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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:**

Put data into 2 lists STAT CALC 8:LinReg(a+bx) *If r does not appear: 2nd 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**

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 ___**

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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**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**

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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4.2 Correlation The Correlation Coefficient r Properties of r 1.

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