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Regression analysis


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multiple regression analysis

Regression analysis

  2. 2. <ul><li>An introduction to regression model </li></ul><ul><li>Performing it on SPSS </li></ul>
  3. 3. INTRODUCTION <ul><li>What is regression model? </li></ul><ul><li>An explanatory method </li></ul><ul><li>Forecast expressed as a function of a certain no. of variables that influences its outcome </li></ul>
  4. 4. 2 types of variables <ul><li>DEPENDENT </li></ul><ul><li>-which we want to forecast </li></ul><ul><li>2. INDEPENDENT </li></ul><ul><li>-or predictor variables </li></ul>
  5. 5. <ul><li>Eg: </li></ul><ul><li>Predict how much an individual enjoys his/her job </li></ul><ul><li>Dependent variable: job satisfaction </li></ul><ul><li>Independent variables: </li></ul><ul><li>salary, academic qualification, age, sex, </li></ul><ul><li>no. of years, socio-economic status…. </li></ul>
  6. 6. assumptions <ul><li>LINEAR RELATIONSHIP exists </li></ul><ul><li>HOMOSCEDASTICITY exists </li></ul><ul><li>Residuals are INDEPENDENT of one another </li></ul><ul><li>MULTICOLLINEARITY doesn’t exist </li></ul>
  7. 7. Analysis for Linearity Not Linear Linear  x x Y x Y x
  8. 8. Residual Analysis for Homoscedasticity Non-constant variance  Constant variance x x Y x x Y residuals residuals
  9. 9. SCATTER PLOTS <ul><li>-helps to visualize, graphically the relationship between pairs of variables </li></ul>
  10. 10. Regression Equation where a is y intercept & b 1 , b 2, ..b i are regression coefficients
  11. 11. How a & b can be calculated? <ul><li>Method of least squares </li></ul><ul><li>this method determines the values in such a way that the sum of squared deviations (errors) is minimized </li></ul><ul><li>and hence the name least squares </li></ul>
  12. 12. <ul><li>b=(∑x*y/n) ─ (x * y) </li></ul><ul><li> ( ∑x 2 / n) ─ (x) 2 </li></ul><ul><li>a = y- bx </li></ul><ul><li>where y = ∑y/n </li></ul><ul><li>x= ∑x/n </li></ul><ul><li>n is the no. of observations </li></ul>
  13. 13. forecasting <ul><li>Once the relationship is determined , it can be used to make any no. of forecasts simply by inserting the values of X’ s </li></ul><ul><li>y = a+b 1 x 1 +b 2 x 2 +…+b i x i </li></ul><ul><li>Caution: the basic relationship should be assessed periodically </li></ul>
  14. 14. terminology <ul><li>b - standard regression coefficient: </li></ul><ul><li>Measure of how strongly each predictor variable influences the dependent variable </li></ul><ul><li>E.g.: if b=2.5 </li></ul><ul><li>change of one standard deviation in the predictor will change 2.5 standard deviations in the forecasting variable </li></ul>
  15. 15. terminology <ul><li>R </li></ul><ul><li>Measure of correlation between observed & predicted value of the dependent variable </li></ul><ul><li>R -1 t0 1 </li></ul><ul><li>R= n*∑x i *y i -∑x i *∑y i </li></ul><ul><li>√ (n∑x i 2 - (∑x i ) 2 ) √(n∑y i 2 - (∑y i ) 2 ) </li></ul>
  16. 16. Scatter Plots of Data with Various Correlation Coefficients Y X Y X Y X Y X Y X r = -1 r = -.6 r = 0 r = +.3 r = +1 Y X r = 0 <ul><li>Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall </li></ul>
  17. 17. terminology….. <ul><li>R 2 </li></ul><ul><li>variation in Y accounted for by the set of predictors </li></ul><ul><li>Measure of how good a forecasting of dep. variable by knowing the independent variables. </li></ul><ul><li>When applied to reality, R 2 over estimate the success </li></ul>
  18. 18. terminology… <ul><li>Adjusted R 2 </li></ul><ul><li>The adjustment takes into account the size of the sample and number of predictors </li></ul><ul><li>Gives most useful measure of success of our model ( goodness of fit) </li></ul><ul><li>R 2 range:0 to 1. </li></ul><ul><li>If R 2 =0.75, success will be 75% </li></ul>
  19. 19. Is each X contributing to the prediction of Y? <ul><li>Test if each regression coefficient is significantly different than zero given the variables standard error. </li></ul><ul><ul><li>T-test for each regression coefficient </li></ul></ul>
  20. 20. Performing regression in spss <ul><li>Eg:importance of several psycholinguistic variables on spelling performance </li></ul>
  21. 21. variables <ul><li>Independent: </li></ul><ul><li>standardized spelling score(spellsc), chronological age(age), reading age(readage), standardized reading score(standsc) </li></ul><ul><li>Dependent variable: </li></ul><ul><li>percentage correct spelling(spelperc) </li></ul>
  22. 22. Performing regression in spss <ul><li>SPPS=Statistical Packages in Social Sciences </li></ul>
  23. 23. Enter the data
  24. 24. Cont.. <ul><li>>Analyze>regression> linear </li></ul><ul><li>dialogue box appears </li></ul><ul><li>now enter dependent and independent variables </li></ul>
  25. 26. Selection methods: on relative contribution of independent variables <ul><li>simultaneous/ enter method </li></ul><ul><li>Hierarchical method </li></ul><ul><li>Statistical methods </li></ul><ul><li>a. Forward </li></ul><ul><li>b. Backward </li></ul><ul><li>c. Stepwise </li></ul><ul><li>d. Remove </li></ul>
  26. 27. Now click the statistics button Now click ‘continue’> then ‘ok’
  27. 28. Output:
  28. 32. Cont… <ul><li>Here reading age is not a significant predictor </li></ul><ul><li>result: </li></ul><ul><li>percentage correct spelling= </li></ul><ul><li>-232+.406*chronological age </li></ul><ul><li>+.394*standardized reading score </li></ul><ul><li>+.786*standardized spelling score </li></ul>
  29. 33. references <ul><li>Forecasting methods for management </li></ul><ul><li>by Spyros Makridas & Steven C Wheelwright </li></ul><ul><li>SPSS for psychologists </li></ul><ul><li>by Nicola Brace, Richard Kemp & Rosemary Snelger </li></ul><ul><li>Research Methods for M.Com </li></ul><ul><li>by L.R Potti </li></ul>
  30. 34. <ul><li>THANKYOU… </li></ul>