The classical linear regression model is written such that the coefficients of the independent variables measure the sensitivities of the dependent variable on the independent variables. It is usually assumed that there is an error term which measures the unexplained variance of the dependent variable that is not accounted for by the independent variable. Therefore, only a proportion of the variance is explained by the regression analysis.
c) Any particular normal distribution can be related to the normal distribution because the normality assumption allows us to perform statistical tests concerning the estimated parameters using the normal distribution and related tests involving chi-square, t-distributions and F-distributions.
d) It is not appropriate to take natural logarithms of interest rates, expressed as percentages because natural logarithms of interest rates are taken to minimize autocorrelations and render the interest rates scale free. However, interest rates expressed as percentages are scale free and uncorrelated already and therefore there is no need to take natural logarithms again.
e) The Durbin Watson statistic can be used to estimat...
2. a) Omitting a significant variable from a regression analysis overstates the marginal impact of other variables in the model. For example, lets consider the impact of education on earnings. This relationship can be written in the form of a regression model as follows:
(1) (Greene, 2003: p. 9).
The above regression neglects the possibility that most people have higher incomes when they are older than when they are young, regardless of their education. (Greene, 2003: p. 9). Thus overstates the marginal impact of education on earnings. If age and education are positively related, then the regression model will associate all the observed increases in income with increases in education. Therefore a better way to study the determinants of income is to include the effects of age in the regression as follows:
according to Greene (2003: p. 9) earnings tend to rise less rapidly in the later earning years than in the early ones. To accommodate this possibility, the above model can be extended as follows:
(3) (Greene, 2003: p. 9).
b). Regression analysis studies the relationship between two or more variables. One variable is considered independent while two or more variables are considered to be independent. (Anderson et al, 2005). The aim of the regression analysis is to measure how changes in the dependent variable are explained by changes in the independent variables. Including an insignificant variable as one of the independent variables may minimize the effects of the actual variable causing the variation in the independent variable. Like in the example above, if truly age is not a determinant of income as