3.1 power point

8/7/2019 3.1 Power Point

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Section 3.1

Scatterplots and Correlation


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Are Baseballs Juiced?

Do these data provide convincing

evidence that baseballs have begun

to fly farther over time?


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What Do You Want?

Sometimes explanatory variables are called

independent variables, and response variables are

called dependent variables.

When examining relationships among variables, twoquestions become important. Do you want to simply

explore the nature of the relationship, or do you

think that some of the variables help explain or even

cause changes in the others?


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Which Is Response, Which Is

Explanatory? Neith

er? Researchers give several different amounts

of alcohol to mice, then measure the change

in each mouses body temperature in the 15

minutes after taking the alcohol.

Jim wants to know the relationship between

mean SAT Math and Verbal scores. He

doesnt believe either score explains the

other.

Julie wonders if she can predict a states

mean SAT Math score if she knows its

mean SAT Verbal score.


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Whats the Relationship?

If there is an explanatory variable, always plot it on

the horizontal axis (x-axis)

A scatterplot shows the relationshipbetween two quantitative variables

measured on the same individuals.


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Interpreting a ScatterplotAs in any graph of data, look for the overall pattern

and striking deviations from that pattern:


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Describing a Scatterplot Trend: positive, negative, or none

Unusual Features: clusters,outliers, or influential points

Shape: linear, curved, or neither

Strength: strong, moderate, orweak; constant or varying

strength


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Not just quantitative

(Southern states in blue)

Categorical variables can becommunicated by colors and symbols


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Related by Association

Two variables can have a positiveassociation

High values associated

with high values


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High values associated

with low values

a negative association


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or no clear association or pattern.


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Which Correlation is Stronger?

Set 1

Neither!

or

Set 2

Our eyes are not good judges of how

strong a linear relationship is.

They are the same set of data, plotted ondifferently sized fields.


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Do My Eyes Deceive Me?

Data analysis of a scatterplot needs to

be supplemented by a numerical

measure:


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Correlation Coefficient: -1 r 1


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Cautions!

Only measures thestrength oflinearrelationshipsnot

curves, no matterhow strong they are

Correlation is notresistant

*CORRELATION CAUSATION*

Correlation alone is not a numericalsummarymeans and standard

deviations ofboth x and y are needed

Bothvariablesmust be

quantitative


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You Try It!

Freshmen at the Webb Schools go on a backpackingtrip at the start of each school year. Students are

divided into hiking groups of size 8 by selection of

names from a hat. Prior to departure, each students

body weight and backpack weight are measured (both in

pounds). Here are data from one hiking group in arecent year:

1. Enter values into L1 and L2

2. 2nd StatPlot; 1st graph; Xlist:L1; Ylist:L2; Zoom; 9

3. Correlation Coefficient (r): Stat; Calc;

LinReg(a+bx); L1, L2

4. Ifrand r2 dont show, go to 2nd; Catalog; DiagnosticOn

Body weight (lb): 120 187 109 103 131 165 158 116

Backpack (lb): 26 30 26 24 29 35 31 28

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