The ten assumptions of the Gaussianstandardclassical linear regression model

1
The ten assumptions of the Gaussian/standard/clas
sical linear regression model

• 1. A Population Regression Function (PRF) that is
  linear in the parameters provides a good
  explanation of observed variation in the data. In
  other words a model of the following form
  describes the data correctly.

2
The ten assumptions of the Gaussian/standard/clas
sical linear regression model

• 2. Along the Population Regression Function
  (PRF), the values of the independent variable, X,
  are fixed in repeated sampling, i.e., X is
  nonstochastic.

3
The ten assumptions of the Gaussian/standard/clas
sical linear regression model

• 3.Along the Population Regression Function (PRF),
  the distribution of actual Y values at each X
  value is such that the distribution of the
  deviations of actual Ys from the Y values at
  each value of X along the PRF has a mean of 0. In
  other words E(ui Xi ) 0.

4
The ten assumptions of the Gaussian/standard/clas
sical linear regression model

• 4. Along the Population Regression Function
  (PRF), the distribution of actual Y values at
  each X value is such that the distribution of the
  deviations of actual Ys from the Y values at
  each value of X along the PRF has the same
  variance at all values of X. In other words
• Var(ui Xi) s2, or homoscedasticity is
  required.

5
The ten assumptions of the Gaussian/standard/clas
sical linear regression model

• 5. Along the Population Regression Function
  (PRF), the distribution of actual Y values at
  each X value is such that a deviation of an
  actual Y value from the Y value on the PRF at
  some value of X is not related to the deviation
  at any other value of X. In other words Cov(ui,
  uj Xi , Xj) 0, or no autocorrelation is
  required.

6
The ten assumptions of the Gaussian/standard/clas
sical linear regression model

• 6. Along the Population Regression Function
  (PRF), the distribution of actual Y values at
  each X value is such that a deviation of an
  actual Y value from the Y value on the PRF at
  some value of X is not related to the value of X.
  In other words Cov(ui, Xi ) 0.

7
The ten assumptions of the Gaussian/standard/clas
sical linear regression model

• 7. The number of observations is greater than the
  number of variables or the number of parameters
  to be estimated.

8
The ten assumptions of the Gaussian/standard/clas
sical linear regression model

• 8. There is more than one value of X. In other
  words Var(X) gt 0.

9
The ten assumptions of the Gaussian/standard/clas
sical linear regression model

• 9. The model specification is correct (variables,
  functional form, error characteristics).

10
The ten assumptions of the Gaussian/standard/clas
sical linear regression model

• 10. There is not an exact relationship among the
  independent variables. In other words, there is
  no multicollinearity.