Problema 2 Lactate concentration in the blood is often used to predict endurance 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 casess changes 171.4 178.68 187.42 182.39 174.18 174.38 in their performance. 183 170.46 169 81 159.17 165.05 168.75 To identify these predictors, 24 we -trained formale cyclists were selected and tasted physics on a cycle 183.6 201.23 185.6 182.39 178.28 192 34 argonometer. The physical test consisted in performing 180.75 191.17 182 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 226.25 287.28 230.43 217.02 219.78 253.4 plasma lactate and obtain predictive values 202 2 219.56 214.98 180.77 197.63 following: 205.02 104 3 244.41 232 31 206.44 195.55 238.41 Lactate threshold (P-Tac] Aintzone Barrona climbing to the top of 162 1 145.76 160 81 137 165.12 138 27 DMax (DM=x) So ragain (Navarro] in the Armas Tomar 171 9 182.15 202 81 188.67 190.02 173.35 LT-log-log (P-Tlac.Il) cycle tour. / MIRARI NAZABAL P-4 TOLL - [P-4mM) 202 3 223.77 193.84 183.09 200.02 222.17 Work rate corresponding to : 1 mM increase 171.1 182.53 182.85 189.02 171.95 164.44 from baseline (Risc 1.PB) 183.7 194.69 214.03 181.27 190.37 194 84 209 8 180.9 185 154.47 170.28 190.69 Endurance performance (AV. Power] was assessed 7 days later using a one-hour bicycle test in 195.95 204.26 190 22 174.16 183.62 176.43 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 196 220.31 188.14 187.34 172.32 199.02 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 (b] Is it a mode with a good fit? Does this mean that the regression is significant? 208 8 254.33 230.8 278.86 207.55 244.33 161.1 153.86 138.38 115.58 130.91 143.7 52.25 145.23 138.49 120.02 128.74 140.84 (c) Check if the regression coefficients of the variables P-Tlac and P-Tlac II are equal. 169.05 206.53 175.74 131.83 158.19 182.18 CyclingPower.xis dataset (d) If = broker has values of P-Tlac = 175, DMex = 198, P-Time.ll = 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 0.95, 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.II and P-ATM. f) What is the estimated variance of the error? Give a confidence interval for the estimated variance of the g 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 (@) with this new model