Question 1

Paper 2, calculatorHard6 marks

A running club records the weekly training time, xx hours, and 5 km race time, yy minutes, for eight recreational runners. The scatter diagram of the results is shown in Figure 1.

0246810121416182024252627282930313233Weekly training time, x (hours)5 km time, y (minutes)
(a)

Use a GDC to determine the Pearson product-moment correlation coefficient, rr and the equation of the regression line of yy on xx Give rr and the coefficients of the regression equation to three significant figures.

[2]
(b)

Use your regression equation from part (a) to estimate the 5 km time for a runner who trains for 20 hours per week.

[1]
(c)

A coach proposes that the club should:

  • recommend 20 hours of training per week because the regression predicts a faster 5 km time, claiming that adding training will cause every runner’s time to improve;
  • estimate the weekly training time needed by a runner targeting a 5 km time of 27.0 minutes by rearranging the regression equation from part (a).

Comment on the statistical validity of these two proposals.

[3]

More AA 4.2 Correlation and regression questions