Answer to Question #165534 in Statistics and Probability for Collins Amoako

Question

In a study analyzing the determinants of demand for gasoline in the United States, the results 

shown below were obtained. The dependent variable is miles traveled per car per year (K) and 

the explanatory variables are C, number of cars (millions); M, miles per gallon; Pg, retail 

gasoline price index deflated by consumer price index (1953=100); PT, price of public transport

(1967=100); Pop, population (millions); L, labour force; Y, per capita disposable income in 1958 

prices.

a. Do the coefficients have the expected signs? Explain

b. Is there a multicollinearity problem? Use at least four diagnosis procedures to answer this 

question. If there is multicollinearity, what might be causing it?

c. If there is multicollinearity problem discuss two remedial measures to remedy the situation

Answer 1

Multicollinearity is a linear relationship between two or more factorial variables in a multiple regression equation. If such dependence is functional, then one speaks of complete multicollinearity. If it is a correlation, then there is partial multicollinearity. If full multicollinearity is rather a theoretical abstraction (it manifests itself, in particular, if a dummy variable with k quality levels is replaced by k dichotomous variables), then partial multicollinearity is very real and is almost always present. We can only talk about the degree of its severity. For example, if the explanatory variables include disposable income and consumption, then both of these variables, of course, will be highly correlated.

The absence of multicollinearity is one of the desirable prerequisites of the classical linear multiple models. This is due to the following considerations:

a) In the case of complete multicollinearity, it is generally impossible to construct estimates of the parameters of linear multiple regression using the least-squares method.

b) In the case of partial multicollinearity, the estimates of the regression parameters may be unreliable and, in addition, it is difficult to determine the isolated contribution of factors to the effective indicator.

The main reason for the occurrence of multicollinearity is the presence in the studied object of processes that simultaneously affect some input variables, but are not taken into account in the model. This may be the result of poor-quality research of the subject area or the complexity of the interrelationships of the parameters of the studied object.

(c) Multicollinearity is suspected of being:

- a large number of insignificant factors in the model;

- large standard errors of the regression parameters;

- instability of estimates (a small change in the initial data leads to a significant change).