**C**ardiorespiratory fitness (CRF), an important component of health-related physical fitness, is the ability to perform large-muscle, dynamic, moderate-to-high intensity exercise for prolonged periods of time^{(3)}. Standard tests for determining CRF involve directly measuring maximal oxygen consumption (˙VO_{2max}) during graded, maximal exertion exercise on a treadmill or cycle ergometer^{(28)}. However, despite a high level of accuracy, direct measurement ˙VO_{2max} tests are often impractical since testing procedures require expensive indirect calorimetry equipment, trained technicians, highly-motivated subjects, and in some cases physician supervision. Alternatively, regression models involving submaximal^{(11,19)} and maximal^{(9,27)} exercise have been developed to estimate˙VO_{2max}. Because epidemiological evidence now suggests that CRF is inversely related to all-cause mortality ^{(6)}, there is compelling reason to explore new ways to enhance both the practicality and accuracy of ˙VO_{2max} regression models.

Recently, ˙VO_{2max} regression models have been developed that exclusively use non-exercise (N-EX) predictor variables such as age, gender, body composition, and level of physical activity^{(2,18)}. The N-EX regression models generate˙VO_{2max} estimations comparable in accuracy to some exercise (EX) regression models (Table 1) and may provide a practical way to predict CRF without requiring expensive experimentation or exercise testing. However, current N-EX regression models do not match the predictive accuracy of the best EX regression models (Table 1), may not generalize well to younger, high fit individuals^{(20)}, and appear limited in their ability to accurately categorize CRF in large epidemiological studies ^{(29)}.

For a regression equation to accurately predict ˙VO_{2max} the model should account for any variable (i.e., genetic endowment, level of training, body composition, gender, age) known to be important in the estimation of ˙VO_{2max}^{(22)}. Bouchard et al.^{(8)} have reported that about 25% of the total variance of aerobic power (˙VO_{2max}) is a result of heredity or genetic endowment. A potential weakness of N-EX regression equations is that currently employed predictor variables (i.e., age, gender, body composition) may be limited in their ability to account for inheritable differences in CRF. In addition, self-report physical activity questions presently used by N-EX regression models likely have limited accuracy in describing an individual's present level of training ^{(5)}. On the other hand, exercise-based data (i.e., total treadmill time to exhaustion, submaximal HR, etc.) may be better able to account for genetic and/or environmental factors related to CRF which might explain why certain EX regression models are more accurate in predicting ˙VO_{2max} than are N-EX regression models(Table 1). As such, the predictive accuracy of N-EX regression models may be improved if self-reported data could in some way simulate exercise-based data and thereby more effectively account for variables known to be important in the prediction of ˙VO_{2max}.

Thus, this investigation sought to (a) develop a self-report instrument designed to simulate exercise-based data that could improve the accuracy of N-EX regression models and (b) compare the accuracy of N-EX regression models developed in the present study with previously developed N-EX regression models.

## METHODS

One hundred college students (males = 50; females = 50), aged 18 to 29 yr, satisfied the requirements of this study. Volunteers were primarily recruited from physical activity classes at Arizona State University. All subjects completed a brief Physical Activity Readiness Questionnaire (PAR-Q)^{(24)} to screen for cardiovascular contraindications and signed an informed consent document in accordance with Arizona State University Human Subjects Committee guidelines.

Before exercise testing, subjects reported their perceived functional ability (PFA) to walk, jog, or run for 1-mile, 3-miles, and 30-min, respectively. The PFA questions (Fig. 1) were designed to quantify subjects' perceived ability to sustain an exercise intensity considered “not too easy and not too hard.” For each PFA question, subjects were instructed to record an odd or even numbered response^{(1-13)} that best described their present level of functional ability. In the event that subjects were unfamiliar with pace times for walking, jogging, or running in minutes per mile, they were instructed to use the other descriptive information (slow, medium, fast) to help them identify an appropriate PFA score.

The self-report questions developed by Ainsworth et al.^{(2)} and Jackson et al. ^{(18)} were used to estimate subjects' present level of physical activity. The Ainsworth et al. ^{(2)} question asked respondents to indicate their frequency of participation in strenuous exercise over a typical 7-d period involving durations of at least 15 min or more. The original Jackson et al.^{(18)} question was slightly modified as suggested by Kolkhorst and Dolgener ^{(20)}(Fig. 2) and asked subjects to rank their level of physical activity (on a 10-point scale) over the previous 6 months.

Initially, subjects reported an estimate of their body weight in pounds and body height in feet and inches. Following this, a test administrator measured subjects' body weight with a physician's balance beam scale and body height with a calibrated wall scale (subjects dressed in running apparel and no shoes). Paired *t*-tests were employed to assess statistical differences between self-reported and measured body weight, height, and body mass index (BMI). Three-site skinfold measures were also evaluated for females(triceps, suprailiac, and thigh) ^{(17)} and males (chest, abdominal, and thigh) ^{(16)} using Lange calipers to determine body density and percent body fat (% fat). The anthropometric measures were taken after completion of the questionnaires and prior to exercise testing.

Subjects performed a maximal graded exercise test (GXT) on a calibrated motor-driven treadmill (Model 24-72, Quinton, Inc., Bothell, WA). Before the maximal GXT, subjects were informed of all exercise procedures, allowed to practice treadmill walking/jogging as needed, and asked to begin ventilating through a one-way breathing apparatus (nostrils occluded) so that metabolic data could be evaluated during exercise testing.

Subjects walked at a self-selected, brisk pace (5% grade) for the first 3-min stage of the maximal GXT and then were given the option to either continue walking (5% grade) or jog at a comfortable pace (level grade) for the second 3-min stage. Subjects indicated with hand signals when an acceptable walking and/or jogging speed was achieved. The first two stages served as a 6-min warm-up for the GXT and most subjects (*N* = 97) elected to jog(range = 3.0 miles·h^{-1} to 7.0 miles·h^{-1}) after Stage 1. Following the warm-up, treadmill grade was increased by 1.5% every minute (constant speed) until subjects were unable to continue despite verbal encouragement. Exercise heart rate (HR) was measured with an electronic monitoring system (Polar Inc.) and recorded after Stages 1 and 2 along with ratings of perceived exertion (RPE) ^{(7)}. A computerized metabolic cart (Model 2900, SensorMedics, Inc., Yorba Linda, CA) was used to quantify expired gas concentrations and ventilatory minute volumes, calculate oxygen uptake (˙VO_{2}) and respiratory exchange ratio (RER) values, and output these data to an on-line printer every 20 s. Calibration of the metabolic cart (i.e., gas analyzers and ventilation module) was performed immediately before each GXT using standard gas of known concentrations and a SensorMedics 3-L calibration syringe.

Maximal RPE (RPE_{max}), maximal heart rate (HR_{max}), maximal RER(RER_{max}), and ˙VO_{2max} were recorded for each GXT.˙VO_{2max} was computed by averaging the highest consecutive three˙VO_{2} values (a 1-min sample) generated immediately before termination of the GXT. ˙VO_{2} values were deemed maximal when two of the following three criteria were achieved ^{(19)}: (a) a leveling off of ˙VO_{2} despite an increase in power output, (b) an observed HR_{max} no more than 15 beats below predicted HR_{max} (220- age), and (c) a RER_{max} equal to or greater than 1.1. Subjects who failed to satisfy the maximal ˙VO_{2} criteria were dropped from the study (*N* = 6).

Multiple linear regression analyses were employed to generate N-EX˙VO_{2max} prediction models from (a) strictly questionnaire-based data and (b) a combination of measured and questionnaire-based data. The significance of additional explained variance (change in R^{2}) was used to identify which of the PFA questions, physical activity questions, and anthropometric data should be included in the multiple regression analyses. Dummy coding was used for the gender variable (0 = females and 1 = males). PRESS (predicted residual sum of squares) statistics^{(15)}, were computed to estimate the degree of shrinkage one could expect when the ˙VO_{2max} prediction equations are used across independent data sets. Statistical significance was set at *P*< 0.05.

The present sample was also employed to cross validate three N-EX regression equations developed in previous studies^{(2,14,18)}. Predictor variables employed for the Ainsworth et al. ^{(2)} N-EX equation included gender (0= male, female = 1), measured BMI, age, and self-reported frequency of strenuous exercise (≥15 min duration) over a typical 7-d period. Both N-EX regression models developed by Jackson et al. ^{(18)} and Heil et al. ^{(14)} employed gender (0 = female, 1 = male),% fat, age, and a self-report rating of physical activity as predictor variables. However, the CV analyses of the Jackson et al.^{(18)} and Heil et al. ^{(14)} models used the modified (10-point) physical activity question(Fig. 2) instead of the original (7-point) question. Paired *t*-tests, Pearson Product Moment correlation values (r) between observed and predicted ˙VO_{2max} values, SEE, and Error (E) values were used to cross validate these regression models^{(21)}. SEE and E estimates are identical when the sum of residual scores equal zero (i.e., Σ(Y-Y′) = 0). Differences between SEE and E values indicate the tendency for a given regression equation to systematically under or overpredict ˙VO_{2max}^{(10,18)}. The percentage of subjects whose residual scores were equal to or less than ± 4.5 ml·kg^{-1}·min^{-1} was also computed^{(30)}. This pre-specified range (± 4.5 ml·kg^{-1}·min^{-1}) has been employed in prior studies^{(10,12)} to represent a cutpoint that describes acceptable ˙VO_{2max} predictions.

## RESULTS

Descriptive data for the total (*N* = 100), female (*N* = 50), and male (*N* = 50) samples are presented inTable 2. Volunteers for this study were mostly Caucasian(88%) undergraduates, who reported a nonsmoking status (93%). The range of˙VO_{2max} values of the present sample are typical of college students (males: range = 29 to 61 ml·kg^{-1}·min^{-1}; females: range = 31 to 51 ml·kg^{-1}·min^{-1}). All subjects achieved at least two of three criteria for maximal exercise and also reported high RPE scores indicative of maximal work. For example, the average RER_{max} value for this study equaled 1.15 ± 0.05; the average HR_{max} equaled 191.1 ± 7.2 beats·min^{-1} which is within 6.6 beats of predicted maximum HR (220 - age); and the average RPE_{max} score equaled 19.5 ± 0.5 which corresponds to a“very, very hard” exercise intensity based on the Borg 6-to-20 point scale.

Evaluation of the change in R^{2} involving the PFA questions revealed that questions dealing with specific distances (i.e., 1 and 3 miles,Fig. 1) each accounted for a unique portion of explained variance in observed ˙VO_{2max} (*t*'s = 2.85 and 3.86,*P* < 0.001). Further, inclusion of the PFA question involving a timed duration (i.e., 30 min) did not explain additional variance in observed˙VO_{2max} (t = 0.57, *P* = 0.55) and therefore was excluded from the regression analyses. Because the PFA questions involving specific distances both explained a unique portion of observed ˙VO_{2max} variance, the PFA variable (Table 3) was computed by summing the response of each of these PFA questions (Fig. 1). The average sum of the PFA questions (Fig. 1) equaled 16.7 (range = 9 to 25) for males and 14.8 (range = 7 to 22) for females, which indicates, on average, that subjects perceived an ability to jog between a slow-to-medium pace for the prescribed distances.

The modified physical activity (PA-R) question of Jackson et al.^{(18)} (t = 3.72, *P* < 0.0001) was a better predictor of ˙VO_{2max} than the Ainsworth et al.^{(2)} (t = 0.54, *P* = 0.59) question and therefore it was used in the regression analyses. Based on responses to the modified PA-R question (Fig. 2) and Ainsworth et al.^{(2)} question, subjects participated in an average of 30 min to less than 60 min per week of vigorous physical activity over the previous 6 months, with a frequency of about three to four sessions of strenuous exercise (duration ≥ 15 min) during a typical 7-d period. Females reported a slightly higher level of habitual physical activity (PA-R = 5.5± 1.7) than did the males (PA-R = 4.9 ± 1.6).

Measured body mass, height, and BMI ranged from 44 kg to 116 kg, 1.5 m to 1.95 m, and 17 kg·m^{-2} to 37 kg·m^{-2}, respectively, whereas% fat averaged 18.9% with a% fat range from 3% to 37%. Significant paired differences were observed between self-reported and measured body weight (*P* < 0.001), body height (*P* < 0.001), and BMI(*P* < 0.001); however, these significant differences are primarily a result of the high correlation (r = 0.97 to 0.99) between the self-reported and measured data. Evaluation of the change in R^{2} involving full models(including gender, PFA, and PA-R) demonstrated comparable results for both self-reported and measured body weight (change in R^{2} = 0.122 to 0.136,*P* < 0.05) and BMI (change in R^{2} = 0.127 to 0.143,*P* < 0.05). The unique contribution of percent fat (change in R^{2} = 0.129, *P* < 0.05) was also similar.

The N-EX regression equation (Model 1, Table 3), derived strictly from self-report predictor variables (gender, BMI, PFA, PA-R), demonstrated predictive accuracy (R = 0.85, SEE = 3.44 ml·kg^{-1}·min^{-1}) similar to regression models (R = 0.85 to 0.86, SEE = 3.34 to 3.47 ml·kg^{-1}·min^{-1}) which included either self-reported body mass and/or measured anthropometric data. There were also no meaningful differences between male and female prediction models. Standardized β-weights self-report N-EX regression model (Model 1, Table 3) for gender, self-report BMI, PFA, and PA-R variables equaled 0.53, -0.45, 0.46, and 0.17, respectively. The magnitude of each β-weight's difference from zero can be loosely interpreted as an indication of a given variables impact on predicting˙VO_{2max}^{(14)}. Zero-order correlations between criterion ˙VO_{2max} and gender, self-reported BMI, PFA, and PA-R equaled 0.37, -0.29, 0.72, and 0.35, respectively. PRESS statistics (R_{P}= 0.84 and SEE_{P} = 3.6 ml·kg^{-1}·min^{-1}) for the questionnaire-based N-EX regression model demonstrated minimal shrinkage in predictive accuracy (Model 1, Table 3). Illustrated inFigures 3 and 4 are plots of individual data points for predicted versus observed ˙VO_{2max} values for the N-EX regression models (Table 3).

Cross-validation results of previously developed N-EX regression models are provided in Table 4. Presented are means and standard deviations of relative ˙VO_{2max} estimations, simple correlations (r) between observed and predicted ˙VO_{2max}, SEE, E, and the percent of measured ˙VO_{2max} values within ± 4.5 ml·kg^{-1}·min^{-1} of predicted VO_{2max}. The Heil et al. ^{(14)} N-EX model generated a mean˙VO_{2max} estimation not significantly different than observed˙VO_{2max}, whereas the estimated means for the Ainsworth et al.^{(2)} and Jackson et al. ^{(18)} regression models were significantly different from observed VO_{2max}. However, the Jackson et al. ^{(18)} and Heil et al.^{(14)} models demonstrated higher predictive accuracy than the Ainsworth et al. ^{(2)} model in terms of r values, SEE, E, and percent of measured ˙VO_{2max} values within ± 4.5 ml·kg^{-1}·min^{-1} of predicted V0_{2max}.

## DISCUSSION

The principal finding of this study is that the PFA data improved the ability of the N-EX regression models to accurately estimate˙VO_{2max} in a sample of physically active college students. The zero-order and squared partial correlation between PFA and observed˙VO_{2max} equaled 0.72 and 0.155, respectively (Model 1,Table 3). The standardized β-weight for PFA (0.46) was similar to the β-weights for gender (0.53) and self-reported BMI(-0.46). Inclusion of PFA in the N-EX regression equation (Model 1,Table 3) with gender, BMI, and PA-R, already in the model, improved the R and SEE from 0.75 and 4.31 ml·kg^{-1}·min^{-1}, respectively, to 0.85 and 3.44 ml·kg^{-1}·min^{-1}. In addition, when exercise-based data (treadmill jogging speed and corresponding steady-state exercise HR) from the present study were included in Model 1 (Table 3) instead of PFA data, the accuracy of prediction (R = 0.84, SEE = 3.62 ml·kg^{-1}·min^{-1}) did not improve. Thus, for these college students the PFA data (a self report of one's perceived ability to perform aerobic-type exercise) were as valuable in explaining observed˙VO_{2max} variance as were actual aerobic-type exercise data. Accordingly, it appears that the PFA data explain a portion of observed˙VO_{2max} variance not presently accounted for by typical non-exercise predictor variables such as gender, BMI, and self-reported physical activity.

A number of studies have documented the relationship between self-report physical activity and ˙VO_{2max}^{(2,13,14,17,25)}. The original PA-R (7-point scale) developed by Jackson et al. ^{(18)} demonstrated a zero-order correlation with observed ˙VO_{2max}(expressed in ml·kg^{-1}·min^{-1}) equal to 0.59 when applied to a heterogeneous sample of males and females (aged 18 to 70 yr). The present study, however, yielded a somewhat lower zero-order correlation with observed ˙VO_{2max} (r = 0.35, *P* < 0.0001), possibly because between-subject variability was less for this relatively healthy, physically active sample of college students. Based on mean PA-R values, females rated themselves slightly higher than males in performing habitual vigorous aerobic activity (Table 2); however, trends in previous research indicate that males normally rate themselves more physically active ^{(1)}.

Additional predictor variables important in ˙VO_{2max} estimation include age, gender, and body mass (or body composition). Various studies have shown age to be inversely related to ˙VO_{2max} with typical age-related decrements in ˙VO_{2max} averaging about 4 ml·kg^{-1}·min^{-1} per decade in adults as demonstrated by cross-sectional studies ^{(23,26)}. However, because this study involved a homogeneous sample of college students (aged 18-29 yr), age was not statistically significant in predicting˙VO_{2max} and consequently was dropped from the regression model(Table 3). Consistent with previous research^{(9,18,19)}, this study found gender statistically significant in predicting ˙VO_{2max} since males, on average, possessed a higher ˙VO_{2max} than females(Table 2). Various studies have also shown body mass, BMI, and/or body composition (% fat) to be meaningful predictor variables in˙VO_{2max} regression models^{(2,11,17)}. Interestingly, the present sample of college students were relatively accurate (on average) in self reporting their body mass and height. Therefore, no meaningful differences were found between regression models involving either self-reported or measured body mass or BMI. We elected to use self-reported BMI as the predictor variable (Model 1, Table 3) instead of self-reported body mass since self-reported BMI may be a more meaningful predictor variable in the educational and/or research setting.

The PRESS-related statistics provide a convenient cross-validation tool for regression models that employ relatively small data sets^{(15)}. An advantage of the PRESS technique is that the full data set can be used to build the regression model whereas in traditional data-splitting methods a given percentage of the data is usually partitioned into the validation (model building) and cross-validation groups. Thus, in the present study all participants (*N* = 100) were used to build the regression models (Table 3). An additional advantage of the PRESS technique is that specific cross-validation estimates of shrinkage are quantified. As such, use of the present regression model on similar, independent cross-validation samples should yield observed ˙VO_{2max} estimates that approximate the PRESS-statistics (R_{P} = 0.84 to 0.85, SEE_{P} = 3.5 to 3.6 ml·kg^{-1}·min^{-1}) presented in Table 3.

The present N-EX regression results (Tables 3) achieved higher predictive accuracy than the validation(Table 1) and cross-validation (Table 4) results of the Jackson et al. ^{(18)}, Heil et al.^{(14)}, and Ainsworth et al. ^{(2)} N-EX regression models. Only when the PFA variable was removed from the self-reported N-EX regression model (Table 3) was the accuracy (R = 0.75, SEE = 4.31 ml·kg^{-1}·min^{-1}) similar to the CV results of the better Jackson et al.^{(18)} (r = 0.71, SEE = 4.62 ml·kg^{-1}·min^{-1}) and Heil et al.^{(14)} (r = 0.74, SEE = 4.43 ml·kg^{-1}·min^{-1}) N-EX models. Our CV results of the Jackson et al. ^{(18)} N-EX model, however, do not concur with Kolkhorst and Dolgener ^{(20)} who found that the N-EX model developed by Jackson et al. ^{(18)} grossly underestimated observed ˙VO_{2max} in a sample of high fit college students. However, these differences between the present and previous research^{(18,20)} may be a result of sample characteristic differences and/or differences in response to the original versus modified PA-R question. Cross validation of the Ainsworth et al.^{(2)} N-EX model demonstrated relatively poor predictive accuracy (Table 5) as only 50% of subjects in the sample exhibited a residual score less than or equal to ± 4.5 ml·kg^{-1}·min^{-1}. The reason for this poor predictive accuracy appears to be related to the physical activity question which exhibited a low zero-order correlation (r = 0.05) between frequency of strenuous physical activity and observed ˙VO_{2max}. Thus, the modified PA-R question designed to categorize one's overall level of physical activity appears more accurate for college students than the Ainsworth et al.^{(2)} question designed to quantify the frequency of strenuous aerobic-type exercise.

Regression models involving submaximal or maximal exercise(Table 1) may be the preferred method for estimating˙VO_{2max} in certain circumstances (i.e., when developing aerobic-type exercise prescriptions or when monitoring improvement of CRF throughout an exercise program). However, the present self-report N-EX regression model (Model 1, Table 3) is unique in that˙VO_{2max} estimations can be computed entirely from questionnaire-based data. As such, this regression model may prove useful in large sample epidemiological studies when it is not feasible to measure the CRF of each subject and in large university wellness or physical education classes when traditional exercise tests are not practical to administer. Future work is now warranted to evaluate the specific utility and accuracy of self-report N-EX regression models in a variety of settings.

There are several potential limitations of the PFA and PA-R questions used in the present study. First, the predictive ability of the PFA questions depend on respondents being somewhat familiar with walking, jogging, or running exercise and knowing when a respective exercise intensity is considered “not too easy and not too hard.” Certain individuals who are unfamiliar with prolonged exercise and/or unfamiliar with how long it takes to cover the prescribed distance may be limited in their ability to estimate an accurate PFA score. In addition, individuals who dislike jogging or running may underestimate their PFA score not because they are unable to jog or run but because they would rather walk for exercise. Future research is needed to cross validate the accuracy of the PFA questions in a variety of samples. Second, weaknesses specific to the original PA-R question (7-point scale) have been previously discussed ^{(20)}. Although the present study did attempt to improve the PA-R question with a longer 6-month time reference and expanded 10-point scale, certain individuals may have a difficult time distinguishing between light, moderate, and vigorous physical activity which could limit response accuracy. Third, as with all self-report data, a given response to the PFA and PA-R questions may be influenced by a variety of social, cognitive, and psychological factors. A tendency to under or overestimate one's perceived functional ability and/or level of physical activity could be influenced by any combination of these three factors. It is also currently unknown whether the setting (i.e., laboratory versus field) influences the response accuracy of these self-report questions.

Finally, the present N-EX regression models (Table 3) should provide valid estimations of ˙VO_{2max} for physically active college students who possess typical CRF scores (˙VO_{2max} values from 29 ml·kg^{-1}·min^{-1} to 61 ml·kg^{-1}·min^{-1}). However, future cross validation of the present N-EX regression model is recommended prior to their use in sedentary college-aged individuals and/or older (≥30 yr) populations. In the event that the present N-EX regression equation is employed to estimate the ˙VO_{2max} in older (≥30 yr) individuals, an appropriate age-correction factor ^{(4)} should be used to account for the effect that age has on ˙VO_{2max}.

## CONCLUSION

This study found that N-EX regression models using gender, BMI, PA-R, and PFA data predict ˙VO_{2max} with accuracy comparable with the better EX regression models, but not the best EX regression models. The PFA questions were as useful in explaining observed ˙VO_{2max} variance as actual aerobic-type exercise data and helped the present N-EX regression models generate relatively accurate estimations of ˙VO_{2max} in a sample of relatively healthy, physically active college students. The modified PA-R question also appears acceptable for use in this type of college sample, as does self-report BMI data. Future research is warranted to establish the validity and reliability of the PFA and PA-R questions across a variety of samples. Although the N-EX regression models developed in this study appear to provide a valid and convenient method for predicting ˙VO_{2max} in physically active college students, further cross validation of the equation is recommended prior to use in other samples.

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