Suppose X 1 were a continuous predictor, and F is a factor with three levels, represented by two dummy variables X 2 with values equal to 1 for the second level of F and X 3 with values equal to 1 for...

Suppose X₁
were a continuous predictor, and F is a factor with three levels, represented by two dummy variables X₂
with values equal to 1 for the second level of F and X₃
with values equal to 1 for the third level of F. The response is Y. Consider three mean functions:

includes an additional unknown parameter δ that may need to be estimated. All of these mean functions specify that for a given level of F the plot of E(Y|X1, F) is a straight line, but in each the slope and the intercept changes. For each of these three mean functions, determine the slope(s) and intercept(s), and on a plot of Y on the vertical axis and X1 on the horizontal axis, sketch the three fitted lines. The model (5.21) is a generalization of (5.20). Because of the extra parameter δ that multiplies some of the βs, this is a nonlinear model; see Saw (1966) for a discussion.