Korelasi dan Regresi

HERTANTO WAHYU SUBAGIO

KORELASI DAN REGRESI LINEAR

Korelasi
* menunjukkan arah hubungan
* Uji :
r product moment Pearson
Spearman
Kendall
* Nilai : -1 s/d +1

Corre la t ion be t w e e n
Pla sm a volum e a nd body w e ight
in 8 he a lt hy m e n

Subject
1.
2
2.
3.

4.
5.
6.
7.
8.

Body weight (kg)
58.0
70
70.0
0
74.0
63.5
62.0
70.5
71.0
66.0

Plasma vol. (l)
2.75

2
2.86
86
3.37
2.76
2.62
3.49
3.05
3.12

Scatter Plot

Some possibilities in scatter plot

Formula

SPSS output
Correlations

Tekanan sistolik (mm Hg)

Tekanan diastolik (mm
Hg)

Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N

Tekanan
Tekanan
sistolik
diastolik
(mm Hg)
(mm Hg)
1 000
1,000
,814

814**
,
,000
30
30
,814**
,814
1,000
,000
,
30
30

**.. Correlation is significant at the 0
0.01
01 level (2-tailed)
(2-tailed).

X m e m pe nga ruhi Y ?

Teka
anan sistolik (m
mm Hg)

60

70

80

Tekanan diastolik (mm Hg)

50

100

120

140

160

180

200

90

100

Diagram Pencar

110

120

130

Regresi
* Mampu memprediksi DV dari perubahan IV

* Uji :
- regresi sederhana : Y
Y=a+bX.
a+bX.
- regresi majemuk : Y = a + b1X1 + b2X2 ……….biXi
* Tidak otomatis menunjukkan sebab akibat

Line a r re g
gre ssion
• Give s t he e quat ion of t he st ra ight line t hat be st de sc ribe s
it a nd e na ble s t he pre dic t ion of one va ria ble from t he ot he r

T he e quat ion is : y = a + bx
a = intercept
b = slope = regression coefficient
y = dependent var
var.
x = independent var.

T he va lue s for a a nd b a re c a lc ulat e d so a s t o m inim ize t he

sum of t he squa re d ve r t ic a l dist a nc e s of t he point s from t he
line . T his is c a lle d a le a st squa re fit .

Linear Regression

Line

The intercept and slope of regression equation
y=a+bx

Pla sm a vol=0 .0 8 6 +0 .0 .0 4 4 X bodyw e ight

SPSS Output :
•
•
•
•
•
•

Descriptive statistics
Correlations
Variables entered/removed
Model summary
Anova
Coefficients

Descriptive Statistics

Tekanan sistolik (mm Hg)
Tekanan diastolik (mm
Hg)

Mean
M
141,67

Std Deviation
Std.
D i ti

20,57

85 67
85,67

15 13
15,13

N
30
30

Correlations

Pearson Correlation

Sig. (1-tailed)

N

r = 0 .8 1 4

Tekanan sistolik (mm Hg)
Tekanan diastolik (mm
Hg)
Tekanan sistolik (mm Hg)
Tekanan diastolik (mm
Hg)
Tekanan sistolik (mm Hg)
Tekanan diastolik (mm
Hg)

Tekanan
sistolik
(mm Hg)
1,000

Tekanan
diastolik
(mm Hg)
,814

,814

1,000

,

,000

,000

,

30

30

30

30

Variables Entered/Removedb

Model
1

Variables
Entered
Tekanan
diastolik a
(mm Hg)

Variables
Removed

Method
,

Enter

a. All requested variables entered
entered.
b. Dependent Variable: Tekanan sistolik (mm Hg)

Model Summary

Model
1

R
R Square
,814a
,662

Adjusted
Adj
sted
R Square
,650

Std. Error of
Std
the Estimate
12,17

a. Predictors: (Constant), Tekanan diastolik (mm Hg)

R2 = Koefisien determinasi
= Sumbangan var bebas terhadap kejadian var dependent

66 2% kejadian var dependent ditentukan oleh var bebas
66.2%

ANOVAb
Sum of
Model
Squares
1
Regression 8121,557
Residual
4145,109
Total
12266,667

df

Mean Square
1
8121,557
28
148,040
29

F
54,861

Sig.
,000a

a. Predictors: (Constant), Tekanan diastolik (mm Hg)
b Dependent Variable: Tekanan sistolik (mm Hg)
b.

F hit ung = 5 4 .8 9 , p = 0 .0 0 0
M ode l re gre si da pat dipa k a i unt uk m e m pre dik si va r de pe nde nt

Coefficientsa

Model
1

(Constant)
Tekanan diastolik
(mm Hg)

Standardi
zed
Unstandardized
U
sta da d ed
Coefficien
Coe
ce
Coefficients
ts
B
Std. Error
Beta
46,900
12,986
1,106

,149

,814

t
3,612

Sig.
,001

7,407

,000

a. Dependent
p
Variable: Tekanan sistolik ((mm Hg)
g)

Y = 46.9 + 1.106 X
Sistole = 46.9 + 1.106 diastole

X m e m pe nga ruhi
hi Y :

?