Scatterplots & Correlation

Section 3.1A

Relationships between two Variables

O A study found that short women are more likely to have heart attacks than tall women….

O Smokers on average die younger than nonsmokers….

O But – to make these conclusions we must first eliminate the effect of other variables.

Lurking VariablesO Can strongly influence the

relationship between two variables.

Case of the Missing Cookies

ScatterplotOUsed to show the relationship

between two quantitative variables measured on the same individuals. Each individual in the data appears as a point in the graph.O Explanatory variable goes on the

horizontal axis.O If there is no explanatory variable

then either variable can go on the horizontal axis.

Has the increase been constant?

Would Vote for a woman

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Types of Correlation

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Describe the correlation

O Apples: circumference, weight

O College freshmen: shoe size, weight

O People: age, grip strength

O Drivers: blood alcohol, reaction time

Caution…..

Association does not imply causation!

Interpreting ScatterplotsO Look for direction (positive, negative, none)

O Look at the form of the relationshipO Straight or curvedO Any clusters

O Look at the StrengthO How closely does it follow the form

O Look for outliersO Individual value hat falls outside the overall

pattern of the relationship

When writing to describe:

O There appears to be a (strong, weak, moderate) (positive/negative) (linear, nonlinear) relationship between _____ (give the x variable) and ______ (give the y variable)

O Do not just say between x & y!

Graph Using a calculator:

Sprint Time (sec) Long Jump (in)5.41 1.715.05 1849.49 488.09 1517.01 907.17 656.83 946.73 788.01 715.68 1305.78 1736.31 1436.04 141

Interpret….

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Period 5 Only Scatter Plot

1.Direction

2.Form

3.Strength

4.Outliers

Influential Pt!

The following data represents 9th grade students who go on a

backpacking trip.Body wt (lb) 120 187 109 103 131 165 158 116Backpack (lb) 26 30 26 24 29 35 31 28

Interpret: Backpack

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HomeworkOPage 159 (1-13) odd