The Florida Citrus Commission is interested in evaluating the performance of two orange juice extractors, brand A and brand B. It is believed that the size of the fruit used in the test may influence the juice yield (amount of juice per pound of oranges) obtained by the extractors. The commission wants to develop a regression model relating the mean juice yield E(y) to the type of orange juice extractor (brand A or brand B) and the size of orange (diameter),x1.
a. Identify the independent variables as qualitative or quantitative.
b. Write a model that describes the relationship between E(y) and size of orange as two parallel lines, one for each brand of extractor.
c. Modify the model of part b to permit the slopes of the two lines to differ.
d. Sketch typical response lines for the model of part b. Do the same for the model of part c. carefully label your graphs.
e. Specify the null and alternative hypotheses you would use to determine whether the model in part c provides more information for predicting yield than does the model in part b.
f. Explain how you would obtain the quantities necessary to compute the F-statistic that would be used in testing the hypotheses you described in part e.