MATH 1342 Elementary Statistics: Section 2.4 Two Variable Relationships

Vocabulary flashcards covering Section 2.4 on Two Variable Relationships, side-by-side boxplots, scatterplots, describing associations, and correlation.

Side-by-side boxplots

Comparative graphs used to display and assess the relationship between a categorical explanatory variable and a quantitative response variable.

Explanatory variable

The variable used to explain or predict changes in another variable; in the 2025 electric vehicle study, this was vehicle class (Hybrid, Plug-in Hybrid [PHEV], and Battery Only [BEV]).

Response variable

The outcome variable being measured or predicted; in the 2025 electric vehicle study, this was acceleration time to $30\,\text{mph}$ in seconds.

Acceleration time comparison among EV classes

In the 2025 EV dataset, hybrids tended to have the highest acceleration time, battery-only (BEV) tended to have the lowest, and plug-in hybrids (PHEV) had an outlier with the highest overall acceleration value.

Scatterplot

A graphical display used to examine the relationship between two quantitative variables plotted on horizontal and vertical axes.

Positive association

A relationship between two variables where, as the explanatory variable increases, the response variable tends to increase.

Negative association

A relationship between two variables where, as the explanatory variable increases, the response variable tends to decrease.

Three components of describing an association

The three characteristics required to thoroughly describe a two-variable relationship: direction (positive vs. negative), shape (linear vs. nonlinear), and strength (very strong, strong, moderate, weak, none).

Linear association

A pattern where the data points in a scatterplot trend along a straight line, as seen in the comparison between Median ACT Score and Mean SAT Score.

Nonlinear association

A pattern where the relationship between two variables curves or bends rather than forming a straight line, such as Austin, TX weather by month.

Weight and City MPG relationship

An association characterized as a moderately strong negative linear association, indicating that heavier vehicles tend to have lower fuel economy on city streets.

Correlation

A numerical measure of the strength and direction of the linear association between two quantitative variables, taking a value between $-1$ and $1$.

$$r$$

The statistical symbol used to denote the correlation coefficient of a sample.

$$\rho$$

The Greek letter 'rho', used to denote the correlation coefficient of a population.

Nonlinear limitation of correlation

The condition where correlation fails to properly capture curved relationships; a variable pair can have a correlation near zero even when a strong nonlinear association exists (such as driving speed and fuel efficiency).