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

VariablesOResponse Variable

O Measures the outcome of a study.O It’s the dependent variable.

OExplanatory Variable O May help explain or influence

changes in a response variable.O It’s the independent variable.

Identify the explanatory and response variable.

O How does drinking beer affect the level of alcohol in our blood? The legal limit for driving in all states is 0.08%. In a study, adult volunteers drank different numbers of cans of beer. Thirty minutes later, a police officer measured their blood alcohol levels.

Identify the explanatory and response variable.

O The National Student Loan Survey provides data on the amount of debt for recent college graduates, their current income, and how stressed they feel about college debt. A sociologist looks at the data with the goal of using amount of debt and income to explain the stress caused be college debt.

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.

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

Has the increase been constant?

Would Vote for a woman

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0 50 100 150

Years (since 1900)

% R

espo

ndin

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Series1

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

Interpret: Backpack

80 100 120 140 160 180 2000

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Backpack (lb)

Backpack (lb)

Types of Correlation

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102030405060708090

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Caution…..

Association does not imply causation!

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….

40

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120

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Sprint (seconds)5 6 7 8 9

Period 5 Only Scatter Plot 1.Direction

2.Form

3.Strength

4.Outliers

HomeworkOPage 159 (1-13) odd