IB Maths AA HL Sl 4 4 Correlation and Regression Questions

Practise interpreting scatter diagrams, correlation and lines of best fit, distinguishing strength from direction and treating regression predictions with caution.

Exam points

Calculate or interpret Pearson correlation and describe the strength and direction of a linear relationship.
Determine the parameters of a linear regression model and use the model to estimate or predict a response.
Interpret residual or contextual limitations of regression, including the distinction between correlation and causation.

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Study SL 4.4—Correlation and regression conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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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 IB Maths AA HL Sl 4 4 Correlation and Regression Questions 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

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$r=0.901017 \ldots$
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

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IB Maths AA HL Sl 4 4 Correlation and Regression Questions question 1

Question (a)

Question (b)