Linear correlation coefficient and linear regression principles

Flouris, Metsios and Koutedakis (2006) studied the contribution of muscular strength in cardio-respiratory fitness tests, which are multistage shuttle run test (MSR), square shuttle run test (SSR) and maximal laboratory treadmill test (MT). The last minutes of an endurance race depended on muscular strength and anaerobic power. There however has no study yet on how lower extremity muscular strength performed in cardio respiratory fitness tests. The purpose of this study is to determine the levels of muscular strength independent using MT, MSR, and SSR. The participants of the study were thirty-eight healthy male individuals aged between 18 and 29 years old. To qualify for healthy individuals, those who smoke and hard benign medical history, were excluded from the study. Participants visit the data collection sites individually on three different occasions phased with a minimum of 96 hours between assessments. All these three assessments were done within two weeks. Time of assessment was between late morning and early afternoon. The first visit was for laboratory assessments: 1) progressive maximal laboratory treadmill test (MT) to exhaustion, where maximal attained speed (MAS) and maximal oxygen uptake (VO2MAX) were measured, and 2) isokinetic dynamometry, where measures of concentric peak torques of knee extensors (PTEX) and flexors (PTFL) and combined torque generated by both legs (PTC) were obtained. The remaining visits were for the field assessments of 20 meter multistage shuttle run test (MSR) and 20 meter square shuttle run test (SSR), where for each test the maximal attainment speed was measured. The linear regression analysis used in the square shuttle run test (SSR) was the equation: MASMSR = PTEX + PTFL + PTC. The beta-coefficients derived through the regression analysis however were not reported. From the isokinetic dynamometry measures, only combined peak torques of both legs had significant R2 increase, which was 0.04. This means that combined peak torques of both legs explained four percent of the variation in the data for maximal attained speed while performing the square shuttle run test. The relationship between MASMSR and PTFL was found to be highly positive, r(38)=0.58, p