Regresi Linear Sederhana
This document discusses linear regression analysis. It explains that regression is used to predict the value of the dependent variable Y given the independent variable X, while correlation measures the strength of association between two variables without implying causation. The key aspects of a simple linear regression model are the intercept (留) and slope (硫). Hypothesis testing involves ANOVA to test the overall model and t-tests to test individual parameters. Assumptions that must be checked include independent and normally distributed residuals, equal variance of residuals, and a linear relationship between X and Y. Transforming variables can help satisfy assumptions when they are not met.
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Regresi Linear Sederhana
- 2. When do we use regression? Dont use it to determine the strength of association between to variables. Do use it if you want to predict the value of Y given X . X 1 X 2 Korelasi X Y Regresi
- 3. Regression or correlation? Correlation : degree of association between two variables X and Y; no causal relationship assumed ! Regression : to predict the value of the dependent variable if the independent variable were changed; causal relationship assumed !
- 4. Model regresi sederhana Semua model regresi sederhana terdiri dari 2 parameter; intersep ( 留 ) dan slope ( 硫 ). Model taksiran Tiap psg pengamatan memenuhi 硫 = Y X (slope) sisaan X X Y (intercept) i X i Y i Observed Expected
- 5. Dugaan slope 硫 adalah b yaitu : Dugaan intersp 留 adalah a yaitu : Koefisien Regression dan correlation correlation r adalah : sehingga, b = r jk X dan Y memiliki varians sama and if b = 0 maka r = 0.
- 6. Hypothesis testing : testing model parameters Uji Serentak (ANOVA) F = MS R / MS e > F 1,,n - 2 Uji Parsial Uji tiap hypothesis dgn t -test: Note: hipotesis 2-arah ! Y Y H 01 : = 0 Y = 0 X Y H 02 : b = 0 X Y Observed Expected
- 7. Asumsi Residual Residuals are independent and normally distributed. The variance of the residuals is equal for all X (homoscedasticity). The relationship between Y and X is linear. There is no measurement error on X (Model I regression).
- 8. Pemeriksaan asumsi residual Analisis residual I: independence Plot residuals vs dugaan, lihat bentuk polanya. Lakukan ACF plot. Estimate Residual
- 9. Pemeriksaan asumsi residual Plot residuals against estimates; look for patterns. Do normal probability plot. Check with Lilliefors test. Analisis residual II: NORMALITY NEDs Residual Normal Non-normal Residual Estimate
- 10. Plot residuals against estimates; look for patterns. Check with Levenes test by grouping Y s into several classes. Pemeriksaan asumsi residual Analisis residual III: homokedastisitas Estimate Residual Group 1 Group 2 Group 3 Residual Estimate
- 11. Plot residuals against estimates; look for patterns. Pemeriksaan asumsi residual Analisis residual IV: linieritas Residual X Y Estimate
- 12. Apa yang harus dilakukan jika aasumsi tidak terpenuhi ? Try transforming the data, but remember: (1) for some data, no transformation will work; (2) finding an appropriate transformation may not be easy. Use non-linear regression.
- 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. Transformasi dalam regresi 10 20 50 100 150 Chirps/min o C 10 20 40 80 120 160 Chirps/min (log scale)
- 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