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REGRESSION ANALYSIS   M.Ravishankar [ And it’s application in Business ]
Introduction. . . ,[object Object],[object Object],[object Object]
Regression Analysis. . . ,[object Object],[object Object],[object Object]
Regression types. . . ,[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object]
Regression Analysis. . . ,[object Object],[object Object],[object Object],[object Object]
Regression Analysis. . . ,[object Object],[object Object]
Simple Linear Regression Model. . . ,[object Object],[object Object],[object Object]
Types of Regression Models. . .
Estimated Regression Model. . . The sample regression line provides an  estimate  of the population regression line Estimate of the regression  intercept Estimate of the regression slope Estimated  (or predicted) y value Independent variable The individual random error terms  e i   have a mean of zero
Simple Linear Regression Example. .  . ,[object Object],[object Object],[object Object],[object Object]
Sample Data   House Price in $1000s (y) Square Feet  (x) 245 1400 312 1600 279 1700 308 1875 199 1100 219 1550 405 2350 324 2450 319 1425 255 1700
 
Output. . . The regression equation is: Regression Statistics Multiple R 0.76211 R Square 0.58082 Adjusted R Square 0.52842 Standard Error 41.33032 Observations 10 ANOVA   df SS MS F Significance F Regression 1 18934.9348 18934.9348 11.0848 0.01039 Residual 8 13665.5652 1708.1957 Total 9 32600.5000         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 98.24833 58.03348 1.69296 0.12892 -35.57720 232.07386 Square Feet 0.10977 0.03297 3.32938 0.01039 0.03374 0.18580
Graphical Presentation . . . ,[object Object],Slope  = 0.10977 Intercept  = 98.248
Interpretation of the Intercept,  b 0 ,[object Object],[object Object]
Interpretation of the Slope Coefficient,  b 1 ,[object Object],[object Object]
Example: House Prices Estimated Regression Equation: Predict the price for a house with 2000 square feet House Price in $1000s (y) Square Feet  (x) 245 1400 312 1600 279 1700 308 1875 199 1100 219 1550 405 2350 324 2450 319 1425 255 1700
Example: House Prices Predict the price for a house with 2000 square feet: The predicted price for a house with 2000 square feet is 317.85($1,000s) = $317,850
[object Object],Coefficient of Determination, R 2 Note:   In the single independent variable case, the coefficient of determination is where: R 2  = Coefficient of determination   r = Simple correlation coefficient
Examples of Approximate R 2   Values R 2  = +1 y x y x R 2  = 1 R 2  = 1 Perfect linear relationship between x and y:  100% of the variation in y is explained by variation in x
Examples of Approximate R 2   Values y x y x 0 < R 2  < 1 Weaker linear relationship between x and y:  Some but not all of the variation in y is explained by variation in x
Examples of Approximate R 2  Values R 2  = 0 No linear relationship between x and y:  The value of Y does not depend on x.  (None of the variation in y is explained by variation in x) y x R 2  = 0
Output. . . 58.08%  of the variation in house prices is explained by variation in square feet Regression Statistics Multiple R 0.76211 R Square 0.58082 Adjusted R Square 0.52842 Standard Error 41.33032 Observations 10 ANOVA   df SS MS F Significance F Regression 1 18934.9348 18934.9348 11.0848 0.01039 Residual 8 13665.5652 1708.1957 Total 9 32600.5000         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 98.24833 58.03348 1.69296 0.12892 -35.57720 232.07386 Square Feet 0.10977 0.03297 3.32938 0.01039 0.03374 0.18580
Standard Error of Estimate. . . ,[object Object],Where SSE  = Sum of squares error   n = Sample size   k = number of independent variables in the model
The Standard Deviation of the Regression Slope ,[object Object],where: = Estimate of the standard error of the least squares slope = Sample standard error of the estimate
Output. . . Regression Statistics Multiple R 0.76211 R Square 0.58082 Adjusted R Square 0.52842 Standard Error 41.33032 Observations 10 ANOVA   df SS MS F Significance F Regression 1 18934.9348 18934.9348 11.0848 0.01039 Residual 8 13665.5652 1708.1957 Total 9 32600.5000         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 98.24833 58.03348 1.69296 0.12892 -35.57720 232.07386 Square Feet 0.10977 0.03297 3.32938 0.01039 0.03374 0.18580
Reference. . . ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
M.RAVISHANKAR MBA(AB) 2008-2010 Batch NIFTTEA KNITWEAR FASHION INSTITUTE TIRUPUR [email_address]
 
 

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Regression analysis

  • 1. REGRESSION ANALYSIS M.Ravishankar [ And it’s application in Business ]
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  • 9. Types of Regression Models. . .
  • 10. Estimated Regression Model. . . The sample regression line provides an estimate of the population regression line Estimate of the regression intercept Estimate of the regression slope Estimated (or predicted) y value Independent variable The individual random error terms e i have a mean of zero
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  • 12. Sample Data House Price in $1000s (y) Square Feet (x) 245 1400 312 1600 279 1700 308 1875 199 1100 219 1550 405 2350 324 2450 319 1425 255 1700
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  • 14. Output. . . The regression equation is: Regression Statistics Multiple R 0.76211 R Square 0.58082 Adjusted R Square 0.52842 Standard Error 41.33032 Observations 10 ANOVA   df SS MS F Significance F Regression 1 18934.9348 18934.9348 11.0848 0.01039 Residual 8 13665.5652 1708.1957 Total 9 32600.5000         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 98.24833 58.03348 1.69296 0.12892 -35.57720 232.07386 Square Feet 0.10977 0.03297 3.32938 0.01039 0.03374 0.18580
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  • 18. Example: House Prices Estimated Regression Equation: Predict the price for a house with 2000 square feet House Price in $1000s (y) Square Feet (x) 245 1400 312 1600 279 1700 308 1875 199 1100 219 1550 405 2350 324 2450 319 1425 255 1700
  • 19. Example: House Prices Predict the price for a house with 2000 square feet: The predicted price for a house with 2000 square feet is 317.85($1,000s) = $317,850
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  • 21. Examples of Approximate R 2 Values R 2 = +1 y x y x R 2 = 1 R 2 = 1 Perfect linear relationship between x and y: 100% of the variation in y is explained by variation in x
  • 22. Examples of Approximate R 2 Values y x y x 0 < R 2 < 1 Weaker linear relationship between x and y: Some but not all of the variation in y is explained by variation in x
  • 23. Examples of Approximate R 2 Values R 2 = 0 No linear relationship between x and y: The value of Y does not depend on x. (None of the variation in y is explained by variation in x) y x R 2 = 0
  • 24. Output. . . 58.08% of the variation in house prices is explained by variation in square feet Regression Statistics Multiple R 0.76211 R Square 0.58082 Adjusted R Square 0.52842 Standard Error 41.33032 Observations 10 ANOVA   df SS MS F Significance F Regression 1 18934.9348 18934.9348 11.0848 0.01039 Residual 8 13665.5652 1708.1957 Total 9 32600.5000         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 98.24833 58.03348 1.69296 0.12892 -35.57720 232.07386 Square Feet 0.10977 0.03297 3.32938 0.01039 0.03374 0.18580
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  • 27. Output. . . Regression Statistics Multiple R 0.76211 R Square 0.58082 Adjusted R Square 0.52842 Standard Error 41.33032 Observations 10 ANOVA   df SS MS F Significance F Regression 1 18934.9348 18934.9348 11.0848 0.01039 Residual 8 13665.5652 1708.1957 Total 9 32600.5000         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 98.24833 58.03348 1.69296 0.12892 -35.57720 232.07386 Square Feet 0.10977 0.03297 3.32938 0.01039 0.03374 0.18580
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  • 29. M.RAVISHANKAR MBA(AB) 2008-2010 Batch NIFTTEA KNITWEAR FASHION INSTITUTE TIRUPUR [email_address]
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