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Lecture

# Pearson's correlation coefficient, determining strength of correlation, fitting lines

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Department
Statistics
Course
STAT 301
Professor
Brett Hunter
Semester
Fall

Description
11 November Obtain a numeric assessment of the relationship by calculating Pearson’s correlation coefficient, r y1−y S y n x −x n Z i i r = ∑ 1 (¿) = ∑ i=1( )Sx i=1 n−1 n−1 ¿ S xs the standard deviation of the X variable S ys the standard deviation of the Y variable Properties of r r does not depend on the units of measurement of either X or Y r does not depend on which of the variables is labeled X and which is labeled Y -1 ≤ r ≤ 1 A positive number suggests a positive relationship and a negative number suggest a negative relationship Magnitude indicates strength of relationship. The closer |r| is to 1, the stronger the relationship. Rules for determining strength of correlation |r| < .5 → weak linear relationship .5 ≤ |r| < .8 → moderate linear relationship .8 ≤ |r| < 1 → stronger linear relationship A value of r = 0 does not indicate that there is no relationship between X and Y, but that there is no linear relationship. A strong relationship between X and Y does not mean that a large value of one variable causes the value of the other variable to be large. Correlation does not imply causation!!! Strongly related variables are often also strongly related to other variables. Fitting Lines A line is defined by two pieces of information A y-intercept A slope The equation of a line is y = b0+ b 1 Where b i0 the y-intercept, b is1the slope The y-intercept is the value of y when x = 0 The slope is the amount by which y increases (or decreases) for every 1-unit
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