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AP Statistics Section 3.1B Correlation. 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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A scatterplot displays the direction, form and the strengthof the relationship between two quantitative variables. Linear relations are particularly important because a straight line is a simple pattern that is quite common.
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.
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
The correlation ( r) measures the direction and the strength of the linear relationship between two quantitative variables.
The formula for correlation of variables x and y for n individuals is:
TI 83/84: Put data into 2 lists, say STAT CALC 8:LinReg(a+bx) ENTER Note: If r does not appear,2nd0 (Catalog) Scroll down to “Diagnostic On” Press ENTER twice
Find r for the data on sparrowhawk colonies from section 3.1 A
Important facts to remember when interpreting correlation:1. Correlation makes no distinction between __________ and ________ variables. explanatory response
2. r does not change when wechange the unit of measurement of x or y or both.
3. Positive r indicates a ________ association between the variables and negative r indicates a ________ association. positive negative
4. The correlation r is always between ___ and ___. Values of r near 0 indicate a very _____ relationship. weak
Example 1: Match the scatterplots below with their corresponding correlation r
2. Correlation does not describe curvedrelationships between variables, no matter how strong.
3. Like the mean and standard deviation, the correlation is NOT resistant to outliers.
4. Correlation is not a complete summary of two-variable data. Ideally , give the mean and standard deviations of both x and y along with the correlation.