Chapter 4 Scatterplots and Correlation

What does each dot in a scatterplot represent?

each ( X,Y ) pair

Outline:

(1) plot data with scatterplot; look for overall pattern of relationship and deviations from that pattern, especially outliers (2) compute a summary # called correlation coefficient as a measure of strength of linear relationship (3) Model linear relationships with a straight line equation called the regression equation

What is the inequality that correctly identifies the set of values that a correlation 𝑟 can possibly take.

-1 < r < 1

Correlation is not

A complete summary of two verbal data

Values of r near 0 indicate

A very weak relationship

Scatterplots..

Are most useful for displaying the relationship between two quantitative variables

Variables can be:

Both quantitative, categorical, or one of each

Sometimes explanatory variables and response variables

Cannot be designated

r has no units and does not change when we

Change the units of measurement of X, Y or both

What best describes correlation?

Correlation measures the strength of the linear relationship between two quantitative variables

When examining a relationship between two quantitative variables, we look at...

Form, direction, strength, and outliers.

Two variables are not associated if

Knowing the value of one variable does not give you any information about the value of the other variable

Negative r (correlation) indicates

Negative association

Correlation does not describe curved relationships between variables

No matter how strong the relationship is

What is the first rule in analyzing bivariate data when both variables are quantitative?

Plotting data

Positive r (correlation) indicates

Positive association between the variables

The points on a scatterplot lie very close to a straight line. The correlation between 𝑥 and 𝑦 is close to

either −1 or 1, we can't say which

What type of data is graphed with a scatterplot?

Two quantitative variables measured on each individual

Changing the units will not affect the correlation because...

Units do not affect correlation

To add a categorical variable to an existing scatterplot....

Use a different color or symbol for each category

When should you model with a straight line?

When the relationship between X and Y is linear and X and Y are quantitative

Which axis is the explanatory variable?

X-axis

Which axis is the response variable?

Y-axis

Explanatory variables

are denoted by X and explain or influence changes in a response variable a.k.a. the independent variable

Response variables

are denoted by Y and are the outcome of a study a.k.a. the dependent variable

Changing units does not...

change the correlation.

correlation makes no distinction between

explanatory and response variables

If the correlation between two variables is close to 0 , you can conclude that a scatterplot would show

no straight‑line pattern, but there might be a strong pattern of another form.

Correlation requires that both variables be

quantitative

Correlation is not resistant,

r is strongly affected by a few outlying observations

positive association

values of one variable tend to be higher when values of the other variable are higher

negative association

values of one variable tend to be lower when values of the other variable are higher