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# Regression Analysis

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• 1. Regression Analysis
• What is regression ?
• Best-fit line
• Least square
• 2. What is regression ?
• Study of the behavior of one variable in relation to several compartments induced by another variable.
• By the use of regression line or equation, we can predict scores on the dependent variable from those of the independent variable. There are different nomenclatures of independent and dependent variables.
• 3. COMPARTMENTS
• NON CROSS CLASSIFIED
• AGE
• EDUCATION
• CROSS CLASSIFIED
• ELDER EDUCATED
• ELDER UNEDUCATED
• YOUNGER EDUCATED
• YOUNGER UNEDUCATED
• 4. NOMENCLATURE
• 5. 2 - WAY TABLE
• 6. Regression lines (Best - fit line)
• 7. Change in best -fit line
• 8. Equation for a straight line
• Y = a + bX (simple regression)
• Y = a+ b1X1+b2X2+……..bnXn
• Y= Predicted score
• a = Intercept/origin of regression line
• b = regression coefficient representing unit of change in dependent variable with the increase in 1 unit on X variable
• 9. b coefficient estimation
• SumXY-[(sum X)(sum Y)/ N]
• bxy = ---------------------------------------
• Sum Y2 - [(sum Y)^2/N]
• Sum of deviation XY
• bxy = --------------------------------
• Sum of deviation X square
• 10. Estimation of ‘a’
• axy = Mean X - bxy(predicted Y )
• Predicting by graph
• 11. Least square
• Goal of linear regression procedure is to fit a line through the points. Specifically , the program will compute a line so that the squared deviations of the observed points from that line are minimized. This procedure is called least square.
• A fundamental principle of least square method is that variation on a dependent variable can be partitioned, or divided into parts, according to the sources of variation.
• 12. Least square estimation
•  ( Y - Y mean )^2 =  (Y hat - Y mean) ^2 +  (Y - Y hat) ^2
• a) Total sum of squared deviations of the observed values (Y) on the dependent variable from the dependent variable mean (Total SS)
• b) Sum of squared deviations of the predicted values (Y hat) for the dependent variable from the dependent variable mean (Model SS)
• c) Sum of squared of the observed values on the dependent variable from the predicted values (Y -hat) , that is, the sum of the squared residuals (Error SS)