Relationship Between Variables

These flashcards cover essential concepts about the relationship between variables, including definitions, examples, and distinctions between types of relationships.

What is a variable?

Any attribute or characteristic of a person, place, or thing that can be measured or manipulated and can take on different values.

What are the types of variable relationships?

Linear relationship, nonlinear relationship, and unrelated relationship.

What defines a linear relationship?

A relationship that can be represented and explained by a straight line on a scatter plot.

What is a positive linear relationship?

Two variables move in the same direction; when one variable increases, the other also increases.

Can you give an example of a positive linear relationship?

More study time results in higher test scores.

What is a negative linear relationship?

Two variables move in opposite directions; when one variable increases, the other decreases.

Can you provide an example of a negative linear relationship?

More screen time leads to poorer sleep quality.

What is a nonlinear relationship?

A relationship that can be represented by a curvilinear line on a scatter plot.

What is a quadratic curvilinear relationship?

Where the graph has a U-shape or inverted U-shape, with one turning point.

Can you give an example of a quadratic relationship?

Stress level impacts performance where low stress leads to low performance, moderate stress leads to high performance, and too much stress drops performance.

What is a cubic curvilinear relationship?

A relationship that changes direction twice and has two turning points.

Can you provide an example of a cubic relationship?

Technology usage varies with age: low in young children, high in teens and young adults, lower in older adults.

What is a quartic curvilinear relationship?

A more complex curve that can form W-shaped or M-shaped patterns with three turning points.

Can you give an example of a quartic relationship?

Consumer spending changes during economic cycles: rises in growth, falls in slowdown, rises again in recovery, and falls in recession.

What is a quintic curvilinear relationship?

Described by a polynomial equation, requiring at least one curve to represent the data.

Can you provide an example of a quintic relationship?

Long-term climate change impacts crop production: yield increases and decreases due to various climate factors.

What is an unrelated relationship?

A relationship where changes in one variable are not systematically related to changes in another variable.

What is correlation?

A measure or degree of relationship between two variables, which can be positive, negative, or zero.

What is a causal relationship?

Exists if the occurrence of the first variable causes the occurrence of the second variable.

How does correlation relate to causation?

For a causal relationship, the variables must be correlated, but correlation does not imply causation.

What is an example that shows correlation does not imply causation?

A negative correlation between a student's anxiety before a test and their score, but anxiety does not necessarily cause the lower score.