Regression analysis is a procedure used to measure the relationship of one variable with one or more other variables. Regression provides a rational statement rather than a causal statement with regard to the relationship. The basic formula for a regression equation is:

For a regression equation to provide meaningful information, it should comply with the basic criteria of goodness of fit and specification analysis. Specification analysis is determined by examining the population relationships for: (1) linearity within a relevant range, (2) constant variance (homoscedasticity), (3) independence of observations (serial correlation), (4) normality, and (5) multicollinearity.
{Required:}

(a) Explain what is meant by the phrase "regression provides a rational statement rather than a causal statement."

(b) Explain the meaning of each of the following symbols which appear in the basic formula for a regression equation.

(c) Identify the statistical factors which are used to test a regression equation for goodness of fit and, for each item identified, indicate whether a high or low value describes a "good" fit.

(d) Explain what each of the following terms means with respect to regression analysis.
1. Linearity within a relevant range.
2. Constant variance (homoscedasticity).
3. Serial correlation.
4. Normality.
5. Multicollinearity.

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