Editing Econometrics (section)

==Basic models: linear regression==
A basic tool for econometrics is the [[multiple linear regression]] model.<ref name="Greene Econometrics – 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.<ref name="Greene Econometrics – multiple linear regression model">{{cite book|author=Greene, William|title=Econometric Analysis|date=2012|publisher=Pearson Education|isbn=9780273753568|pages=47–48|edition=7th|chapter=Chapter 1: Econometrics | quote = Ultimately, all of these will require a common set of tools, including, for example, the multiple regression model, the use of moment conditions for estimation, instrumental variables (IV) and maximum likelihood estimation. With that in mind, the organization of this book is as follows: The first half of the text develops fundamental results that are common to all the applications. The concept of multiple regression and the linear regression model in particular constitutes the underlying platform of most modeling, even if the linear model itself is not ultimately used as the empirical specification.}}</ref> Estimating a linear regression on two variables can be visualized as fitting a line through data points representing paired values of the independent and dependent variables.

[[File:Okuns law differences 1948 to mid 2011.png|thumb|right|Okun's law representing the relationship between GDP growth and the unemployment rate. The fitted line is found using regression analysis.]]

For example, consider [[Okun's law]], which relates [[Gross domestic product|GDP]] growth to the unemployment rate. This relationship is represented in a linear regression where the change in unemployment rate (<math>\Delta\ \text{Unemployment}</math>) is a function of an intercept (<math> \beta_0 </math>), a given value of GDP growth multiplied by a slope coefficient <math> \beta_1 </math> and an error term, <math>\varepsilon</math>:

:<math> \Delta\ \text {Unemployment} = \beta_0 + \beta_1\text{Growth} + \varepsilon. </math>

The unknown parameters <math> \beta_0 </math> and <math> \beta_1 </math> can be estimated. Here <math> \beta_0 </math> is estimated to be 0.83 and <math> \beta_1 </math> is estimated to be -1.77. This means that if GDP growth increased by one percentage point, the unemployment rate would be predicted to drop by 1.77		* 1 points, [[Ceteris paribus|other things held constant]]. The model could then be tested for [[statistical significance]] as to whether an increase in GDP growth is associated with a decrease in the unemployment, as [[Statistical hypothesis testing|hypothesized]]. If the estimate of <math> \beta_1 </math> 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]].