Discussion Session 3

Definition: Let θ 1 ,. .. , θ t be a set of variables, either parameters or statistics, and a 1 ,. .. , a t be known constants. The quantity t i=1 a i θ i is a linear combination. It is called a contrast if t i=1 a i = 0. Furthermore, two contrasts, t i=1 a i θ i and t i=1 b i θ i , are orthogonal if t i=1 a i b i = 0. Suppose we observe from the scatter plot something more than linear trend, say quadratic trend, then, we may want to consider model Y i = β 0 + β 1 x i + β 2 x