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# Regresi Linear Sederhana

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### Regresi Linear Sederhana

1. 1. Regresi linear sederhana
2. 2. When do we use regression? <ul><li>Don’t use it to determine the strength of association between to variables. </li></ul><ul><li>Do use it if you want to predict the value of Y given X . </li></ul>X 1 X 2 Korelasi X Y Regresi
3. 3. Regression or correlation? <ul><li>Correlation : degree of association between two variables X and Y; no causal relationship assumed ! </li></ul><ul><li>Regression : to predict the value of the dependent variable if the independent variable were changed; causal relationship assumed ! </li></ul>
4. 4. Model regresi sederhana <ul><li>Semua model regresi sederhana terdiri dari 2 parameter; intersep ( α ) dan slope ( β ). </li></ul><ul><li>Model taksiran </li></ul><ul><li>Tiap psg pengamatan memenuhi </li></ul>β =  Y  X (slope) sisaan X  X  Y  (intercept)  i X i Y i Observed Expected
5. 5. <ul><li>Dugaan slope β adalah b yaitu : </li></ul><ul><li>Dugaan intersp α adalah a yaitu : </li></ul>Koefisien Regression dan correlation <ul><li>correlation r adalah : </li></ul><ul><li>sehingga, </li></ul><ul><li>b = r jk X dan Y memiliki varians sama </li></ul><ul><li>and if b = 0 maka r = 0. </li></ul>
6. 6. Hypothesis testing : testing model parameters <ul><li>Uji Serentak (ANOVA) </li></ul><ul><li>F = MS R / MS e > F 1,,n - 2 </li></ul><ul><li>Uji Parsial </li></ul><ul><li>Uji tiap hypothesis dgn t -test: </li></ul><ul><li>Note: hipotesis 2-arah ! </li></ul>Y  Y H 01 :  = 0 Y = 0 X Y  H 02 : b = 0 X Y  Observed Expected
7. 7. Asumsi Residual <ul><li>Residuals are independent and normally distributed. </li></ul><ul><li>The variance of the residuals is equal for all X (homoscedasticity). </li></ul><ul><li>The relationship between Y and X is linear. </li></ul><ul><li>There is no measurement error on X (Model I regression). </li></ul>
8. 8. Pemeriksaan asumsi residual <ul><li>Analisis residual I: independence </li></ul><ul><li>Plot residuals vs dugaan, lihat bentuk polanya. </li></ul><ul><li>Lakukan ACF plot. </li></ul>Estimate Residual
9. 9. Pemeriksaan asumsi residual <ul><li>Plot residuals against estimates; look for patterns. </li></ul><ul><li>Do normal probability plot. </li></ul><ul><li>Check with Lilliefors test. </li></ul><ul><li>Analisis residual II: NORMALITY </li></ul>NEDs Residual Normal Non-normal Residual Estimate
10. 10. <ul><li>Plot residuals against estimates; look for patterns. </li></ul><ul><li>Check with Levene’s test by grouping Y ’s into several classes. </li></ul>Pemeriksaan asumsi residual <ul><li>Analisis residual III: homokedastisitas </li></ul>Estimate Residual Group 1 Group 2 Group 3 Residual Estimate
11. 11. <ul><li>Plot residuals against estimates; look for patterns. </li></ul>Pemeriksaan asumsi residual <ul><li>Analisis residual IV: linieritas </li></ul>Residual X Y Estimate
12. 12. Apa yang harus dilakukan jika aasumsi tidak terpenuhi ? <ul><li>Try transforming the data, but remember: (1) for some data, no transformation will </li></ul><ul><li>work; </li></ul><ul><li>(2) finding an appropriate transformation may not be easy. </li></ul><ul><li>Use non-linear regression. </li></ul>
13. 13. Transformasi dalam regresi 0 200 400 600 1.2 2.4 3.6 4.8 6.0 7.2 Length (mm) Weight (kg) 10 100 1000 0.001 0.01 0.1 1.0 8.0 Length (mm; log scale) Weight (kg; log scale) Weight versus length in the beetle Scorpaenichthys marmoratus
14. 14. Transformasi dalam regresi 10 20 50 100 150 Chirps/min o C 10 20 40 80 120 160 Chirps/min (log scale)
15. 15. Transformasi dalam regresi 0 10 20 30 40 50 60 70 Relative brightness (times) 0 1 2 3 4 5 6 7 Millivolts Electrical resistance as a function of illumination in cephalopod eyes. 70 1 2 5 10 20 50 Relative brightness (times) in log scale 0 1 2 3 4 5 6 7 Millivolts