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

Choose the regression line that matches the variable being predicted from the explanatory variable.
Interpret regression estimates in context and recognise when reversing variables gives an invalid prediction.

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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.

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.

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