This document discusses simple regression and correlation analysis. It defines key terms like dependent and independent variables. Regression analysis finds the linear relationship between two variables, while correlation determines the strength of their relationship. The document explains the objectives of regression analysis, describing population and sample regression lines. It provides formulas to calculate coefficients, the standard error, and the coefficient of determination. Sample problems and their interpretations are presented to illustrate the concepts. Hypothesis tests for the regression coefficient and overall model are also introduced.

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
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in
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i
n
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n
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n
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1
2
1
11
1
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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
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 
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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
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t
2
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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 