in
i
ixx
2
1
1
2


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

 

n
yx
yxS
n
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i
n
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in
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iixy
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 
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11
1
 

n
i
iiE yySS
1
2
ˆ
2
ˆ 2


n
SSE

  2
1
2
1
2
ynyyySS
n
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i
n
i
iT   
 

n
i
iR yySS
1
2
ˆ
ERT SSSSSS 

10. The Standard Error of The Estimate : A
Measure of Goodness of Fit
• The standard error of the estimate, Se, is a measure of
the average amount by which the actual observations for
Y vary around the regression line.
• Dalam data, hal ini identik dengan standar deviasi data.
• The standard error of the estimate dihitung :
2

n
SSE
MSE
MSESe 
 

n
i
iiE yySS
1
2
ˆ

11. The Standard Error of The Estimate : A
Measure of Goodness of Fit
• Sebagai latihan, hitunglah MSE untuk contoh yang
terakhir.
• Interpretasi yang disajikan, memiliki arti yang sama
dengan standard deviasi data ( ).X

12. Correlation dan Coefficient of
determination
• Coefficient of determination dirumuskan :
• The coefficient of determination measures the
explanatory power of the regression model by measuring
what portion of the change in Y is explained by the
change X.
• Semakin besar nilai coefficient determination, maka
makin baik.
• Nilai coefficient determination : 0-1.
T
E
T
R
SS
SS
SS
SS
R  12

13. • Hitunglah nilai coefficient of determination untuk contoh
terakhir.
• Interpretasi : ..... percent of the change in number of
passengers is explained by changes in advertising
expenditures.
• Correlation analysis is measure of strength of that
relationship
• Koefisien of korelasi :
– Bernilai
– r > 0, maka berkembang ke arah yang sama.
– r < 0, maka berkembang ke arah yang berbeda.
– r = 0, maka tidak ada hubungan.
2
Rr 
11  r
Correlation dan Coefficient of
determination

14. Uji Koefisien Regresi
• Hipotesis :
• Hitung t0, yaitu
• Tolak H0 jika
0:
0:
11
10




H
H
xx
o
S
t
2
1
ˆ
ˆ



2,
2


n
o tt 

15. Uji ANOVA
• Hipotesis : H0 = X tidak mempengaruhi Y.
H1 = X mempengaruhi Y.
• Tolak H0 jika 2,1,  no FF 