page_title: Econometrics
section_title: Basic models: linear regression
hierarchical_section_title: Econometrics / Basic models: linear regression
caption_attribution_description: English: Chart using United States data representing the version of Okun's law using differences in unemployment rate. Data is from St. Louis Fred database http://research.stlouisfed.org/fred2/. Series IDs are UNRATE and GDPC1. Data are quarterly. Differences in UNRATE and percentage change in GDPC1 are charted.
context_page_description: Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. More precisely, it is "the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference". An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships". The first known use of the term "econometrics" was by Polish economist Paweł Ciompa in 1910. Jan Tinbergen is considered by many to be one of the founding fathers of econometrics. Ragnar Frisch is credited with coining the term in the sense in which it is used today.
  A basic tool for econometrics is the multiple linear regression model. Econometric theory uses statistical theory and mathematical statistics to evaluate and develop econometric methods. Econometricians try to find estimators that have desirable statistical properties including unbiasedness, efficiency, and consistency.
context_section_description: A basic tool for econometrics is the multiple linear regression model. In modern econometrics, other statistical tools are frequently used, but linear regression is still the most frequently used starting point for an analysis. Estimating a linear regression on two variables can be visualised as fitting a line through data points representing paired values of the independent and dependent variables.
  For example, consider Okun's law, which relates GDP growth to the unemployment rate. This relationship is represented in a linear regression where the change in unemployment rate () is a function of an intercept (), a given value of GDP growth multiplied by a slope coefficient  and an error term, :
  The unknown parameters  and  can be estimated.  Here  is estimated to be −1.77 and  is estimated to be 0.83. This means that if GDP growth increased by one percentage point, the unemployment rate would be predicted to drop by 0.83 - 1.77		*1 points.  The model could then be tested for statistical significance as to whether an increase in growth is associated with a decrease in the unemployment, as hypothesized. If the estimate of  were not significantly different from 0, the test would fail to find evidence that changes in the growth rate and unemployment rate were related. The variance in a prediction of the dependent variable (unemployment) as a function of the independent variable (GDP growth) is given in polynomial least squares.
caption: Okun's law representing the relationship between GDP growth and the unemployment rate. The fitted line is found using regression analysis.
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