An experimenter wants to design an experiment for estimating the rate of change in a dependent variable Y as an independent variable X is changed. He is convinced from previous experience that the...

An experimenter wants to design an experiment for estimating the rate of change in a dependent variable Y as an independent variable X is changed. He is convinced from previous experience that the relationship is linear in the region of interest, between X = 0 and X = 11. He has enough resources to obtain 12 observations. Use σ²(
₁), equation 1.26, to show the researcher the best allocation of the design points (choices of X-values). Compare σ²(
₁) for this optimum allocation with an allocation of one observation at each interger value of X from X = 0 and X = 11.