Two-Variable Data Checkpoint
A free Statistics and Data Analysis lesson from the “Two-Variable Data” unit, with a worked example and practice problems including step-by-step solutions.
This checkpoint reviews two-way tables, conditional relative frequency, scatter plots, regression lines, residuals, and prediction limits.
What you'll learn
- Review the major skills from this part of the course
- Choose an appropriate statistical method
- Explain results in context
Worked example
Problem. A scatter plot with points rising left to right shows:
- When x increases and y tends to increase, the direction is positive.
- That is positive association.
Answer: positive association
Lesson preview: this page shows 5 practice items. The interactive activity contains 25 practice items and 25 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. Review case A: A scatter plot with points rising left to right shows:
Choices: negative association · no association · a categorical variable only · positive association
Show solution
- When x increases and y tends to increase, the direction is positive.
- That is positive association.
Answer: positive association
2. Review case B: Correlation by itself can prove:
Choices: association, not causation · cause and effect every time · that the sample was random · that there are no outliers
Show solution
- Correlation measures association.
- It does not prove causation without a stronger design.
Answer: association, not causation
3. Review case C: A regression line is y = 5x + 8. Predict y when x = 4.
Show solution
- Substitute x = 4.
- 5(4) + 8 = 28.
Answer: 28
4. Review case D: A model predicts 19, but the actual value is 21. Find the residual using actual - predicted.
Show solution
- Residual = actual - predicted.
- 21 - 19 = 2.
Answer: 2
5. Review case E: Predicting inside the observed x-range is called:
Choices: extrapolation · random assignment · standard error · interpolation
Show solution
- Interpolation stays inside the data range.
- Extrapolation goes beyond the observed data.
Answer: interpolation
Practice this interactively with instant feedback and an AI tutor.
Practice Two-Variable Data Checkpoint Take the free placement check