AP - Statistics:: Exploring Two-Variable Data

When investigating a possible relationship between two variables, which is generally the EXPLANATORY variable, and which is the RESPONSE variable?

- **A)** The response variable always causes changes in the explanatory variable
- **B)** The explanatory variable is thought to help explain or predict changes in the response variable, which is the outcome of interest
- **C)** There is never a meaningful distinction between the two
- **D)** Explanatory and response variables must both be categorical

For two CATEGORICAL variables, which type of table summarizes the relationship between them?

- **A)** A stem-and-leaf plot
- **B)** A boxplot
- **C)** A scatterplot
- **D)** A two-way table (contingency table)

In a two-way table analysis, if the conditional distributions of the response variable are very SIMILAR across all categories of the explanatory variable, what does this suggest?

- **A)** There is little to no association between the two variables
- **B)** The data must contain an error
- **C)** The two variables must be quantitative, not categorical
- **D)** There is a very strong association between the two variables

For two QUANTITATIVE variables, which graph is used to display their relationship?

- **A)** A two-way table
- **B)** A scatterplot, with the explanatory variable on the x-axis and the response variable on the y-axis
- **C)** A segmented bar chart
- **D)** A pie chart

When describing a scatterplot, which characteristics should be addressed (analogous to shape/center/spread for one variable)?

- **A)** Only whether the points are red or blue
- **B)** Only the range of the x-axis
- **C)** Only the number of points plotted
- **D)** Direction (positive/negative), Form (linear/curved), Strength (how closely points follow a pattern), and any Outliers/unusual points (sometimes summarized as DFSO or similar mnemonics)

A scatterplot shows a POSITIVE association if:

- **A)** All points lie exactly on a horizontal line
- **B)** As the explanatory variable increases, the response variable tends to increase as well
- **C)** The variables show no consistent pattern
- **D)** As the explanatory variable increases, the response variable tends to decrease

The CORRELATION COEFFICIENT \(r\) measures:

- **A)** The causal effect of one variable on another
- **B)** The average of the two variables
- **C)** The strength of any relationship, linear or not
- **D)** The strength and direction of a LINEAR relationship between two quantitative variables, ranging from \(-1\) to \(1\)

A correlation coefficient of \(r=-0.85\) indicates:

- **A)** A strong, negative linear relationship between the two variables
- **B)** No relationship at all
- **C)** A weak, positive linear relationship
- **D)** A perfect positive linear relationship