Abstract
Regressions are introduced as straight lines fitted through a scatterplot. The calculation of a regression as the ‘line of best fit’, obtained by minimising the sum of squared vertical deviations about the line (the least squares approach), is developed. This provides the least squares formulae for estimating the intercept and slope, and the interpretation of the regression line is discussed. The links between correlation, causation, reverse regression and partial correlation are investigated. Further issues involving regressions, such as how to deal with non-linearity, the use of time trends and lagged dependent variables as regressors, and the computation of elasticities, are all developed and illustrated using various economic examples.
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Notes
The method of least squares is traditionally thought to have been originally proposed by Carl Friedrich Gauss in the early years of the 19th century, although there is now some dispute about this: see, for example, Robin L. Plackett, ‘The discovery of the method of least squares’, Biometrika 59 (1972), 239–251,
and Stephen M. Stigler, ‘Gauss and the invention of least squares’, Annals of Statistics 9 (1981), 463–474. Notwithstanding these debates over priority, least squares has since become one of the most commonly used techniques in statistics, and is the centrepiece of econometrics.
The idea that consumption and income grow at the same trend rate is an implication of the fundamental equation of neoclassical economic growth, which has a steady-state solution which exhibits ‘balanced growth’. The model is of en referred to as the Solow growth model: Robert M. Solow, ‘A contribution to the theory of economic growth’, Quarterly Journal of Economics 71 (1956), 65–94.
This unit elasticity result is a key component of the popular error correction model of consumption: see, for example, James Davidson, David Hendry, Frank Srba and Stephen Yeo, ‘Econometric modelling of the aggregate time series relationship between consumer’s expenditure and income in the United Kingdom’, Economic Journal 88 (1978), 661–692.
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© 2014 Terence C. Mills
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Mills, T.C. (2014). Regression. In: Analysing Economic Data. Palgrave Texts in Econometrics. Palgrave Macmillan, London. https://doi.org/10.1057/9781137401908_6
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DOI: https://doi.org/10.1057/9781137401908_6
Publisher Name: Palgrave Macmillan, London
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