IB Maths AA HL 4.4 Correlation and regression Question Bank

Practise IB Mathematics SL/HL 4.4 by applying correlation and regression methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 3]

A class is given two tests, Test A and Test B. Each test is scored out of a total of 100 marks. The scores of the students are shown in the following table.

Table for Question SL 4.4—Correlation and regression question 1 — IB Maths AA HL

Let x be the score on Test A and y be the score on Test B.
The teacher finds that the equation of the regression line of y on x for these scores is y=0.822 x+18.4.

(a)

Find the value of Pearson's product-moment correlation coefficient, r.

Giovanni was absent for Test A and Paulo was absent for Test B.

The teacher uses the regression line of y on x to estimate the missing scores.
Paulo scored 10 on Test A.

The teacher estimated his score on Test B to be 27 to the nearest integer using the following calculation:

y=0.822(10)+18.4 \approx 27

[ 2 ]

$r=0.901017 \ldots$
r=0.901

(b)

Give a reason why this method is not appropriate for Paulo.

Giovanni scored 90 on Test B.

The teacher estimated his score on Test A to be 87 to the nearest integer using the following calculation:

90=0.822 x+18.4, \text { so } x=\frac{90-18.4}{0.822} \approx 87

[ 1 ]

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SL 4.4—Correlation and regression question 1

Question (a)

Question (b)