IB Maths AI HL AI 4.2 Correlation and regression questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper
Paper 1Paper 2
Difficulty
EasyMediumHard

Question 1

Paper 1Easy6 marks

A student records the distance downstream from a spring and the number of aquatic invertebrate taxa found at each of six fieldwork sites. Figure 1 shows the results.

012345678910024681012Distance downstream from the spring, d (km)Number of aquatic invertebrate taxa, N
(a)

Using your GDC, find Spearman’s rank correlation coefficient, rsr_s for these data. Give your answer to three significant figures.

[2]
(b)

Using your GDC, find Pearson’s product moment correlation coefficient, rr for these data. Give your answer to three significant figures.

[2]
(c)

The student wants to describe a monotonic association, and considers the point (10,5)(10,5) to be unusual compared with the other observations. State which coefficient is more appropriate for this purpose and give a reason.

[2]

Question 2

Paper 1Easy6 marks

A running coach records the weekly training time, xx hours, and 5 km race time, yy minutes, for six runners.

xx2457910
yy31.829.428.726.325.523.9
(a)

Use your graphic display calculator to find Pearson’s product-moment correlation coefficient, rr Give your answer to three significant figures.

[1]
(b)

Describe the direction and strength of the correlation.

[1]
(c)

Use your graphic display calculator to find the equation of the regression line of yy on xx in the form y=ax+by=ax+b Give the values of aa and bb to three significant figures.

[2]
(d)

Use the regression line to estimate the 5 km race time for a runner who trains for 6.5 hours per week. Give your answer to three significant figures.

[1]
(e)

Interpret the value of aa in this context.

[1]

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