Correlation Correlation Coefficient r Quantitative assessment of the

Correlation

Correlation Coefficient (r) Quantitative assessment of the strength of the relationship between x & y. It is the measure of the extent to which x & y are linearly related. *It is strong if the points lie close to a straight lint and is weak if they are widely scattered about a line.

Correlation (r) � It’s a number between -1 and 1. � The closer it is to the ends, the stronger the positive or negative relationship. � It gives the strength and direction. Strong Negative -1 No Correlation 0 Strong Positive 1

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Pearson’s Correlation Coefficient Think about z-scores of the x & y

Pearson’s Correlation Coefficient Think about z-scores of the x & y

Pearson’s Correlation Coefficient Think about z-scores of the x & y

Correlation Coefficient

Find the correlation coefficient. x y 6 5 10 3 14 7 19 8 21 12

Find correlation coefficient. x y 15 219 27 189 31 195 42 173 88 121 92 138 66 152 51 140

AP Exam Tip If you are asked to interpret a correlation start by looking at a scatterplot of the data. Then be sure to address direction, form, strength, and outliers and put your answer in context.

Properties of “r” � It does not depend on the unit of measurement. � It doesn’t depend upon which of the 2 variables is “x” � It’s between -1 and 1 � It equals -1 or 1 if all points lie on a straight line � It is strongly affected by a few outliers

Scatterplots show relationships – not cause and effect.

Try One! � Create scatterplot � Find the correlation � Describe the association Fat (g) Sodium 29 920 31 1150 34 1200 35 39 39 43 1095 1180 1120 1260

Homework � Page 160 (14 -18, 21, 26)