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Journal of Undergraduate Research

Keywords

resistant estimators, linear regression models, data

College

Family, Home, and Social Sciences

Department

Economics

Abstract

Regression analysis is a technique routinely used by researchers in many disciplines to fit some type of mathematical model to observed data. A basic two dimensional linear regression model is mathematically expressed as yi = + xi + Ji for i = 1, n, where y1 … Yn is an observed sample of n data points on the dependent variable y, x1 . . . xn is an observed sample of n data points on an explanatory variable, x, and the parameters and define the true linear relationship between x and Y. The variable J represents a random disturbance term that is assumed to be generated by some probability distribution with zero mean. Some estimation technique is applied to the observed data, x and y, to obtain estimates of and , designated a and b respectively. For a given sample of x’s , we can imagine collecting several different samples of y’s that would each produce slightly different estimates of and . Hence, a and b can be considered variables that fluctuate over a given space on the number line (random variables). An estimation technique is efficient if it produces estimates, a and b, that have the smallest possible variance.

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Economics Commons

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