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.
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Question 1out of 10
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 2out of 10
Question 3out of 10
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 4out of 10
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 5out of 10
Question 6out of 10
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 7out of 10
Question 8out of 10
Question 9out of 10
Question 10out of 10
Time left: 00:00:00
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?
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