exam1 - 1(taste and y 2(odor 4 Test whether the 8 chemical...

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Statistics 579 Applied Multivariate Methods Exam 1 In 1963, a study was conducted in Japan on relationships among the sensory and chemical characteristics of 30 brands of Seishu wine. There were 2 sensory characteristics: y 1 (taste) and y 2 (odor); and 8 chemical characteristics: x 1 (pH), x 2 (acidity 1), x 3 (acidity 2), x 4 (sake meter), x 5 (direct reducing sugar), x 6 (total sugar, x 7 (alcohol), and x 8 (formyl-nitrogen). The data set can be downloaded from the Files page of the Stat 579 web page (http://www.bus.utk.edu/stat/Stat579/files.htm). 1. Determine if there are any outliers in these data (but do not eliminate any observations in any of the subsequent analyses). 2. Determine if the 10 variables in this data set can be regarded as arising from a multivariate normal distribution. 3. Using Fisher’s method with a bias adjustment, find a 95% confidence interval for the true population correlation between y
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Unformatted text preview: 1 (taste) and y 2 (odor). 4. Test whether the 8 chemical characteristics can be regarded as statistically independent. 5. Perform a Principal Components Analysis using all 10 variables, and determine the actual dimensionality of the space in which the data fall (i.e., determine the number of principal components that would adequately describe these data). 6. Perform Factor Analyses using all 10 variables. After determining the number of factors needed, compare the results produced from using both the iterated Principal Factor Method and the Maximum Likelihood method. Use a Varimax Rotation with both methods. Specifically, which variables load on which factors, and do the 2 methods produce the same results? Recognizing your lack of expertise in the field of oenology, make an attempt at interpreting the factors....
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