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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.
    • An introduction to regression model
    • Performing it on SPSS
  • 3. INTRODUCTION
    • What is regression model?
    • An explanatory method
    • Forecast expressed as a function of a certain no. of variables that influences its outcome
  • 4. 2 types of variables
    • DEPENDENT
    • -which we want to forecast
    • 2. INDEPENDENT
    • -or predictor variables
  • 5.
    • Eg:
    • Predict how much an individual enjoys his/her job
    • Dependent variable: job satisfaction
    • Independent variables:
    • salary, academic qualification, age, sex,
    • no. of years, socio-economic status….
  • 6. assumptions
    • LINEAR RELATIONSHIP exists
    • HOMOSCEDASTICITY exists
    • Residuals are INDEPENDENT of one another
    • MULTICOLLINEARITY doesn’t exist
  • 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
    • -helps to visualize, graphically the relationship between pairs of variables
  • 10. Regression Equation where a is y intercept & b 1 , b 2, ..b i are regression coefficients
  • 11. How a & b can be calculated?
    • Method of least squares
    • this method determines the values in such a way that the sum of squared deviations (errors) is minimized
    • and hence the name least squares
  • 12.
    • b=(∑x*y/n) ─ (x * y)
    • ( ∑x 2 / n) ─ (x) 2
    • a = y- bx
    • where y = ∑y/n
    • x= ∑x/n
    • n is the no. of observations
  • 13. forecasting
    • Once the relationship is determined , it can be used to make any no. of forecasts simply by inserting the values of X’ s
    • y = a+b 1 x 1 +b 2 x 2 +…+b i x i
    • Caution: the basic relationship should be assessed periodically
  • 14. terminology
    • b - standard regression coefficient:
    • Measure of how strongly each predictor variable influences the dependent variable
    • E.g.: if b=2.5
    • change of one standard deviation in the predictor will change 2.5 standard deviations in the forecasting variable
  • 15. terminology
    • R
    • Measure of correlation between observed & predicted value of the dependent variable
    • R -1 t0 1
    • R= n*∑x i *y i -∑x i *∑y i
    • √ (n∑x i 2 - (∑x i ) 2 ) √(n∑y i 2 - (∑y i ) 2 )
  • 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
    • Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall
  • 17. terminology…..
    • R 2
    • variation in Y accounted for by the set of predictors
    • Measure of how good a forecasting of dep. variable by knowing the independent variables.
    • When applied to reality, R 2 over estimate the success
  • 18. terminology…
    • Adjusted R 2
    • The adjustment takes into account the size of the sample and number of predictors
    • Gives most useful measure of success of our model ( goodness of fit)
    • R 2 range:0 to 1.
    • If R 2 =0.75, success will be 75%
  • 19. Is each X contributing to the prediction of Y?
    • Test if each regression coefficient is significantly different than zero given the variables standard error.
      • T-test for each regression coefficient
  • 20. Performing regression in spss
    • Eg:importance of several psycholinguistic variables on spelling performance
  • 21. variables
    • Independent:
    • standardized spelling score(spellsc), chronological age(age), reading age(readage), standardized reading score(standsc)
    • Dependent variable:
    • percentage correct spelling(spelperc)
  • 22. Performing regression in spss
    • SPPS=Statistical Packages in Social Sciences
  • 23. Enter the data
  • 24. Cont..
    • >Analyze>regression> linear
    • dialogue box appears
    • now enter dependent and independent variables
  • 25.  
  • 26. Selection methods: on relative contribution of independent variables
    • simultaneous/ enter method
    • Hierarchical method
    • Statistical methods
    • a. Forward
    • b. Backward
    • c. Stepwise
    • d. Remove
  • 27. Now click the statistics button Now click ‘continue’> then ‘ok’
  • 28. Output:
  • 29.  
  • 30.  
  • 31.  
  • 32. Cont…
    • Here reading age is not a significant predictor
    • result:
    • percentage correct spelling=
    • -232+.406*chronological age
    • +.394*standardized reading score
    • +.786*standardized spelling score
  • 33. references
    • Forecasting methods for management
    • by Spyros Makridas & Steven C Wheelwright
    • SPSS for psychologists
    • by Nicola Brace, Richard Kemp & Rosemary Snelger
    • Research Methods for M.Com
    • by L.R Potti
  • 34.
    • THANKYOU…