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

Construct and interpret scatter diagrams and lines of best fit, calculating or using Pearson’s correlation coefficient r to quantify association.
Classify correlation as positive, negative, zero, strong, weak or absent, and use a regression line for cautious prediction while distinguishing correlation from causation.

[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 $=20.9(\mathrm{~cm})$

All question bank results loaded

IB Maths AA SL 4.4 Correlation and Regression Questions question 1