Problema 2 Lactate concentration in the blood is often used to predict andurance in athletes. Identifying some predictors of AV.Power P.4mM P.Tlac P.Tlac.ll DMax Rise.1.PB endurance can help coaches and athletes assess changes 171.4 178.69 187.42 182.39 174.16 174.38 in their performance 163 170.46 169.81 159.17 165.05 168.75 To identify these predictors, 24 well-trained formela cyclists were selected and tested physics on a cycle 183.6 201.23 185.6 182.39 179.28 92 34 argonometer. The physical test consisted in performing 189.75 191.17 182 25 141.17 170.6 180.8 stages of three minutes until exhaustion. Within 30 seconds of completing each three-minute stage, 165 8 135.11 124.79 98.49 133.68 27.91 Capillary blood was drawn from the index finger to analyze 226.25 267 28 230.43 217.02 219.78 253.4 plasma lactate and obtain predictive values 202 2 219.56 214.98 180.77 197.63 205.02 following: 194 3 244.41 232 31 206.44 196.55 238.41 Lactate threshold (P-Tlac) Aintrane Barrene climbing to the top of 162 1 146.76 160.81 137 165.12 138 27 DMax (DM=x) So ragain (Navarra] in the Armas Tamar 1719 182.15 202 81 186.87 190.02 173.35 LT-lag-log (P-Tlac.Il) cycle tour. / MIRARI NAZABAL P-4 T TOLL -: [P-4mM) 202 3 223.77 103.84 183.09 200.02 222 17 Work rate corresponding to = 1 miM increase 171.1 182.53 182 85 189.02 171.95 164.44 from bassline (Rise 1.PB) 183.7 194.60 214.03 181.27 190.37 194.84 208 8 180.9 185 154.47 170.26 190.69 Endurance performance (AV. Power] was assessed 7 days later using = one-hour bicycle test in 196.95 204.26 190 22 174.16 183.62 178.43 which the athletes had to achieve the highest possible power output. The results are in the 188.8 233.9 218.03 206.44 203.73 241.63 data file Cycling Power.ads. 160.4 161.26 144.13 144.03 144.68 158.57 (:) Calculate the regression hyperplane and the correlation matrix. Do the results 196 220.31 188.14 187.34 172.32 198 02 obtained agree? What do you think might be happening?* 187 4 160.58 188.15 119.1 170.57 172 38 178.3 171.07 183.3 132.95 161.93 155.09 208 8 254.33 230.8 278.86 207.55 244.33 (b) Is it = model with a good fit? Does this mean that the regression is significant? 161.1 153.85 138.38 115.58 130.91 143.7 152.25 146.23 138.49 129.02 128.74 140.84 (c) Check if the regression coefficients of the variables P-Tlac and P-Time II are equal. 180.05 206.53 175.74 131.83 158.19 182 18 CyclingPowerads dataset (d) If a broker has values of P-Tlac = 175, DMVex= 198, P-Tell = 131, P-4mM= 206 and Rise 1.PB = 182, what is the estimate of her performance resistance (AV.Power) and standard error for this estimate? With a probability of 0.98, between what values is the resistance performance (AV.Power] of a specific broker that has the above values? (=) Calculate the partial correlation between AV.Power and Rise.1 PB if we remove the information from P-Tlac, DMax, P-Tlac.Il and P-4TM. f) What is the estimated variance of the error? Give a confidence interval for the estimated variance of the 95% error. Calculate the VIF and propose a simp fied model with only three predictor variables that improves these values. Calculate the standard error of the mean and concrete predictions of part (d) with this new model
