🏅 Top 10 in the last 30 days
No results yet. Be the first!
Test
Correlation and linear model
This test evaluates relationships between two variables using correlation and a linear model. Students interpret the correlation coefficient and R², calculate predictions and residuals and assess model suitability and the limits of causal conclusions.
Questions: 10Estimated time: 18 minutes
Start a test→
Enable solution history?
Test results will be stored only on this device in your browser’s local storage. They will not be sent to the Catestia.com database. If you disable this feature, all saved history will be permanently deleted.
Disable and delete history?
Disabling solution history will permanently delete all test results saved on this device. Are you sure you want to continue?
Preparing the test…
Question 1out of 10
What should be considered when deciding whether a linear model is suitable?
The dependent variable is the response predicted by the model. Assess fit using R², residual patterns, context and prediction range. Correlation alone does not prove causation; a third factor may explain it.
Question 2out of 10
Two trend models are y = x + 4 and y = 2x − 8. For what value of x do both models give the same prediction?
Set the two model predictions equal: a₁x + b₁ = a₂x + b₂. Collect the x terms on one side, the constants on the other, and solve the resulting linear equation.
Question 3out of 10
For three observations, the pairs (observed value; predicted value) are: (2; 10), (27; 23), (48; 40). Calculate the root mean square error (RMSE). Give the exact value.
For each pair find the residual eᵢ = yᵢ − predictionᵢ. Square the residuals, calculate the mean of their squares, and take the square root: RMSE = √((e₁² + e₂² + e₃²) / 3).
Question 4out of 10
Which variable in a linear model is called dependent?
The dependent variable is the response predicted by the model. Assess fit using R², residual patterns, context and prediction range. Correlation alone does not prove causation; a third factor may explain it.
Question 5out of 10
The correlation coefficient is r = 0.90. What is the direction?
The correlation sign gives direction: r > 0 positive and r < 0 negative. Compare linear strength using |r|: closer to 1 means stronger. A negative r can indicate a strong relationship.
Question 6out of 10
Compare correlations r₁ = 0.20 and r₂ = 0.30. Which is stronger?
The correlation sign gives direction: r > 0 positive and r < 0 negative. Compare linear strength using |r|: closer to 1 means stronger. A negative r can indicate a strong relationship.
Question 7out of 10
For three observations, the pairs (observed value; predicted value) are: (14; 11), (19; 25), (44; 38). Calculate the root mean square error (RMSE). Give the exact value.
For each pair find the residual eᵢ = yᵢ − predictionᵢ. Square the residuals, calculate the mean of their squares, and take the square root: RMSE = √((e₁² + e₂² + e₃²) / 3).
Question 8out of 10
A linear regression model has R² = 0.16, its line is decreasing, sₓ = 5, and sᵧ = 20. Find the slope of the regression line.
First find the correlation coefficient: |r| = √R². Determine its sign from the direction of the regression line. Then use the slope formula a = r · sᵧ / sₓ. Keep the sign of r.
Question 9out of 10
Why does strong correlation not necessarily mean causation?
The dependent variable is the response predicted by the model. Assess fit using R², residual patterns, context and prediction range. Correlation alone does not prove causation; a third factor may explain it.
Question 10out of 10
Compare correlations r₁ = 0.80 and r₂ = 0.90. Which is stronger?
The correlation sign gives direction: r > 0 positive and r < 0 negative. Compare linear strength using |r|: closer to 1 means stronger. A negative r can indicate a strong relationship.
Time left: 00:00:00
Best results on this test
Top 10 registered students. Only each student’s best result in the period counts.
Sample questions
- The correlation coefficient is r = ___. What is the direction?
- Use R², the direction of the regression line and the variables' standard deviations to find the slope of the regression line.
- Find the value of x for which two linear trend models give the same prediction.
- Which variable in a linear model is called dependent?
- Compare correlations r₁ = ___ and r₂ = ___. Which is stronger?
Related mathematics tests
Antiderivatives and indefinite integrals
Families of antiderivatives, integration rules, linear arguments and recovering a function from a given value.
Normal distribution
Standardization, interval and tail probabilities, thresholds and distribution parameters.
Binomial theorem
Binomial expansions, coefficients, constant terms, parameters and coefficient sums.
Function analysis using derivatives
This test uses the first derivative to analyse a function. Tasks include finding critical points, intervals of increase and decrease, local extrema and absolute maximum or minimum values.
The test is finished
Your test result is
????
We've marked wrong answers in red.
🏆
Congratulations! This is your personal best on this test!
Try the test again and aim to improve your score!
What's next?
Answered all questions ahead of schedule.
You can finish the test now or review your answers and complete the test later by pressing the appropriate button.