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Partial Correlation

Partial correlation measures the degree of association between two random variables, with the effect of a set of controlling random variables removed. The partial correlation between X and Y given a set of n controlling variables Z = {Z1, Z2,…,Zn}, is the correlation between the residuals RX and RY resulting from the linear regression of X with Z and of Y with Z. The first order partial correlation is nothing else than a difference between a correlation and the product of the removable correlations divided by the product of the coefficient of alienation of the removable correlations. A simple way to compute the partial correlation for some data is to solve the two associated linear regression problems, get the residuals and calculate the correlation between the residuals.

The semi-partial correlation statistic is similar to the partial correlation statistic. Both measure variance after certain factors are controlled for, but to calculate the semi-partial correlation one holds the third variable constant for either X or Y. Whereas for partial correlations one holds the third variable constant for both. This correlation is viewed as ore practically relevant. It is less theoretically useful however, because it is less precise about the unique contribution of the independent variables. 

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Range, Coefficient of Variation and Higher Dispersion

Two samples are given. Find each sample's A) standard deviation and B) Coefficient of variation. The decide C) which sample has the higher dispersion, and D) which sample has the higher relative dispersion. A: 8,7,2,4,9 B: 11,7,8,11,3,11,7 It says do not round until the final answer. Then round to the nearest hundredth. o

Confusing Correlation and Causation

Find an article in a newspaper, magazine or on the internet that confuses correlation and causation. Give a brief summary of the article and explain why you chose this article. For the article above, list other variables that could contribute to the relationship between the two variables.

Correlation Coefficient with Scatterplot

An investigator at a diet center is interested in the habits of clients entering his center's weight loss program. Given the pairs of observations below, where X = number of hours per week spent watching television and Y = number of pounds gained in the past year: a) Construct the scatterplot, (but first read d and e below).

Relationship and Task Conflicts

include tables, figures, and graphs Identify the measure of quality mostly effected by relationship conflict AND Task Conflict? Strength of the correlations between the variables? Significance of the correlations Can you improve quality in the workplace?