Ap statistics section 3 1b correlation
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AP Statistics Section 3.1B Correlation PowerPoint PPT Presentation


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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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AP Statistics Section 3.1B Correlation

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Ap statistics section 3 1b correlation

AP Statistics Section 3.1BCorrelation


Ap statistics section 3 1b correlation

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

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.


Ap statistics section 3 1b correlation

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


Ap statistics section 3 1b 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

The formula for correlation of variables x and y for n individuals is:


Ap statistics section 3 1b correlation

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

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


Ap statistics section 3 1b correlation

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

explanatory

response


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

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

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

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

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


Ap statistics section 3 1b correlation

6 4 2 1 3 5


Cautions to keep in mind

Cautions to keep in mind:


1 correlation requires both variables be quantitative

1. Correlation requires both variables be quantitative.


2 correlation does not describe curved relationships between variables no matter how strong

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

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


What effect does adding an outlier have on r and why

What effect does adding an outlier have on r and why?


Ap statistics section 3 1b correlation

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.


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