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.