What is 'Econometrics'
Econometrics is the application of statistical and mathematical theories in economics for the purpose of testing hypotheses and forecasting future trends. It takes economic models, tests them through statistical trials and then compare and contrast the results against reallife examples. Econometrics can therefore be subdivided into two major categories: theoretical and applied.
BREAKING DOWN 'Econometrics'
Econometrics uses a combination of economic theory, math and statistical inferences to quantify and analyze economic theories by leveraging tools such as frequency distributions, probability and probability distributions, statistical inference, simple and multiple regression analysis, simultaneous equations models and time series methods.
An example of a reallife application of econometrics would be to study the income effect. An economist may hypothesize that as a person increases his income, his spending will also increase. The hypothesis can be tested and proven using econometric tools like frequency distributions or multiple regression analysis.
Econometrics was pioneered by Lawrence Klein, Ragnar Frisch and Simon Kuznets. All three won the Nobel Prize in economics for their contributions.
The Methodology of Econometrics
Econometrics uses a fairly straightforward approach to economic analysis. The first step to econometric methodology is to look at a set of data and define a specific hypothesis that explains the nature and shape of the set. The explanatory variables being analyzed are specified during this step; the relationship between the dependent and independent variables are also specified. This stage of econometrics relies heavily on economic theory that will be tested for validity in the later stages.
The second step in the methodology is to choose the specific statistical tool or model that will test the hypothesis being posed. An effective model outlines a specific mathematical relationship between the explanatory variable and the dependent variable being tested. The most common relationship is linear, meaning that any change in the explanatory variable will have a positive correlated with the dependent variable. This is why the multiple linear regression model is the most used tool in econometrics, because it expresses relationships linearly.
The third step is the most passive in that all the data is imputed into a econometric software program. The program then uses the statistical model of choice to estimate the results, using the economic data provided.
The fourth and final step is the most important in proving the validity of a hypothesis. Economists will take the results from the program and conduct a small test. The test will help the economist understand whether or not the model resulted in good predictions or not. If the economist finds what he expected than he may safely assume that the hypothesis is true. If, however, the economist does not find what he expected, new hypotheses or inferences are needed.

Mathematical Economics
Mathematical economics is a form of economics that relies on ... 
Lawrence Klein
An American economist and winner of the 1980 Nobel Memorial Prize ... 
Ragnar Frisch
A Norwegian economist and joint winner in 1969 of the very first ... 
Hypothesis Testing
A process by which an analyst tests a statistical hypothesis. ... 
Trygve Haavelmo
A Norwegian economist who won the 1989 Nobel Memorial Prize in ... 
Error Term
A variable in a statistical and/or mathematical model, which ...

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