The authors of the article An Ultracentrifuge Flour

Chapter 13, Problem 13.44

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The authors of the article An Ultracentrifuge Flour Absorption Method (Cereal Chemistry, 1978: 96101) studied the relationship between water absorption for wheat flour and various characteristics of the flour. In particular, the authors used a first-order multiple linear regression model to relate absorption y (%) to flour protein x1 (%) and starch damage x2 (Farrand units). The data and accompanying SPSS output follow on p.546: x1 x2 y x1 x2 y8.5 2 30.9 12.9 24 47.08.9 3 32.7 12.0 25 46.810.6 3 36.7 12.9 28 45.910.2 20 41.9 13.1 28 48.89.8 22 40.9 11.4 32 46.210.8 20 42.9 13.2 28 47.811.6 31 46.3 11.6 35 49.212.0 32 47.6 12.1 34 48.312.5 31 47.2 11.3 35 48.610.9 28 44.0 11.1 40 50.212.2 36 47.7 11.5 45 49.611.9 28 43.9 11.6 50 53.211.3 30 46.8 11.7 55 54.313.0 27 46.2 11.7 57 55.8a. Interpret 1 and 2.b. What proportion of observed variation in absorption canbe explained by the model relationship?c. Does the chosen model appear to specify a useful linearrelationship between absorption and at least one of thetwo predictors?d. If flour protein remains in the model, is elimination ofthe predictor starch damage justified?e. When x1 10 and x2 25, y 42.253 and sY .350.Calculate and interpret a confidence interval and a predictioninterval.f. Including an interaction predictor x3 gives 3 .04304and s3 .01773. At significance level .01, should thispredictor be retained?

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