5.1 Graphical Representations Between Two Quantitative Variables

Construct scatterplots depicting the relationship between two quantitative variables.

• A bivariate quantitative data set consists of observations of ordered pairs from two quantitative variables, collected from the same individuals in a sample or population, and can be used to construct a scatterplot.
• A scatterplot shows the relationship between two quantitative variables for each observation, one corresponding to the value on the x-axis and one corresponding to the value on the y-axis. The explanatory variable is placed on the x-axis and is the variable whose values are used to explain or predict the corresponding values for the response variable, which is placed on the y-axis.

Describe the characteristics of a scatterplot.

• A description of the association shown in a scatterplot includes form, direction, strength, and unusual features.
• The form of the association shown in a scatterplot, if any, can be described as linear or non-linear.
• The direction of the association shown in a scatterplot, if any, can be described as positive or negative. A positive association means that as values of the explanatory variable increase, the values of the response variable tend to increase. A negative association means that as values of the explanatory variable increase, the values of the response variable tend to decrease.
• The strength of the association shown in a scatterplot is how closely the points follow the general pattern. Strength can be described as strong, moderate, or weak.
• Unusual features of a scatterplot include clusters of individual points or points that don’t fit in the general pattern of association between the two variables.

Justify a claim using scatterplots depicting the relationship between two quantitative variables.

• Scatterplots depicting the relationship between two numeric variables may reveal information that can be used to justify claims about the variable in context. 149 Regression Analysis UNIT 5