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Regression analysis

Regression analysis. Linear regression Logistic regression. Relationship and association. Straight line. Best straight line?. Best straight line!. Least square estimation. Simple linear regression. Is the association linear?. Simple linear regression. Is the association linear?

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Regression analysis

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  1. Regression analysis Linear regression Logistic regression

  2. Relationship and association

  3. Straight line

  4. Best straight line?

  5. Best straight line! Least square estimation

  6. Simple linear regression Is the association linear?

  7. Simple linear regression Is the association linear? Describe the association: what is b0 and b1 BMI = -12.6kg/m2+0.35kg/m3*Hip

  8. Simple linear regression Is the association linear? Describe the association Is the slopesignificantlydifferent from 0? Help SPSS!!!

  9. Simple linear regression Is the association linear? Describe the association Is the slopesignificantlydifferent from 0? Howgood is the fit? How far are the data points fom the line onavarage?

  10. The CorrelationCoefficient, r R = 0.7 R = 0 R = -0.5 R = 1

  11. r2 – Goodness of fitHowmuch of the variation canbeexplained by the model? R2 = 0.5 R2 = 0 R2 = 0.2 R2 = 1

  12. Multiple linear regression Couldwaistmeasuredescirbesome of the variation in BMI? BMI =1.3 kg/m2 + 0.42 kg/m3 * Waist Orevenbetter:

  13. Multiple linear regression Adding age: adj R2 = 0.352 Addingthigh: adj R2 = 0.352?

  14. Assumptions Dependent variable must be metric continuous Independent must be continuous or ordinal Linear relationship between dependent and all independent variables Residuals must have a constant spread. Residuals are normal distributed Independent variables are not perfectly correlated with each other

  15. Non-parametric correlation

  16. RankedCorrelation Kendall’s  Spearman’s rs Korrelation koefficienten er mellem -1 og 1. Hvor -1 er perfekt omvendt korrelation, 0 betyder ingen korrelation, og 1 betyder perfekt korrelation. Pearson is the correlation method for normal data Remember the assumptions: Dependent variable must be metric continuous Independent must be continuous or ordinal Linear relationship between dependent and all independent variables Residuals must have a constant spread. Residuals are normal distributed

  17. Kendall’s  - Et eksempel

  18. Kendall’s  - Et eksempel

  19. Spearman – det samme eksempel

  20. Korrelation i SPSS

  21. Korrelation i SPSS

  22. Logistic regression

  23. Logistic Regression • If the dependent variable is categorical and especially binary? • Use some interpolation method • Linear regression cannot help us.

  24. The sigmodal curve

  25. The sigmodal curve • The intercept basically just ‘scale’ the input variable

  26. The sigmodal curve • The intercept basically just ‘scale’ the input variable • Large regression coefficient → risk factor strongly influences the probability

  27. The sigmodal curve • The intercept basically just ‘scale’ the input variable • Large regression coefficient → risk factor strongly influences the probability • Positive regression coefficient→risk factor increases the probability • Logisticregessionusesmaximumlikelihoodestimation, not leastsquareestimation

  28. Does age influence the diagnosis? Continuous independent variable

  29. Does previous intake of OCP influence the diagnosis? Categorical independent variable

  30. Odds ratio

  31. Multiple logistic regression

  32. Predicting the diagnosis by logistic regression What is the probabilitythat the tumor of a 50 yearoldwomanwho has beenusing OCP and has a BMI of 26 is malignant? z = -6.974 + 0.123*50 + 0.083*26 + 0.28*1 = 1.6140 p = 1/(1+e-1.6140) = 0.8340

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