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Estimated Regression Equation

  • As we calculated the intercept and the slope coefficient in case of simple linear regression by minimizing the sum of squared errors, similarly we estimate the intercept and slope coefficient in multiple linear regression
    • Sum of Squared Errors   is minimized and the slope coefficient is estimated.
  • The resultant estimated equation becomes:
  • Now the error in the ith observation can be written as:

  • Interpreting the Estimated Regression Equation
  • Intercept Term (b0): It's the value of dependent variable when the value of all independent variables become zero

  • Slope coefficient (bk): It's the change in the dependent variable from a unit change in the corresponding independent (Xk) variable keeping all other independent variables constant
    • In reality when the value of the independent variable changes by one unit, the change in the dependent variable is not equal to the slope coefficient but depends on the correlation among the independent variables as well
    • Therefore, the slope coefficient are called partial slope coefficients as well

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