IB Maths AA 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 and interpret Pearson’s correlation coefficient to describe linear association.
Use a regression line to estimate parameters and predict a response from explanatory data.
Interpret the sign, strength and context of correlation without claiming causation.

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In a study, measurements for arm span, $A \mathrm{~cm}$ , and foot length, $F \mathrm{~cm}$ , are taken from a large group of adults.
For this group, the regression line of F on A is found to be F=0.335 A-32.6, and the regression line of A on F is found to be A=2.89 F+99.3. Each regression line passes through the mean point.

For this group of adults, find the mean arm span and the mean foot length.

The heights, $H \mathrm{~cm}$ , of adults in the group can be modelled by a normal distribution with mean 163 cm and standard deviation $\sigma \mathrm{cm}$ .

It is found that 88 % of the group have a height between 153 cm and 173 cm .

recognition that the lines intersect at the mean point (may be seen on a sketch)
$2.89 F+99.3=\frac{F+32.6}{0.335}$ OR $0.335 A-32.6=\frac{A-99.3}{2.89}$
159.686… or $20.8948 \ldots$
the mean arm span $=160(\mathrm{~cm})$ , the mean foot length $=20.9(\mathrm{~cm})$

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IB Maths AA SL 4.4 Correlation and Regression Questions question 1