KORELASI DAN REGRESI LINEAR
HERTANTO WAHYU SUBAGIO
Korelasi * menunjukkan arah hubungan * Uji : r product moment Pearson Spearman Kendall * Nilai : -1 s/d +1
Correlation between Plasma volume and body weight in 8 healthy men
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 mempengaruhi Y ?
Diagram Pencar 200
180
Teka anan sistolik (m mm Hg)
160
140
120
100 50
60
70
80
Tekanan diastolik (mm Hg)
90
100
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
Linear regression g •Gives the equation of the straight line that best describes it and enables the prediction of one variable from the other
The equation is : y = a + bx a = intercept b = slope = regression coefficient y = dependent var var. x = independent var. The values for a and b are calculated so as to minimize the sum of the squared vertical distances of the points from the line. This is called a least square fit.
Linear Regression
Line
The intercept and slope of regression equation y=a+bx
Plasma vol=0.086+0.0.044 X bodyweight
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 = 0.814
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 hitung = 54.89, p = 0.000 Model regresi dapat dipakai untuk memprediksi var dependent
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 mempengaruhi hi Y :
?
