# Hypothesis Testing

Reference work entry

First Online:

**DOI:**https://doi.org/10.1057/978-1-349-95189-5_810

## Abstract

For those who believe that economic hypotheses have to be confirmed by empirical observations, hypothesis testing is an important subject in economics. As a classical example, when an economic relation is represented by a linear regression model:where where

$$ Y= X\beta +\upvarepsilon $$

*Y*is a column vector of*n*observations on the dependent variable*y*,*X*is an*n*×*k*matrix with each column giving the corresponding n observations on each of*k*explanatory variables (which typically include a column of ones),*β*is a column of*k*regression coefficients and ε is a vector of*n*independent and identically distributed residuals with mean zero and variance σ^{2}, it is of interest to test a hypothesis consisting of*m*linear restrictions on*β*:$$ R\beta =r $$

*R*is*m*×*k*and*r*is*m*× 1. A most common case occurs when there is only one restriction (*m*= 1) and (2) is reduced to*β*_{i}= 0, the hypothesis being that the*i*th explanatory variable has no effect on*y*.This is a preview of subscription content, log in to check access

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