By Patrick Kent Watson, Sonja Sabita Teelucksingh
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Extra resources for A Practical Introduction to Econometric Methods Classical and Modern
1 of the previous chapter. This represents an item of communication between the computer and the user. The user, assumedly, will have read the corresponding manuals and will understand the “coded” messages shown. We must not, however, assume that a third party will understand this output largely because we have no right to assume that he or she is familiar with EViews. 1. 1 The values in parentheses below the estimated slope coefficients are the corresponding t-ratios. Notice that the t-ratio associated with the constant term is not reported.
Letting R represent the real number line, then the following expressions are easily verifiable: E (aX) = a μ x , a ⑀ R E (a + bX) = a + bμ x , a, b ⑀ R Var (aX) = a 2 σ 2x , a ⑀ R Var (a ± bX) = b 2 σ 2x , a, b ⑀ R Let Y be another random variable with mean μy and variance σ 2y . It is also possible to define the covariance between X and Y as: [ ( )] Cov (X, Y) = E (X − μ x ) Y − μ y = σ xy By definition, the coefficient of correlation between X and Y is defined as: ρxy = σ xy σ xσ y If X and Y are independent, then σxy and, consequently, ρxy are equal to zero.
The presence of pseudo-collinearity in a regression model does not prevent OLS estimation; the danger here, however, lies, in the interpretation of the output from the estimation phase. As will become more evident later, the investigator must exercise great caution when attempting to draw definitive conclusions from a model in which pseudocollinearity is present. Let us examine some of the more dire consequences of this pseudo-collinearity which, following a time-honoured tradition, we will refer to as multicollinearity.