Matakuliah
Tahun
: L0104 / Statistika Psikologi
: 2008
Regresi dan Korelasi Linear
Pertemuan 19
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa akan dapat menganalisis dugaan
parameter persamaan regresi, koefisien korelasi
dan determinasi.
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Outline Materi
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Model matematik
Metode kuadrat terkecil
Asumsi-asumsi model
Pendugaan parameter regresi dan
peramalan
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Simple Linear Regression
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Simple Linear Regression Model
Least Squares Method
Coefficient of Determination
Model Assumptions
Testing for Significance
Using the Estimated Regression Equation
for Estimation and Prediction
• Computer Solution
• Residual Analysis: Validating Model Assumptions
• Residual Analysis: Outliers and Influential
Observations
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The Simple Linear Regression Model
• Simple Linear Regression Model
y = β0 + β1x + ε
• Simple Linear Regression
Equation
^
E(y) ^= β0 + β1x
• Estimated Simple Linear Regression Equation
y = b0 + b1x
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Least Squares Method
• Least Squares Criterion
min  (y i  y i ) 2
where:
yi = observed value of the dependent variable
^
for the ith observation
yi = estimated value of the dependent
variable
for the ith observation
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The Least Squares Method
• Slope for the Estimated Regression Equation
 xi y i  (  xi  y i ) / n
b1 
2
2
 xi  (  xi ) / n
• y-Intercept for the Estimated
Equation
_ Regression
_
b0 = y - b1x
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where:
_xi = value of independent variable for ith observation
_yi = value of dependent variable for ith observation
x = mean value for independent variable
y = mean value for dependent variable
n = total number of observations
Contoh Soal: Reed Auto Sales
• Simple Linear Regression
Reed Auto periodically has a special week-long
sale. As part of the advertising campaign Reed
runs one or more television commercials during
the weekend preceding the sale. Data from a
sample of 5 previous sales are shown below.
Number of TV Ads
1
3
2
1
3
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Number of Cars Sold
14
24
18
17
27
Contoh Soal: Reed Auto Sales
• Slope for the Estimated Regression Equation
b1 = 220 - (10)(100)/5 = 5
24 - (10)2/5
• y-Intercept for the^Estimated
Regression Equation
b0 = 20 - 5(2) = 10
• Estimated Regression Equation
y = 10 + 5x
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Contoh Soal: Reed Auto Sales
• Scatter Diagram
30
Cars Sold
25
20
y = 5x + 10
15
10
5
0
0
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1
2
TV Ads
3
4
The Coefficient of Determination
• Relationship Among SST, SSR, SSE
SST = SSR + SSE
2
2
^ )2
 ( y i  y )   ( y^i  y )   ( y i  y
i
• Coefficient of Determination
r2 = SSR/SST
where:
SST = total sum of squares
SSR = sum of squares due to regression
SSE = sum of squares due to error
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Contoh Soal: Reed Auto Sales
• Coefficient of Determination
r2 = SSR/SST = 100/114 = .8772
The regression relationship is very strong
since 88% of the variation in number of cars sold
can be explained by the linear relationship
between the number of TV ads and the number
of cars sold.
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The Correlation Coefficient
• Sample Correlation Coefficient
rxy  (sign of b1 ) Coefficien t of Determinat ion
rxy  (sign of b1 ) r 2
where:
b1 = the slope of the estimated
regression
yˆ  b0  b1 x
equation
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Contoh Soal: Reed Auto Sales
• Sample Correlation Coefficient
rxy  (sign of b1 )
yˆ  10  5 x
rxy = + .8772
The sign of b1 in the equation
is “+”.
rxy = +.9366
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r2
Model Assumptions
• Assumptions About the Error Term ε
– The error ε is a random variable with mean of
zero.
– The variance of ε , denoted by σ 2, is the
same for all values of the independent
variable.
– The values of ε are independent.
– The error ε is a normally distributed random
variable.
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Selamat Belajar
Semoga Sukses
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