Question: 4

a. Plot the logistic mean response function: E{Y_i} = π_i = F_L(β₀ + β₁X_i) = exp(β₀ + β₁X_i) / 1 + exp(β₀ + β₁X_i), when β₀ = -27 and β₁= 0.2

Hint: Find the X-value which makes E(Y) = π = .50 to start the plot. Take at least 10 different X values to obtain a decent-looking line.

b. For what value of X is the mean response equal to 0.5?

c. Find the odds when X= 150, when X= 151, and the ratio of the odds when X= 151 to the odds when X= 150.

Is this odds ratio equal to exp(β₁) as it should be??

Is the change in odds close to β₁? Should it? Briefly explain.