# Least Squares Regression

Least squares regression is a popular method for developing mathematical relationships from empirical data. As mentioned earlier, it is a method that is well suited to the estimation of trip generation models. To illustrate the least squares approach, consider the hypothetical trip generation data presented in Table 8A.1, which could have been gathered from a typical survey of travelers.

To begin formalizing a mathematical expression, note that the objective is to predict the number of shopping trips made on a Saturday for each household, i; this number is referred to as the dependent variable (Yi). This prediction is to be a function of the number of people in household i (zi), which is referred to as the independent variable. A simple linear relationship between Yi and zi is

Yi = b0 + b1zi (8A.1)

where

Yi = number of shopping trips made by household i,

b0, b1 = coefficients to be determined by estimation, and Z = number of people in household i.

Ideally, one wants to determine the b’s in Eq. 8A.1 that will give predictions

of the number of shopping trips (Yi’s) that are as close as possible to the actual observed number of shopping trips. The difference or deviation between the observed and predicted number of shopping trips can be expressed mathematically as

Deviation = Yi – (b0 + b1zi) (8A.2)

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