IB Maths AA SL 4.10 Regression X on Y Questions

Practise choosing the regression direction that predicts the required variable, interpreting the estimate in context and rejecting reversed predictions.

Exam points

Use the regression line of x on y to make predictions in the correct direction, identifying which variable is predicted and selecting the appropriate fitted equation.
Interpret prediction reliability and limitations, explaining why an x-on-y regression line is not generally suitable for predicting y from x.

[Maximum number: 2]

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.

By using an appropriate regression line, find an estimate of the arm span for an adult with a foot length of 19.8 cm .

attempt to substitute F=19.8 into the regression line for A on F
A=2.89(19.8)+99.3
$=156.522(\mathrm{~cm})$
arm span $=157(\mathrm{~cm})$

Note: Award M0A0 for choosing the wrong regression line to get
$A=156.417 \ldots$ so A=156.

All question bank results loaded

IB Maths AA SL 4.10 Regression X on Y Questions question 1