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.