The most basic form of regression analysis is multiple linear regression. Linear regression techniques attempt to fit a linear function to your data by estimation of an intercept and partial slopes relating to the independent variables in your model. While multiple linear regression is fairly common, if the variable of interest does not behave in a linear manner over the relevant range of your regression, you may be in trouble. This technique is adaptable, but as you start to violate the assumptions of the procedure, your results can become biased or you may suffer from a lack of statistical power.
If the dependent measure that you are interested in can be classified as a 1 or a 0, such as whether or not a quality is present in the population, you may be interested in binary logistic regression. This regression technique relates the independent variable to the rolling average of the dependent variable. The function that accomplishes this is called the logit function. Binary logistic regression results can be difficult to interpret; however, they are more statistically sound then just using linear regression to make binary predictions.
If your data set has many independent variables, you may be interesting in using principal components analysis to perform a data reduction. Once the data reduction is complete, the principal components can be used in a principal components regression. The PCA procedure uses linear algebra and optimization techniques to find orthogonal linear components of the independent variables. The potential components are then rank ordered by the amount of variability in the data that they explain and the researcher is able to sacrifice a small loss of explained variability for a reduction in data and lack of multi-collinearity. The downside to this technique is that the principal components partial slope estimates may be difficult to interpret without back translation to the original values.
Instrumental variables estimation can be used with large data sets when the independent variables are correlated with the error terms in the model. This occurs when the researcher is unsure of the structural model of the relationship being investigated, which is common in large global data sets. Instrumental variable methods can use two-stage least squares estimation, which involves a multiple-step regression analysis that breaks the regression into regression of endogenous variables on exogenous variables first, and then uses those predicted values to perform another regression. While this technique is powerful, sometimes it is hard to find an instrumental variable that only affects the dependent variable through the effect on the independent variable.