For children aged 5 to 12, a study gives the regression line h=6.1a+78h=6.1a+78h=6.1a+78 for predicting height h h\,h cm from age a a\,a years. A separate regression of age on height is a=0.12h−7.9a=0.12h-7.9a=0.12h−7.9.
Use the first regression line to predict the height of a child aged 9 years.
Use the second regression line to predict the age of a child whose height is 135 cm.
Explain why rearranging the first regression line would not, in general, give the second regression line.
State whether each prediction is interpolation or extrapolation, giving a reason.