ABSTRACT
This chapter covers topics likely to be encountered when dealing with the construction of simple (straight line) linear regression models from data that do not exhibit any undesireable properties. For = 1 2 , let represent the th observed value of a continuous
response variable and the corresponding value for a continuous explanatory variable . Assume is measured without error and suppose that for each the corresponding observed responses are prone to random devi-= 1
0 1 represent unknown regression parameters. The general structure of a simple linear regression model in algebraic form
is = 0 + 1 +
Moreover, it is assumed that, for each = 1 2 , the error terms have constant variances 2, are independent, and are identically and normally distributed with ∼ N(0 2). In matrix form, the model has the appearance
y = Xβ + ε, where it is assumed that the design matrix, X, has full column rank ; the response vector y is a solution of y = Xβ + ε, and the entries of the error vector ε satisfy the above-mentioned assumptions. A traditional application of simple linear regression typically involves a
study in which the continuous response variable is, in theory, assumed to be linearly related to a continuous explanatory variable, and for which the data provide evidence in support of this structural requirement as well as for all fundamental assumptions on the error terms.
