The times x x\,x minutes taken by eight cyclists to complete a climb and their recovery pulse rates y y\,y beats per minute are modelled by the regression line y=4.6x+71y=4.6x+71y=4.6x+71. A ninth cyclist takes 18 minutes and has recovery pulse rate 146 beats per minute. The value x=18x=18x=18 is within the observed range for the original eight cyclists.
Find the residual for the ninth cyclist.
Explain how an unusually large residual could affect the sample product moment correlation coefficient if the point were added.
Explain why it would be wrong to remove the point solely to obtain a significant correlation test.