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Let S = XTX be the sample covariance matrix where L and P are latent roots and vectors of XTX respectively. Prove that S has latent root and latent vectors P. Using this result show that correlation loadings of S are given by
where si is the ith diagonal element of S, and consequently correlation loadings are the same for both XTX and S. Show also that XTX and S possess the same standardized PC scores, but that unstandardized scores differ.
For the samples summarized below, test the hypothesis at =0.05 that the two variancees are equal.
Determine the variance of X? (Illustrate your computation either in Table or in Equation form)
Assume that respondents had been asked for party affiliation in a poll. THe responses were coded as 0 (for democra), 1 (for republican), 2 (for independent), or 3 (for any other response).
Let x be a nilpotent element of the commutative ring R i.e. x^m for some positive integer m. Prove that x is either zero or a zero divisor
Determine the average and the variation for Brand 1 price, sales market share, and total revenue, using the weekly market survey data (descriptive statistics).
The number of standard errors that the sample estimate (p 1 - p 2 ) of (p1 - p2) falls from its null hypothesis value of zero is called
A group of children can be classified according to eye color (blue, brown, green), gender (male, female), and hobby (collecting stamps, collecting baseball cards, collecting shells, collecting stickers).
Find the 95% prediction interval for the heart rate reduction expected for an individual receiving a dose of 2.00 mg
Give an example of a problem (business, political, scientific) in which ANOVA analysis would be appropriate. (Hint: the dependent variable is categorical, such as male vs. female or comparing three different types of fertilizer.)
labour productivity improvements in distribution centrecase studyover the past decade singapores economy has grown by
determine the appropriate division of the stakes in a series between two players if the first player is lacking three
a gambler has a fair coin with one head and one tail and a two-headed coin. he selects one of the coins at random and
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