= Week 9 Notes - 2 x Bb Modelling Relation X Bb 7834339 X Bb 7465914 Bb ST2002 Statistics x G what is a coufour X answers

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Week 9 Notes 2 X Bb Modelling Relation X Bb 7834339 X Bb 7465914 Bb St2002 Statistics X G What Is A Coufour X Chegg 1 (148.02 KiB) Viewed 35 times

= Week 9 Notes - 2 x Bb Modelling Relation X Bb 7834339 X Bb 7465914 Bb ST2002 Statistics x G what is a coufour X answers Search X Gif population is no X + → C learn-eu-central-1-prod-fleet01-xythos.content.blackboardcdn.com/5cf4ce7a4424f/7834339?X-Blackboard-Expiration=1650996000000&X-Blackboard-Signature=lsj... ↓ ☆ 7834339 5/8 100% + A » Question 3 (25 Marks). Sixteen male well-trained middle and long distance runners performed a 3 km time trial and a number of running tests in the laboratory where their VO2Max (i.e. the maximum or optimum rate at which the heart, lungs, and muscles can effectively use oxygen during exercise) was measured as a way of measuring their individual acrobic capacity. All the laboratory testing took place on a motorised treadmill while distance running performance was determined by 3 km time trials on an indoor 200m track. The aim of the study was to investigate whether there is sufficient evidence of a dependency of 3 km running time on VO2Max in the population of male runners of interest in order to use their aerobic capacity to predict their 3km running time. A scatterplot (with lowess smoother and line of best fit) is provided, as is output from a regression analysis carried out on these data. a) What are the slope and intercept of the least-squares line? b) What is the observed correlation between VO2Max and 3km finishing time? [2 marks] [1 mark] c) Based on the p-values presented, explain why there is evidence that VO2Max is a significant predictor of 3km finishing? [6 marks] d) Provide an interpretation of the R-sq statistic in terms of how useful is VO2Max as a predictor of 3km finishing time. [2 marks] Provide an interpretation of the residual standard error (highlighted in bold) in terms of using this model to predict 3km finishing time. [2 marks] e) f) A particular athlete recorded a VO2Max of 20 in the lab prior to a 3km event. Use the output below to provide a range of predicted values for his likely finishing time. [4 marks] g) What are the assumptions underlying the model presented and do they look justified based on the residual plots provided? [8 marks] Scatterplot with Lowess Smoother and Line of Best Fit (uncertainty band is for the smoother) 11- 3 10- 0: ⠀
= Week 9 Notes - 2 x Bb Modelling Relation X Bb 7834339 X Bb 7465914 Bb ST2002 Statistics x G what is a coufour X answers Search X Gif population is no X + → C learn-eu-central-1-prod-fleet01-xythos.content.blackboardcdn.com/5cf4ce7a4424f/7834339?X-Blackboard-Expiration=1650996000000&X-Blackboard-Signature=lsj... ↓ ☆ 7834339 6/8 100% + A Scatterplot with line of best fit and Prediction Intervals 10- 8 20 22 VO2Max (ml/kg.min) PTO 6 3 6 2 C 16 Residuals vs Fited 16 18 139 1912 Normal Q-Q 20 0: ⠀
= Week 9 Notes - 2 x Bb Modelling Relation X Bb 7834339 X Bb 7465914 Bb ST2002 Statistics x G what is a coufour X answers Search X Gif population is no X + → C learn-eu-central-1-prod-fleet01-xythos.content.blackboardcdn.com/5cf4ce7a4424f/7834339?X-Blackboard-Expiration=1650996000000&X-Blackboard-Signature=lsj... ✩ ☆ 7834339 6/8 100% + A 1m(formula Running_Time_3km ~ VO2Max, data = running.df) = Residuals: Min 10 Median -0.65128 -0.29101 0.03749 0.15649 0.85426 30 Max Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 15.69623 VO2Max 0.97466 16.104 1.98e-10 *** -0.30154 0.04688 -6.432 1.57e-85 *** Signif. codes: 0¹*** 0.001 '**' 0.01 ¹*' 0.05 0.1 '. 1 Residual standard error: 0.3874 on 14 degrees of freedom Multiple R-squared: 0.7472, Adjusted R-squared: 0.7291 F-statistic: 41.37 on 1 and 14 DF, p-value: 1.569e-05 running new <- data.frame(VO2Max = c(18, 20, 21)) predict(running.model, newdata = running_new, interval= "confidence") fit 1wr upr 1 10.268513 9.927684 10.609342 2 9.665433 9.446523 9.884344 3 9.363894 9.153821 9.573966 predict (running.model, newdata = running_new, interval= "prediction") lwr upr fit 1 10.268513 9.370485 11.16654 2 9.665433 8.806241 10.52463 3 9.363894 8.506911 10.22088 Scatterplot with line of best fit and Prediction Intervals 3 6 0: ⠀
= Week 9 Notes - 2 x Bb Modelling Relation X Bb 7834339 X Bb 7465914 Bb ST2002 Statistics x G what is a coufour X answers Search X Gif population is no X + → C learn-eu-central-1-prod-fleet01-xythos.content.blackboardcdn.com/5cf4ce7a4424f/7834339?X-Blackboard-Expiration=1650996000000&X-Blackboard-Signature=lsj... ↓ ☆ 7834339 6/8 100% + A Scatterplot with line of best fit and Prediction Intervals 10- 8 20 22 VO2Max (ml/kg.min) PTO 6 3 6 2 C 16 Residuals vs Fited 16 18 139 1912 Normal Q-Q 20 0: ⠀
= Week 9 Notes - 2 X Bb Modelling Relation X Bb 7834339 X Bb 7465914 Bb ST2002 Statistics x G what is a coufour X answers Search X Gif population is no X + → C learn-eu-central-1-prod-fleet01-xythos.content.blackboardcdn.com/5cf4ce7a4424f/7834339?X-Blackboard-Expiration=1650996000000&X-Blackboard-Signature=lsj... ↓ ☆ 7834339 7/8 100% + A » Hesiduals vs Fited Normal QQ 16 160 40900001 -1 0 9.0 10.0 9.5 10.5 1 2 Im(Running Time 3km --VO2Max) Theoretical Quan les Fitted values Im(Running Time 3km-VO2Max) Residuals vs Leverage Scale-Location 015 015 09 & Cook's distance- 90 95 100 105 0.00 0.05 0.10 0.15 0.20 025 030 035 Filled vas Leverage Im(Running Time 3km --VO2Max) Im Running Time 3km VO2Max) Question 4 (25 Marks). Data were available on 572 activities from a particular athlete's GPS Fitness Tracker which included the activity (i.c. a cycle, hike, run) and the corresponding tracking data namely distance, maximum heart rate and average speed for the activity in question. The data were split at random into a train and test set (using a ratio of 0.7:0.3) and a classification tree (using conditional inference) was fitted to explore whether the tracking data variables are potentially useful classifiers of activity type. 5 ... Spec TY 7 -0.5 0.0 0.5 1.0 Standard ze residuals 0.5 1.0 1.5 139 150 Standardized res duels 2 Po 0: ⠀