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. For the original eight cyclists, the predicted value at x=18x=18x=18 is within the observed range of xxx-values.
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.
308 exam-style questions on WJEC A Level Maths 4.3 Statistical hypothesis testing (A-level only), covering 4.3.1 Statistical hypothesis testing (A-level only) and 4.3.2 Statistical hypothesis testing (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.