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 1 Paper 2

Difficulty

Easy Medium Hard

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.

(a)

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

[2]

(b)

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

[2]

(c)

The student wants to describe a monotonic association, and considers the point $(10,5)$ 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, $x$ hours, and 5 km race time, $y$ minutes, for six runners.

$x$	2	4	5	7	9	10
$y$	31.8	29.4	28.7	26.3	25.5	23.9

(a)

Use your graphic display calculator to find Pearson’s product-moment correlation coefficient, $r$ 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 $y$ on $x$ in the form $y=ax+b$ Give the values of $a$ and $b$ 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 $a$ in this context.

[1]

Question 3

Paper 1Hard6 marks

During a greenhouse trial, a horticulturist measures the height of a young plant on days 0 to 5. The measurements, rounded to the nearest centimetre, are shown in Figure 1.

(a)

Use your GDC to fit a quadratic least-squares regression curve to the observations. Give its equation, $R^2$ and $SS_{\mathrm{res}}$

[2]

(b)

Use your GDC to fit a linear least-squares regression curve to the observations. Give its $R^2$ $SS_{\mathrm{res}}$ and Pearson’s product moment correlation coefficient, $r$ Show numerically that $R^2=r^2$ for this linear model.

[2]

(c)

A horticulturist claims that the quadratic model must be used to estimate the plant’s height on day 8 because it has the larger $R^2$ Assess this claim using the graph and your results.

[2]

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