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3. A national ski team are reviewing their tness before changing their training routine. They have collected data on their treadmill run time to exhaustion (in minutes) and their 20km ski time (in minutes) with a view to examining any relationship. The following table contains the data for a random sample of 10 members of the ski team. Skier, i l 2 3 4 5 6 7 8 9 10 RunTime (Xi) 7.7 8.4 8.7 9.0 9.6 10.0 10.2 10.4 11.0 11.7 Ski Time (Vi) 71.0 71.4 65.0 68.7 69.4 63.0 64.6 66.9 62.6 61.7 (i) (ii) (iii) 0'!) Summary Statistics : Ex; = 96.70 2y.- = 664.30. 2x? = 943.79 2y? = 44243.40 2::in = 6391.67. Use the summary statistics provided to calculate the correlation coefcient between Run Time and Ski Time. Use the value of the correlation coefcient to comment on the direction and strength of the relationship between the two variables. [5] Write down a simple linear regression model for Ski Time (y) in terms of Run Time (K). State the assumptions of the model and calculate the model parameters including the intercept, the slope and the estimated error variance. [7] At a 5% signicance level, test for a linear relationship between Run Time and Ski Time. Using the appropriate MINITAB output report the results of the test. Include the hypotheses and the formula of the test statistic with the underlying distribution, the observed test statistic and pvalue, test decision and conclusion. [6] Use the regression equation from (ii) to predict the expected Ski Time when Run Time is 10 minutes together with the 95% Condence Interval of the prediction. Calculate the coefficient of determination and comment on the predictive performance of the model. MINITAB oumut Q3 [7] Coefcients Term Coef SE Coef T-Value P-Value VII: Constant 5.79 15.39 0.000 Run_Time 0.594 -3.94 0.004 1 .00 [Question 4 overleaf...]