Problem 145SE

Comparing two orange juice extractors. The Florida CitrusCommission is interested in evaluating the performanceof two orange juice extractors, brand A and brand B. Itis believed that the size of the fruit used in the test mayinfluence the juice yield (amount of juice per pound oforanges) obtained by the extractors. The commission wantsto develop a regression model relating the mean juice yieldE(y) to the type of orange juice extractor (brand A orbrand B) and the size of orange (diameter), x1.

a. Identify the independent variables as qualitative orquantitative.

b. Write a model that describes the relationship betweenE(y) and size of orange as two parallel lines, one foreach brand of extractor.

c. Modify the model of part b to permit the slopes of thetwo lines to differ.

d. Sketch typical response lines for the model of part b.Do the same for the model of part c. Carefully labelyour graphs.

e. Specify the null and alternative hypotheses you woulduse to determine whether the model in part c provides more information for predicting yield than doesthe model in part b.

f. Explain how you would obtain the quantities necessary to compute the F-statistic that would be used intesting the hypotheses you described in part e.

Chapter 9: Multivariate Designs - Means many variables - Study more than 2 variables in a single study - Enhance understanding of bivariate associations Longitudinal design - Measures same variables and same sample at several time points - Use to assess variable relationships across time - Use to see variable stability across time - 3 types of correlations assessed o Cross sectional: two variables measured at the same point in time [bivariate correlations] o Autocorrelations; testing variable against itself measured at two time points. o Cross-lag correlations; early measure of one variable against later measure of the other variable Moderation Language - Violence