Explanatory/Response Variables, Scatterplots, r

How to Make a Scatterplot

Put the explanatory on the x-axis and the response variable on the y-axis. Label and scale your axes. Plot individual data values.

Describing Scatterplots

Direction, form, strength, outliers

Direction

Is it positive or negative? (is the line upward or downward sloping; do the variables move together or against one another?)

Form

Is the pattern linear or nonlinear?

Strength

Does the association appear to be strong, moderately strong, or weak? (based on how close the points are to the line)

Outliers

Do there appear to be any data points that are unusually far away from the general pattern?

Positive association

Above average values tend to accompany that of another variable.

Positive association examples

Height and arm length, calories burned and miles ran, gasoline and travel mileage

Interpreting positive association (temple)

Higher values of (explanatory/independent variable) tend to be associated with higher values of (response/dependent variable)

Negative association

Above average values of one variable tend to accompany below average values of another variable

Negative association examples

Absences and grades, speed and travel time, study time and test scores

Interpreting negative association

Larger values of (explanatory/independent variable) tend to be associated with smaller values of (response/dependent variable)

Correlation/"r"

A number between -1 and 1 measuring the direction and strength of the linear relationship between two quantitative variables

r > 0

Positive association

r < 0

Negative association

Values of r near 0

Weak linear relationship

Values of r near 1

Very strong relationship

Correlation requires

That both variables be quantitative.

Correlation is not

Resistant; r is strongly affected by a few outlying observation