IB Maths AA SL 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]

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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SL 4.4—Correlation and regression question 1