Содержание
- 2. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES Y X2 X1 β0 1 This sequence provides a geometrical
- 3. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES Y X2 X1 β0 3 The model has three dimensions,
- 4. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES Y X2 X1 β0 4 Literally the intercept gives weekly
- 5. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES 5 Y X2 The next term on the right side
- 6. pure X2 effect MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES X1 β0 β0 + β2X2 Y X2
- 7. pure X2 effect pure X1 effect MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES X1 β0 β0 +
- 8. pure X2 effect pure X1 effect MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES X1 β0 β0 +
- 9. pure X2 effect pure X1 effect MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES X1 β0 β0+ β1X1+
- 10. pure X2 effect pure X1 effect MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES 10 X1 β0 β0
- 11. Slope coefficients are interpreted as partial slope/partial regression coefficients: ? b1 = average change in Y
- 12. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES The regression coefficients are derived using the same least squares
- 13. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES The residual ei in observation i is the difference between
- 14. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES We define SSE, the sum of the squares of the
- 15. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES First we expand SSE as shown, and then we use
- 16. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES We thus obtain three equations in three unknowns. Solving for
- 17. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES The expression for b0 is a straightforward extension of the
- 18. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES However, the expressions for the slope coefficients are considerably more
- 19. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES For the general case when there are many explanatory variables,
- 20. In matrix notation OLS may be written as: Y = Xb + e The normal equations
- 21. MATRIX ALGEBRA: SUMMARY A vector is a collection of n numbers or elements, collected either in
- 22. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES: EXAMPLE Data for weekly salary based upon the length of
- 23. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES: EXAMPLE Y-weekly salary ($) X1 –length of employment (months) X2-age
- 24. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES: EXAMPLE
- 25. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES: EXAMPLE Y-weekly salary ($) X1 –length of employment (months) X2-age
- 26. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES: EXAMPLE These are our data points in 3dimensional space (graph
- 27. MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES: EXAMPLE Data points with the regression surface (Statistica 6.0) X1
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