= Econometrics Notation =



== Observations and Measurements ==

The number of observations is ''n''.

The outcome variable is ''y''. The outcome measurement for observation ''i'' is ''y,,i,,''.

If there is a single predictor, it may be specified as ''x''; the measurement is ''x,,i,,''. More commonly, there is a set of predictors specified like ''x,,1,,'', ''x,,2,,'', and so on. The measurements are then ''x,,1i,,'', ''x,,2i,,'', and so on.

When expressing data with [[LinearAlgebra|linear algebra]], the outcome measurements are composed into vector ''y'' with size ''n'', and the predictor measurements are composed into matrix '''''X''''' of shape ''n'' by ''p''.

A very common exception: income is usually represented by ''Y'' or ''y''. In relevant literature, expect to see different letters.



== Error Terms ==

Error terms are variably represented by ''ε'', ''e'', ''u'', or ''v''. The error term for observation ''i'' would be represented like ''ε,,i,,''.



== Statistics ==

There is a mixture of notations for scalar statistics. The conventional estimators for population mean ''μ'', [[Statistics/Variance|variance]] ''σ^2^'', standard deviation ''σ'', [[Statistics/Covariance|covariance]] ''σ,,xy,,'', and [[Statistics/Correlation|correlation]] ''ρ,,xy,,'' are:

{{attachment:average.svg}}

{{attachment:variance.svg}}

{{attachment:sd.svg}}

{{attachment:covariance.svg}}

{{attachment:correlation.svg}}

Frequently for multiple variable statistics, some pieces of [[LinearAlgebra|linear algebra]] notation are introduced. For example, covariances are frequently expressed in a covariance matrix. Covariances of ''x'' and ''y'' are specified as ''σ,,xy,,''; variances are expressed as covariances of ''x'' and ''x''.

{{attachment:covariancem.svg}}



== Distributions ==

The [[Statistics/NormalDistribution|normal distribution]] is commonly used in econometrics, and a shorthand notation has emerged as ''x,,i,, ~ N(μ, σ)''.

For multiple variables, at minimum the distribution is specified as ''NI'' to emphasize independence of the distributions. Some pieces of [[LinearAlgebra|linear algebra]] notation are also introduced.



== Models ==

A linear model of ''k'' variables specifies constant ''β,,0,,'' and coefficients ''β,,1,,'' through ''β,,k,,''. The [[LinearAlgebra|linear algebra]] notation uses a coefficient vector ''β'' of size ''p''.

When the model is fit using [[Statistics/OrdinaryLeastSquares|regression]], the estimated coefficients are notated using a hat, as in ''ˆβ,,0,,''. The linear algebra notation uses ''b'' instead.

The predicted outcome is also notated using a hat, as in ''ŷ,,i,,''.

The generic calculation of the [[Statistics/Residuals|residual]] for observation ''i'' is ''y,,i,, - ŷ,,i,,''. The residual sum of squares (RSS) is what is minimized to fit a model.

And the coefficient of determination is:

{{attachment:rsquared.svg}}



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