The prediction equation for the horseshoe crab data using width and quantitative color (scores 1, 2, 3, 4) is logit( ) = 10.071 0.509c

The prediction equation for the horseshoe crab data using width and quantitative color (scores 1, 2, 3, 4) is logit(πˆ ) = −10.071 − 0.509c + 0.458x. Color has mean = 2.44 and standard deviation = 0.80, and width has mean = 26.30 and standard deviation = 2.11.

a. For standardized versions of the predictors, explain why the estimated coefficients equal (0.80)(−.509) = −0.41 and (2.11)(.458) = 0.97. Interpret these by comparing the partial effects on the odds of a one standard deviation increase in each predictor.

b. Section 4.5.1 interpreted the width effect by finding the change in ˆπ

over the middle 50% of width values, between 24.9 cm and 27.7 cm.

Do this separately for each value of

c, and interpret the width effect for each color.