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<0.001. This means that the more the knees flexed the higher the individual attains greater speed in performing the multi-stage shuttle run test, and the higher the maximal speed attained the more knees flexed. The two variables affect each other without determining the causal factor among the two.

The relationship between MASMSR and PTEX was found too to be highly positive, r(38)=0.53, p<0.001. This means that the more the knees extends, the higher the individual attains greater speed in performing the multi-stage shuttle run test, and the higher the maximal speed attained the more knees extended.

There was no much difference in these correlations. This may be explained by the fact that the more the knees flexed, the more the knees extended to compensate for the previous action, and the more knees extended, the more the knees flexed. This vicious cycle of effect on each other when taken together in a series of actions would result to a high speed running. This explains altogether the relationship of MASMSR and PTFL and MASMSR and PTEX.

The maximal attained speed (MAS) of the three cardio-respiratory tests (MT, MSR, SSR), MASMT was found to be most highly positive with MTVO2MAX, r(38)=0.94, p<0.001. This means that the greater the maximal speed attained in performing the treadmill test, the greater the uptake of oxygen. Taking in oxygen was rather a compensatory reaction mechanism of the body subjected to physical stress such as running a treadmill. There may however be possible autocorrelation in MTVO2MAX and MASMT since the variables were taken in the same occasion, compared to measures taken in the multi-stage shuttle run test and square shuttle run test. This explains a very high correlation between the two variables.

The average oxygen uptake (VO2MAX) measured in MT was between 41 and 53.4 mL/kg/min compared to as measured in MSR (46.4, 58) and SSR (41.8, 51.6). This means that the oxygen uptake when in progressive maximal laboratory treadmill was in lesser amount compared to when the individual was in multi-stage shuttle run test, although this oxygen uptake was in pace with the maximum attained speed.

The y-intercept value and the x-value for MASMSR cannot be determined from the literature although it can be said that the slope or y-intercept was significantly not equal to zero, since all isokinetic dynamometry measures were highly related to maximal attained speed in multistage shuttle run test. The researchers further noted that the beta-coefficients for this linear regression equation was rather “markedly low” but the figures were not reported, since the researcher limited its study in establishing effects of the isokinetric dynamometry variables on the maximal attained speed (MAS) in multistage shuttle run test and not on predicting MAS.

The study did not report the regression equation thus the maximal attained speed cannot be predicted using known values of the isokinetic dynamometry variables. The full use of the regression analysis was therefore not maximized. Further, its taking account of the Coefficient of Determination (R2) only gave the increase of variation for a variable. Although this may be sufficient but the full information needed to make exhaustive analysis of the data was not readily available. Thus, verification of the results, as maybe done by other researcher in the field, cannot be done.

The study implies on the incorporation of resistance regimens in the runner’s training. Regimens may include activities MSR since the activity stimulates knee extensor and knee flexor, which helped in increasing maximal attained speed of the runner.

Flouris, A.D. Metsios, G.S., Koutedakis, Y. (2006). Contribution of muscular strength in cardio-respiratory fitness tests. J. Sports med phys fitness, 46(2), 197-201.