Unit 4: Statistics and Probability
Topic 4.4: Correlation and Regression Questions
Practice 16 exam-style questions for IB Math AA SL Topic 4.4. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1State2 marks
2026• Aimnova practice — 4.4.1
A scatter graph shows points loosely scattered with a slight downward trend. State the type of correlation.
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2026• Aimnova practice — 4.4.1
For ten pairs of values, a calculator gives r = 0.86. Describe the correlation.
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2026• Aimnova practice — 4.4.1
State the range of possible values for the Pearson correlation coefficient, and what r = −1 represents.
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2026• Aimnova practice — 4.4.2
A regression line of y on x is y = 0.75x + 6. The mean of x is 12. Find the mean of y.
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2026• Aimnova practice — 4.4.1
The masses (kg) and lengths (cm) of seven puppies are recorded. The data is (2,30), (3,34), (4,37), (5,41), (6,44), (7,48), (8,52). Find the correlation coefficient r.
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2026• Aimnova practice — 4.4.1
The temperature (°C) and number of heaters sold are (5,48), (8,40), (12,33), (15,25), (20,16). Find r and describe the correlation.
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2026• Aimnova practice — 4.4.2
The temperatures x (°C) and energy use y (kWh) for nine days give y = −1.8x + 95.
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2026• Aimnova practice — 4.4.1
Eight students' sleep hours and reaction times give r = −0.62.
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2026• Aimnova practice — 4.4.2
The hours of revision x and exam mark y for six students are (2,45),(3,52),(5,60),(6,68),(8,80),(9,85). Find the regression line of y on x.
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2026• Aimnova practice — 4.4.2
A regression line for monthly sales y (in $1000s) against advertising spend x (in $1000s) is y = 3.4x + 12. Interpret the gradient and the intercept in context.
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2026• Aimnova practice — 4.4.2
The regression line of y on x is y = 4x − 5. Show that the point (3, 7) is the mean point and state the mean of y.
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2026• Aimnova practice — 4.4.2
A study of x = age (years) and y = value of a car ($1000s) gives a regression line. State which regression line you would use to estimate a car's value from its age, and why.
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2026• Aimnova practice — 4.4.1
A newspaper claims that because cities with more libraries have lower crime rates (r = −0.7), building libraries reduces crime. Comment on this claim.
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2026• Aimnova practice — 4.4.2
Seven data points have mean of x equal to 8 and mean of y equal to 21. The regression line of y on x has gradient 2.5. Find its y-intercept.
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2026• Aimnova practice — 4.4.2
The regression line of y on x is y = 1.5x + 2, and the regression line of x on y is x = 0.5y − 1. Find the mean of x and the mean of y.
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2026• Aimnova practice — 4.4.1
Explain why a data set that follows a strong U-shaped curve can still have a correlation coefficient close to 0.
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