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Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
Regression analysis
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Regression analysis

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multiple regression analysis

multiple regression analysis

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  • 1. REGRESSION ANALYSIS -P H SHAMEER
  • 2. <ul><li>An introduction to regression model </li></ul><ul><li>Performing it on SPSS </li></ul>
  • 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. 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. <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. 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. Analysis for Linearity Not Linear Linear  x x Y x Y x
  • 8. Residual Analysis for Homoscedasticity Non-constant variance  Constant variance x x Y x x Y residuals residuals
  • 9. SCATTER PLOTS <ul><li>-helps to visualize, graphically the relationship between pairs of variables </li></ul>
  • 10. Regression Equation where a is y intercept & b 1 , b 2, ..b i are regression coefficients
  • 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. <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. 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. 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. 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. 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. 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. 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. 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. Performing regression in spss <ul><li>Eg:importance of several psycholinguistic variables on spelling performance </li></ul>
  • 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. Performing regression in spss <ul><li>SPPS=Statistical Packages in Social Sciences </li></ul>
  • 23. Enter the data
  • 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>
  • 27. Now click the statistics button Now click ‘continue’> then ‘ok’
  • 28. Output:
  • 29.  
  • 30.  
  • 31.  
  • 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>
  • 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>
  • 34. <ul><li>THANKYOU… </li></ul>

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