A study of training time x x\,x hours and race improvement y y\,y seconds gives a correlation coefficient of 0.94 and the regression line y=1.8x+2.4y=1.8x+2.4y=1.8x+2.4. The observed point for one athlete is (8,15.1)(8,15.1)(8,15.1).
Describe the association shown by the correlation coefficient.
Calculate the fitted value of y y\,y when x=8x=8x=8 and hence find the residual for this athlete.
Interpret the sign of the residual in context.
Explain why the study does not establish that extra training causes the improvement.