Find each of these four measures of the effect of X1 in each of the following models. Which measure yields the simplest result in each case? How can the several measures be interpreted? How would you...

Find each of these four measures of the effect of X₁
in each of the following models. Which measure yields the simplest result in each case? How can the several measures be interpreted? How would you fit each model to data, assuming convenient forms for the errors [e.g., additive errors for models (a), (b), and (c)]?

(a) Y = α + β₁X1 + β₂X₂.

(b) Y = α + β₁X1 + β₂X2 1 + β+X2.

(c) Y = α + β₁X1 + β₂X2 + β₃X1X2.

(d) Y = exp(α + β₁X1 + β₂X2).

(e) Y = αX^β1

₁
X₂
^β2.