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cpsc+440+chapter+11+linear+correlation+lecture

# cpsc+440+chapter+11+linear+correlation+lecture - Linear...

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CPSC 440, Linear Correlation. Chapter 11. Steel, Torrie, and Dickey 1 Linear Correlation - Chapter 11 Section 11.2 The sample linear correlation coefficient, r, (a.k.a. the simple correlation, the total correlation and the product-moment correlation) is calculated as. .. ? ? ?

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CPSC 440, Linear Correlation. Chapter 11. Steel, Torrie, and Dickey 2 Important points The correlation coefficient r is an unbiased estimate of D (rho) only when the population parameter D is zero. Unlike a variance or a regression coefficient, r is independent of the units of measure. It is an absolute or dimensionless quantity. The use of X and Y is no longer intended to imply an independent and a dependent variable as is usually the case with regression. A lack of tendency to cluster about any line other than one through the mean of the X and Y values and parallel to an axis is typical of data where there is little or no linear correlation. Lack of a linear correlation is more noticeable when the scatter diagram uses standard deviations as units of measurement. These are called standard variables and they have a mean of zero and a variance of 1.
CPSC 440, Linear Correlation. Chapter 11. Steel, Torrie, and Dickey 3 Note that when the correlation is small, r is near zero because the points are equally likely to fall in each of the four quadrants so the numerator tends to be near zero. In c the lines tip toward the x axis because the variance of X is larger.

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CPSC 440, Linear Correlation. Chapter 11. Steel, Torrie, and Dickey 4 What is with all of these?? The coefficient of determination , r or R , is a measure of the 22 proportion of the total sum of squares that is attributable to the independent variable, i.e. it tell us how much (%) of the variability in y that is explained by x. That is what we used in regression analysis. linear correlation coefficient , r, is a measure of the degree to which variables vary together or a measure of the intensity of association.
CPSC 440, Linear Correlation. Chapter 11. Steel, Torrie, and Dickey 5 The coefficient of nondetermination , k , is less commonly 2

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cpsc+440+chapter+11+linear+correlation+lecture - Linear...

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