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AP Statistics Section 3.1B Correlation

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A scatterplot displays the direction, form and the strength of the relationship between two quantitative variables. Linear relations are particularly important because a straight line is a simple pattern that is quite common.

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We say a linear relation is strong if and weak if the points lie close to a straight line they are widely scattered about the line.

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Relying on our eyes to try to judge the strength of a linear relationship is very subjective. We will be determining a numerical summary called the __________. correlation

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The correlation ( r ) measures the direction and the strength of the linear relationship between two quantitative variables.

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The formula for correlation of variables x and y for n individuals is: TI 83/84 Put data into 2 lists STAT CALC 8:LinReg(a+bx) *If r does not appear: 2 nd 0 (Catalog) Scroll to “Diagnostic On” Press ENTER twice

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Find r for the data on sparrowhawk colonies from section 3.1 A

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Important facts to remember when interpreting correlation: 1. Correlation makes no distinction between __________ and ________ variables. explanatory response

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2. r does not change when we change the unit of measurement of x or y or both.

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3. Positive r indicates a ________ association between the variables and negative r indicates a ________ association. positive negative

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4. The correlation r is always between ___ and ___. Values of r near 0 indicate a very _____ relationship. weak

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Example 1: Match the scatterplots below with their corresponding correlation r

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6 4 2 1 3 5

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Cautions to keep in mind:

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1. Correlation requires both variables be quantitative.

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2. Correlation does not describe curved relationships between variables, no matter how strong.

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3. Like the mean and standard deviation, the correlation is NOT resistant to outliers.

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4. Correlation is not a complete summary of two-variable data. Give the mean and standard deviations of both x and y along with the correlation.

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