• A scatterplot displays the relationship between two quantitative variables. Mark values of one variable on the horizontal axis (x axis) and values of the other variable on the vertical axis (y axis). Plot each individual’s data as a point on the graph.
• Always plot the explanatory variable, if there is one, on the x axis of a scatterplot. Plot the response variable on the y axis.
• In examining a scatterplot, look for an overall pattern showing the form, direction, and strength of the relationship, and then for outliers or other deviations from this pattern.
• Form: Linear relationships, where the points show a straight-line pattern, are an important form of relationship between two variables. Curved relationships are other forms to watch for.
• Direction: If the relationship has a clear direction, we speak of either positive association (high values of the two variables tend to occur together) or negative association (high values of one variable tend to occur with low values of the other variable).
• Strength: The strength of a relationship is determined by how close the points in the scatterplot lie to a simple form such as a line. Plot points with different colors or symbols to see the effect of a categorical variable in a scatterplot.
• To display the relationship between a categorical explanatory variable and a quantitative response variable, make a graph that compares the distributions of the response for each category of the explanatory variable.
• A log transformation of one or both variables in a scatterplot can help us to understand the relationship between two quantitative variables.
• A scatterplot smoother is a tool to examine the relationship between two quantitative variables by fitting a smooth curve to the data. The amount of smoothing can be varied using a smoothing parameter.