IB Maths AA HL AA 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, no calculator Paper 2, calculator

Difficulty

Easy Medium Hard

Question 1

Paper 2, calculatorMedium12 marks

A teacher records, for seven students, the number $x$ of optional online revision sets each student completed and the student’s examination mark $y$ out of 100. The students chose how many sets to complete.

$x$	2	3	4	5	6	7	8
$y$	52	56	59	65	66	72	74

(a)

Sketch a scatter diagram for the data.

[1]

(b)

Use your GDC to determine Pearson’s product-moment correlation coefficient $r$ and the equation of the regression line of $y$ on $x$ Give all values to three significant figures.

[4]

(c)

Use the regression line to estimate the examination mark for a student who completes 6 revision sets. Interpret the gradient of the regression line in this context.

[3]

(d)

Use the regression line to estimate the examination mark for a student who completes 12 revision sets. Comment on the reliability of this estimate and on the claim that completing more revision sets causes higher examination marks.

[4]

Question 2

Paper 1, no calculatorMedium6 marks

A grower records the irrigation time, $y$ hours, and the harvested mass, $x$ kg, for five greenhouse beds.

$y$	1	2	3	4	5
$x$	2	3	3	5	6

(a)

Determine, giving your working, the equation of the regression line of $x$ on $y$ in the form $x=a+by$

[3]

(b)

Hence estimate the harvested mass when the irrigation time is 4 hours.

[1]

(c)

The grower wants to estimate the irrigation time from a harvested mass of $4.8$ kg. A trainee rearranges the equation from part (a) and obtains an estimate of 4 hours. Explain whether this is a justified use of a regression line.

[2]

Question 3

Paper 2, calculatorHard6 marks

A running club records the weekly training time, $x$ hours, and 5 km race time, $y$ minutes, for eight recreational runners. The scatter diagram of the results is shown in Figure 1.

(a)

Use a GDC to determine the Pearson product-moment correlation coefficient, $r$ and the equation of the regression line of $y$ on $x$ Give $r$ and the coefficients of the regression equation to three significant figures.

[2]

(b)

Use your regression equation from part (a) to estimate the 5 km time for a runner who trains for 20 hours per week.

[1]

(c)

A coach proposes that the club should:

recommend 20 hours of training per week because the regression predicts a faster 5 km time, claiming that adding training will cause every runner’s time to improve;
estimate the weekly training time needed by a runner targeting a 5 km time of 27.0 minutes by rearranging the regression equation from part (a).

Comment on the statistical validity of these two proposals.

[3]

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