Notes Chapter 7

Bivariate Data

Bivariate DataRelationships between two (or more) variables.

The response variable measures an outcome of a study.

The explanatory variable attempts to explain the observed outcomes.

• When we gather data, we may have in mind which variables are which.

• There may also not be explanatory & response variables if our data does not suggest “causation”.

Displaying the Variables• The most effective way to display a relation

between two quantitative variables is a scatterplot. – It shows the relationship between two quantitative

variables measure on the same individual. – Each individual in the data appears as the point in the

plot fixed by both values. – Always plot the explanatory variable (if there is one)

on the horizontal (the x axis) of a scatterplot.

Interpret a Scatterplot

• First, look for an overall pattern to include:– 1) direction (positive, negative) D– 2) form (linear, exponential, quadratic) S– 3) strength (correlation, r) S– 4) deviations from the pattern (outliers) U

SUDS!!

• Remember on outlier in any graph of data is an individual observation that falls outside the overall pattern of the graph.

• There is no outlier test for bivariate data. It is a matter of…hey, does that point look out of place?

• Categorical variables can be added to scatterplots by changing the symbols in the plot. (See P. 199 for examples)

• Visual inspection is often not a good judge of how strong a linear relationship is. Changing the plotting scales or the amount of white space around a cloud of points can be deceptive. So….

• We use a numerical measure, correlation (r), to supplement our graph.

• Correlation (r) measures the strength and direction of the linear relationship.

• Formula: We get this value from the calculator! (Be sure your diagnostic is turned on)

Facts about Correlation:• 1) positive r – positive association (positive slope)

negative r – negative association (negative slope)• 2) r must fall between –1 and 1 inclusive. • 3) r values close to –1 or 1 indicate that the points lie

close to a straight line.• 4) r values close to 0 indicate a weak linear relationship.• 5) r values of –1 or 1 indicate a perfect linear

relationship.• 6) correlation only measures the strength in linear

relationships (not curves).• 7) correlation can be strongly affected by

extreme values (outliers).