Regression

Abstract

A common problem is that of estimating a linear relationship between 2 variables, x and y. If an electrician charges a flat fee β₀ plus a fixed amount β₁ per outlet when he wires a house, the relationship can be expressed as y = β₀ + β₁ x, where y is his total fee and x is the number of outlets. There is no error in the fee because we can count the number of outlets. For a given number of outlets the fee is invariably the same. In that case both variables are mathematical or nonrandom variables, i.e., they do not have distributions. When y is plotted against x (for any fixed value of β₀ and β₁), the points fall on a straight line with slope β₁ and intercept β₀ and we say that the relationship is linear. The quantities β₀ and β₁ are parameters; they are fixed constants in any given situation but may vary from one situation to another. If β₀ and β₁ were unknown, they could be determined exactly if one had at hand 2 or more distinct values of x and y.