Chapter 14.3, Problem 47E

Exercise 14.26 gave data on fish weight, length, age, and year caught. A multiple regression model was fit to describe the relationship between weight and the predictors length and age.

1. a. Could either length or age be eliminated from the model without significantly affecting your ability to make accurate predictions? Why or why not? Give statistical evidence to support your conclusion.
2. b. Create an indicator variable for year caught. Fit a multiple regression model that includes year, length, and age as predictors of weight. Is there evidence that year is a useful predictor given that length and age are included in the model? Test the relevant hypotheses using α = 0.05.

14.26 This exercise requires the use of a statistical software package. The article “Movement and Habitat Use by Lake Whitefish During Spawning in a Boreal Lake: Integrating Acoustic Telemetry and Geographic Information Systems” (Transactions of the American Fisheries Society [1999]: 939-952) included the accompanying data on 17 fish caught in 2 consecutive years.

1. a. Fit a multiple regression model to describe the relationship between weight and the predictors length and age.
2. b. Carry out the model utility test to determine whether at least one of the predictors length and age are useful for predicting weight.