7 [Maximum mark: 14] Kwami keeps a record of his best 5000m time each week (y minutes) in the xth week after he starts t

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7 Maximum Mark 14 Kwami Keeps A Record Of His Best 5000m Time Each Week Y Minutes In The Xth Week After He Starts T 1 (267.38 KiB) Viewed 59 times

7 [Maximum mark: 14] Kwami keeps a record of his best 5000m time each week (y minutes) in the xth week after he starts training for a competition season. The results are shown below: 2 3 4 5 6 7 9 8 1 x 10 11 12 13 17.6 17.2 16.8 18.1 18.6 16.4 14.6 14.3 18.5 14.2 14.5 y 14 ai Find the mean of Kwami's best times each week. ii Find the standard deviation in Kwami's best times each week. iii Find Pearson's product-moment correlation coefficient for this data. What type of correlation is suggested by this value? The results are illustrated in the following scatter diagram. [4] 19 18 17 16 15 14 13 2 4 6 8 10 12 14 bi Competitions occurred every week from week n until week 12. Athletes generally have improved performance in competitions. Use the graph to suggest the value of n. ii During one of the weeks before competitions began, Kwami was ill. Use the scatter graph to suggest which week this was. [2] For the rest of this question, the result from the week where Kwami was ill should be excluded. ci Create a piecewise linear model to predict y for a given x. [5] ii Compare and contrast, in context, the coefficients of x in each part of the linear model. d Use your model to predict the time Kwami would have achieved in the week he was ill if he had not been ill. [2] e Explain why it would not be valid to use this model to predict Kwami's times in the following season. (17