Reading 11, 3.2 Assumptions of the Linear Regression Model

CFA Level 2, Volume 1, Quantitative methods, Reading 11, Correlation & Regression

(References refer to CFA text book)

3.2 Assumptions of the Linear Regression Model

Classic normal linear regression model assumptions	Why is it important	Other info
1. The relationship between the dependent variable, Y, and the independent variable, X is linear in the parameters b0 and b1.	If you fit a linear model to data which are nonlinearly related your predictions are likely to be serious in error. If the relationship between the independent and dependent variables is nonlinear in the parameters, then estimating that relation with a linear regression model will produce invalid results.	Even if the dependent variable is nonlinear, linear regression can be used as long as the regression is linear in the parameters.
2. The independent variable, X, is not random.	Assumption 2 ensures that linear regression produces the correct estimates of b0 and b1.
3. The expected value of the error term is 0: E(℮) = 0.	Assumption 3 ensures that linear regression produces the correct estimates of b0 and b1.	E(℮) = 0. If the expected error = 0, it means that the forecast is unbiased. If a forecast is biased it means that there are consistent differences between actual outcomes & previously generated forecasts of these quantities, that is, forecasts may have a general tendency to be too high or too low. (2)
4. The variance of the error term is the same for all observations. (also called Homoscedasticity)	Violations of Homoscedasticity make it difficult to gauge the true standard deviation of forecast errors, usually resulting in confidence intervals that are too wide or too narrow.
5. The error term, ℮, is uncorrelated across observations. Consequently, E(℮i, ℮j) = 0 for all i not equal to j	Serial correlation in the residuals mean that there is room for improvement in the model, and extreme serial correlation is often a symptom of a badly mis-specified model. Assumption 5, that the errors are uncorrelated across observations, is  necessary for correctly estimating the variances of the estimated parameters bˆ0 and bˆ1.
6. The error term, ℮, is normally distributed.	Assumption 6, that the error term is normally distributed, allows us to easily test a particular hypothesis about a linear regression model.

Sources

1. www.duke.edu/~rnau/testing.htm

2. Wikipedia.org/wiki/forecast_bias