Multiple regression is a procedure used to measure the relationship of one variable with two or more other variables. Regression provides a relational statement rather than a causal statement with regard to the relationship. The basic formula for a multiple regression equation is:
yi′ = a + bxi + czi + ei
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 data and the relationships of the variables for (a) linearity within a relevant range, (b) constant variance of error terms (homoscedasticity), (c) independence of observations (serial correlation), (d) normality, and (e) multicollinearity.
Required:
(1) Explain what is meant by the following: "Regression provides a relational statement rather than a causal statement."
(2) Explain the meaning of each of the symbols that appears in the basic formula of the multiple regression equation just stated.
(3) Identify the statistical factors used to test a regression equation for goodness of fit and, for each item identified, indicate whether a high value or a low value describes a good fit.
(4) Explain what each of the following terms means with respect to regression analysis:
(a) Linearity within a relevant range
(b) Constant variance (homoscedasticity)
(c) Serial correlation
(d) Normality
(e) Multicollinearity