since the formation of the fick equation , physiologists have been trying to further enhance the knowledge base of heart rate , stroke volume , a - vo2 , and their relationship to vo2 .
when considering maximal cardiorespiratory values , maximal vo2 ( vo2max ) is reached when maximal heart rate ( hrmax ) , maximal a - vo2 ( a - vo2max ) , and maximal q ( qmax ) are reached ( 21 ) . since a plateau - effect of sv occurs at a level > 50% vo2max ( 30 ) , hr is what drives the value of q , given that maximal sv ( svmax ) remains constant .
age is the primary factor related to a decrease in vo2max ( 30 , 31 , 38 , 42 ) .
moreover , hrmax decreases with increasing age ( 33 , 34 , 38 , 42 ) .
however , we may not always be able to measure hrmax or vo2max values directly , and rely upon hrmax regression equations ( mhres ) to estimate our hrmax . since the early work of robinson on the effects of age on maximal heart rate ( hrmax ) ( 33 ) ,
researchers have fashioned numerous linear mhres based on age ( 7 , 10 , 11 , 16 , 23 , 27 , 29 , 32 ) . in 1971 , fox et al . published the 220-age mhre ( 13 , 32 ) yet no statistical analysis backed the equation . in 2002 , robergs et al . exposed the precise mhre from a line of best fit , from which 220-age was derived by fox et al .
( 13 ) : 215.4 - 0.9147  age ( 32 ) . today , it is a common practice of athletes and scientists alike to incorporate apocryphal mhres in a generic manner that lacks scientific merit such as 220-age and 226-age ( 4 , 32 , 40 ) .
another common problem is the failure to utilize mhres in accordance with the specifications from which they were derived .
for example , generalizability of 220-age is lacking as it has been shown to over or under predict based on age ( 15 , 39 , 41 ) , smoking ( 41 ) , bodyweight ( 26 , 41 ) , and conditions such as mental retardation ( 12 ) .
furthermore , empirical hrmax values may ( 19 ) or may not ( 10 , 15 , 39 ) vary between sexes , may ( 19 , 22 , 27 ) or may not ( 10 , 30 , 38 , 39 ) vary based on physical activity status , and may ( 24 ) or may not ( 39 ) vary based on testing protocol ( i.e. , treadmill stress test vs. cycle ergometer stress test ) , which may not always be taken into account when applying or creating mhres to predicted hrmax . in 2001 , tanaka et al . (
39 ) reported a neutral mhre with respect to sex , physical activity status , and testing protocol for which no differences could be seen : hrmax = 208 - 0.7  age .
other mhres published by londeree and moeschberger ( 24 ) ( hrmax = 206  0.7 age ) and gellish et al .
( 9 ) ( hrmax = 207  0.7  age ) resemble the mhre reported by tanaka ( 39 ) . furthermore , robergs and landwehr ( 32 ) , through regression analysis of 30 different mhres , reported the mhre of 208.754  0.734  age , which is also similar to that of tanaka et al .
therefore , the research supporting 208  0.7  age has been well established despite the many mhres that exist within the scientific community .
the current study focused on the ability of scientifically merited and unmerited mhres to predict hrmax based on sex and physical activity specifications .
the purpose of this study was twofold : 1 ) to determine the effects of sex and training status on measured hrmax and 2 ) to determine the accuracy of three commonly used mhres ( e.g. 220  age , 226  age , and 208  0.7  age ) to predict hrmax for females and males , aerobically active and sedentary .
we hypothesized that sex would have no effect on measured hrmax nor on comparisons made between measured and predicted values between each of the three commonly used mhres , i.e. hrmax = 220 - age , hrmax = 226 - age , and hrmax = 208  ( 0.7  age ) , when compared to their opposite sex counterparts .
furthermore , we also hypothesized that there would not be a significant training effect on measured and estimated hrmax .
all potential participants were screened for inclusion prior to testing . specifically , the screening included questions from part 4 of the international physical activity questionnaire ( ipaq ) : long last 7 days telephone format ( 8) as well as the physical activity readiness questionnaire ( par - q & you ) ( 1 ) .
inclusion criteria for the sedentary and active participants included the following : body mass index ( bmi ) between 18.524.9 ( kg  m ) , age of 1825 years , and demonstration of a sedentary lifestyle through ipaq or active running lifestyle .
exclusion criteria for any participants consisted of the following : answering  yes  to any of the questions on the par - q & you questionnaire , diabetes , cancer , and/or any other disease that may have prevented them from exercising to maximal intensity , an eating disorder , abnormal menstrual cycle , currently pregnant , and the use of any medications that affected cardiac , neurological , musculoskeletal , or cognitive function . a total of 52 participants ( 15 aerobically active males , 9 sedentary males , 15 aerobically active females , and 13 sedentary females ) between the ages of 18 and 25 years participated in the study .
week for <3 days  week and < 8000 steps  day over the course of one week ( 6 ) , for a minimum period of 6 months .
aerobically active included participants that were engaged in running > 30 min  day for 5 dayweek of moderate intensity , or > 20 min  day for 3 day  week of vigorous intensity ( 18 ) , for a minimum period of 6 months .
moderate and vigorous intensity guidelines were established through the american college of sports medicine ( acsm ) and defined as bouts of physical activity lasting longer than ten minutes .
those that fell between the two classifications were considered recreationally active and were not included in the study .
data were collected in the center for exercise and health fitness research at the university of pittsburgh . following the participant s arrival in the laboratory , experimental procedures
were explained and the subject signed an informed consent approved by the institutional review board of the university of pittsburgh .
all subjects abstained from alcohol consumption , caffeine , and vigorous exercise for 24 hours and from food intake 3 hours prior to testing .
the subjects were then fitted with a strap - on heart rate monitor ( polar electro .
, kenpele , finland ) and instructed to be seated for 5 minutes to establish resting hr ( hrrest ) .
the mouthpiece , attached to a rudolph model 2700 two - way non - rebreathing respiratory valve ( rudolph , model 2700 , kansas city , mo ) , was fitted comfortably within the subject s mouth to measure respiratory values through the parvo medics truemax 2400 respiratory metabolic analyzer ( truemax 2400 , parvo medics inc . ,
the subjects were then familiarized to the treadmill during a 5 minute warm - up period at a pace with which they were comfortable and did not allow their hr to be greater than 100 beats  min . during this time , they were also given proper instruction on how to prevent injury .
subjects performed a standard bruce maximal stress test ( 5 ) on a trackmaster motor driven treadmill ( fullvision inc . , model tmx425c , newton , ks ) .
the test was volitionally terminated by the subject due to exhaustion . beginning at the third stage until completion , all subjects were given verbal statements of encouragement every 2060 seconds ( 2 ) .
hrmax was defined as the highest hr value attained . during that period of time ,
vo2 and rer measured by the parvo medic s computer software approximately every 15 seconds was averaged to 30 second values .
the vo2max and rer values at the end of the test were recorded . to determine that the subjects achieved a maximal cardiorespiratory effort , the following was required : vo2 < 2.1 ml  kg  min between stages indicative of a plateau and rer  1.1 .
the authors realize such liberally set values to determine a plateau in vo2 and an rer may underestimate true maximal effects , but were deemed necessary for the sedentary group ( 20 ) .
data analysis was performed in three stages : 1 ) descriptive statistics , 2 ) effect of sex and aerobic training status on measured hrmax , and 3 ) effect of sex , aerobic training status , and prediction equation on the prediction equation accuracy . prior to performing the statistical analysis ,
an exploratory data analysis was conducted to determine whether the statistical assumptions were fulfilled for the planned anovas .
measures of central tendency , such as means , and measures of dispersion ( i.e. standard deviations and ranges ) were calculated for the measured heart rate and predicted heart rate variables .
to screen for marked departures from normality , histograms of the dependent variables were examined along with skewness and kurtosis values .
the statistical analyses were performed using spss 16.0 statistical software ( spss , inc . ,
first , a series of single factor anovas were performed to determine group differences between the following variables : age ( yrs ) , height ( m ) , mass ( kg ) , bmi ( kg  m ) , total leisure walking time ( min  week ) , total moderate running time ( min  week ) , total vigorous running time ( min  week ) , hrrest ( beats  min ) , hrmax ( beats  min ) , vo2max [ ( ml  kg )  min ] , and rer .
the four groups included active males , sedentary males , active females , and sedentary females .
secondly , a two factor anova ( sex  aerobic training status ) for measured hrmax was performed . for our third aim ,
a three factor ( sex  aerobic training status  prediction equation ) anova with repeated measures on the third factor was performed on the predicted hrmax data .
prediction equation had three levels ( 220 - age , 226 - age , 208 - 0.7  age ) .
the two dependent variables for this anova were signed residuals ( observed hrmax - predicted hrmax ) and unsigned residuals [ the absolute value of ( observed hrmax - predicted hrmax ) ] .
the residual for each participant would be divided by the standard error of prediction for each participant , yielding a signed or unsigned t - score , depending on whether the signed or unsigned residual was used .
the sex  aerobic training status interaction was included in the model , as was the effects of the prediction equation , prediction equation  sex , prediction equation  aerobic training status , and prediction equation  sex  aerobic training status .
if any interactions were significant , this indicated that the relative accuracy of the three prediction equations varied according to sex , aerobic training status , or the combination of sex and aerobic training status .
all potential participants were screened for inclusion prior to testing . specifically , the screening included questions from part 4 of the international physical activity questionnaire ( ipaq ) : long last 7 days telephone format ( 8) as well as the physical activity readiness questionnaire ( par - q & you ) ( 1 ) .
inclusion criteria for the sedentary and active participants included the following : body mass index ( bmi ) between 18.524.9 ( kg  m ) , age of 1825 years , and demonstration of a sedentary lifestyle through ipaq or active running lifestyle .
exclusion criteria for any participants consisted of the following : answering  yes  to any of the questions on the par - q & you questionnaire , diabetes , cancer , and/or any other disease that may have prevented them from exercising to maximal intensity , an eating disorder , abnormal menstrual cycle , currently pregnant , and the use of any medications that affected cardiac , neurological , musculoskeletal , or cognitive function . a total of 52 participants ( 15 aerobically active males , 9 sedentary males , 15 aerobically active females , and 13 sedentary females ) between the ages of 18 and 25 years participated in the study .
week for <3 days  week and < 8000 steps  day over the course of one week ( 6 ) , for a minimum period of 6 months .
aerobically active included participants that were engaged in running > 30 min  day for 5 dayweek of moderate intensity , or > 20 min  day for 3 day  week of vigorous intensity ( 18 ) , for a minimum period of 6 months .
moderate and vigorous intensity guidelines were established through the american college of sports medicine ( acsm ) and defined as bouts of physical activity lasting longer than ten minutes .
those that fell between the two classifications were considered recreationally active and were not included in the study .
data were collected in the center for exercise and health fitness research at the university of pittsburgh . following the participant s arrival in the laboratory , experimental procedures were explained and the subject signed an informed consent approved by the institutional review board of the university of pittsburgh .
all subjects abstained from alcohol consumption , caffeine , and vigorous exercise for 24 hours and from food intake 3 hours prior to testing .
the subjects were then fitted with a strap - on heart rate monitor ( polar electro . ,
kenpele , finland ) and instructed to be seated for 5 minutes to establish resting hr ( hrrest ) .
the mouthpiece , attached to a rudolph model 2700 two - way non - rebreathing respiratory valve ( rudolph , model 2700 , kansas city , mo ) , was fitted comfortably within the subject s mouth to measure respiratory values through the parvo medics truemax 2400 respiratory metabolic analyzer ( truemax 2400 , parvo medics inc . ,
the subjects were then familiarized to the treadmill during a 5 minute warm - up period at a pace with which they were comfortable and did not allow their hr to be greater than 100 beats  min . during this time , they were also given proper instruction on how to prevent injury .
subjects performed a standard bruce maximal stress test ( 5 ) on a trackmaster motor driven treadmill ( fullvision inc . , model tmx425c , newton , ks ) .
the test was volitionally terminated by the subject due to exhaustion . beginning at the third stage until completion , all subjects were given verbal statements of encouragement every 2060 seconds ( 2 ) .
hrmax was defined as the highest hr value attained . during that period of time , hr continued to be recorded until a decline was seen .
vo2 and rer measured by the parvo medic s computer software approximately every 15 seconds was averaged to 30 second values .
the vo2max and rer values at the end of the test were recorded . to determine that the subjects achieved a maximal cardiorespiratory effort , the following was required : vo2 < 2.1 ml  kg  min between stages indicative of a plateau and rer  1.1 .
the authors realize such liberally set values to determine a plateau in vo2 and an rer may underestimate true maximal effects , but were deemed necessary for the sedentary group ( 20 ) .
data analysis was performed in three stages : 1 ) descriptive statistics , 2 ) effect of sex and aerobic training status on measured hrmax , and 3 ) effect of sex , aerobic training status , and prediction equation on the prediction equation accuracy . prior to performing the statistical analysis ,
an exploratory data analysis was conducted to determine whether the statistical assumptions were fulfilled for the planned anovas .
measures of central tendency , such as means , and measures of dispersion ( i.e. standard deviations and ranges ) were calculated for the measured heart rate and predicted heart rate variables .
to screen for marked departures from normality , histograms of the dependent variables were examined along with skewness and kurtosis values .
the statistical analyses were performed using spss 16.0 statistical software ( spss , inc . ,
first , a series of single factor anovas were performed to determine group differences between the following variables : age ( yrs ) , height ( m ) , mass ( kg ) , bmi ( kg  m ) , total leisure walking time ( min  week ) , total moderate running time ( min  week ) , total vigorous running time ( min  week ) , hrrest ( beats  min ) , hrmax ( beats  min ) , vo2max [ ( ml  kg )  min ] , and rer .
the four groups included active males , sedentary males , active females , and sedentary females .
secondly , a two factor anova ( sex  aerobic training status ) for measured hrmax was performed . for our third aim , a three factor ( sex  aerobic training status  prediction equation ) anova with repeated measures on the third factor
prediction equation had three levels ( 220 - age , 226 - age , 208 - 0.7  age ) .
the two dependent variables for this anova were signed residuals ( observed hrmax - predicted hrmax ) and unsigned residuals [ the absolute value of ( observed hrmax - predicted hrmax ) ] . the residual for each participant
would be divided by the standard error of prediction for each participant , yielding a signed or unsigned t - score , depending on whether the signed or unsigned residual was used .
the sex  aerobic training status interaction was included in the model , as was the effects of the prediction equation , prediction equation  sex , prediction equation  aerobic training status , and prediction equation  sex  aerobic training status .
if any interactions were significant , this indicated that the relative accuracy of the three prediction equations varied according to sex , aerobic training status , or the combination of sex and aerobic training status . post hoc tests were done to follow significant interactions .
to better describe the active and sedentary groups , the amount of walking , moderate running , and vigorous running performed by each subject was assessed with one - way anova ( see table 2 ) .
examination of the distributions indicated that the assumption of normality was not met for the physical activity variables : total walking , moderate running , and vigorous running ( absolute value of skewness  1.5 ) .
the square root transformation was applied to the total walking variable and the transformed data were approximately normal .
one - way anova was applied to the transformed data which yielded significant results ( p = .002 ) ( see table 2 ) .
two nonparametric tests ( mann - whitney u test ) for each variable assessed the differences between active males and females due to the extreme departure from normality for the variables moderate and vigorous running .
the results were not significant in either the moderate ( p=.267 ) or vigorous activity levels ( p=.512 ) .
one - way anova showed no statistical differences in age between the groups ( see table 1 ) but did demonstrate significant differences between the following variables : total walking ( after square root transformation ) , vigorous running , hrrest , hrmax , vo2max , and rer ( table 2 ) . comparisons also revealed that active and sedentary males had a significantly higher vo2max than the females .
both active males and females demonstrated a larger vo2max than their sedentary counterparts signifying a difference between activity levels ( see table 2 ) .
two - way anova found significance for sex and activity but not the sex by activity interaction ( see tables 3 ) .
for the signed residuals , the males and sedentary participants for  sex and  activity level respectively demonstrated the least amount of variability with predictions when averaged over all three mhres ( see table 4 ) .
equation hrmax 
 = 208  ( 0.7  age ) ( equation 3 ) under predicted by 1.09 beats  min whereas the other two equations over predicted by a greater margin ( table 4 ) when averaging all subjects data thereby disregarding sex and activity level .
for  sex males had the least amount of total error when averaged across the three mhres . when averaging all subjects data and disregarding sex and activity level , equation 3 had the least total error ( table 4 ) .
however , once sex was taken into account ( see table 4   equation  sex interaction ) , equation 1 and 3 had the least total error for the males and females respectively . when activity level was taken into account
( see table 4   equation  activity level interaction ) , equation 3 was the most accurate for the active subjects .
interestingly , for the sedentary group , both equation 1 and 3 seemed to have the same amount of accuracy in predicting observed hrmax .
tukey post hoc tests indicated significance between equations 1 and 2 for males and between all pairs of equations for females .
likewise , a significant difference was found between equations 1 and 2 for sedentary and between all pairs of equations for active .
the specific aims of the study were to determine whether there was an effect of sex and/or training status with observed hrmax and if there was a significant difference between three popular mhres versus observed hrmax when sex and training status were taken into account .
for the first purpose of the study , activity level and sex affected hrmax independently from one another .
though the physiological responses of the heart were not directly measured in the current study , lower hrmax values were demonstrated in active participants suggesting a training effect in our sample
. however , such data are controversial as spina et al . demonstrated a decrease in hrmax as a direct result of training ( 37 ) , others noted lower hrmax values with active participants ( 22 , 25 ) , and some have shown no effect in hrmax between either active or sedentary participant ( 10 , 30 , 38 , 39 ) .
likewise , a significantly higher hrmax is seen in males , indicating a sex effect , which is also conflicting .
hermansen and andersen ( 19 ) , suggest sedentary females have highest hrmax , based on averages , not significance , while more studies claim no significance ( 10 , 15 , 39 ) .
lester et al . ( 22 ) utilized cross - sectional data to show an indirect relationship with age for both aerobically active and sedentary males having identical slopes but different intercepts .
such results demonstrate the sedentary to be at a greater disadvantage in regard to a greater blunted hrmax with increasing age in opposition to the aerobically active .
the results of the current study have been recorded while controlling for age . within our study ,
only speculation could account for the hrmax response that led to significance within the aerobically active subjects such as increased parasympathetic response ( 9 ) , reduced baroreflex sensitivity due to decreased baroreceptor density ( 36 ) , increase in left ventricular wall thickness ( 16 ) , increase in peak filling rates of blood into the heart ( 23 ) , increased stroke volume ( 28 ) , among other parameters not measured .
a decrease in hrmax as a result of training is inconsistent among athletes ( 9 ) and , therefore , such significance may be the result of randomly aerobically active subjects fitting such a profile .
literature may suggest a carry - over effect from hrrest to hrmax , thereby establishing cause for lower hrmax seen among physically active .
however , whaley et al . ( 41 ) implied a lower hrrest relating to a lower hrmax from three studies whose data never supports such a conclusion ( 3 , 17 , 35 ) . though hrrest may have been measured among such studies the resting values
were never reported among sedentary and active females ( 3 ) or active males ( 17 ) , nor emphasized , though measured , among healthy sedentary females ( 35 ) .
grimby and saltin ( 17 ) did note a stark contrast in hrmax ( 203 and 148 beats / min ) between two males of near similar vo2max ( l / min ) and blood volume ( l / min ) and corresponding submaximal hr values at the same workload ( 155 and 120 beats / min respectively )
. a training effect can not explain such results as all the males that took part in the study were considered to be aerobically active .
nevertheless the concept of a carry - over effect from hrrest to hrmax is a concept not to be ruled out even though not significantly validated in the present study .
the significance observed in the active vs. sedentary and male vs. female groups independently , does not remain significant when broken down into dependent groups ( i.e. active females , inactive females , active males and inactive males)(table 3 ) .
in other words , the lowest mean hrmax was demonstrated in the active female sample , but the hrrest was lowest in the active male sample .
therefore , a lower hrrest does not correspond to a lower hrmax in this study ( table 3 ) .
the second purpose of the study was to determine the accuracy of three commonly employed mhres to determine sex and/or training effects .
overall , the equation hrmax = 208 - ( 0.7  age ) ( equation 3 ) rendered the most accuracy utilizing these two separate measures for college - age participants .
when considering signed residuals a negative mean value specifies the ability of the equation , on average , to over predict , a positive value under predicts , and a value of zero represents perfect accuracy of the mhre to predict the observed .
therefore , when sex and activity level groups were combined under the  equation  effect , equation 3 produced the slightest amount of error representing the more accurate equation over the sample as a whole ( see table 4 ) .
a value of zero with the signed residuals indicates the same degree of over and under predictions .
because signed residuals do not measure the severity by which the over and under predicting of mhres occurs , the analysis of unsigned residuals is necessary .
therefore , the closer to zero , the more accurate the mhre . under the  equation  , 
equation  activity level  effects , equation 3 remains closest to zero . despite hrmax = 220  age ( equation 1 ) being lower under the  equation  sex 
( for males ) and  equation  activity level  ( for sedentary ) effects , the mean differences demonstrated between equation 1 and 3 is 1.02 and .08 beats  min respectively . it may be argued that small differences seen between the two equations are unlikely to make for significant differences . combining the effects
we would suspect that equation 1 is of better use for the sedentary males , but when examining the non - significant trends of 
equation  sex  activity level  effect , we see hrmax = 226  age ( equation 2 ) is associated with the least error which is highly inconsistent . yet , if we combined the  equation  sex  and  equation  activity level  active females , sedentary females , and active males the non - significant trends of  equation  sex  activity level 
follow through as equation 3 having the least error for signed and unsigned residuals alike ( see table 4 ) . in conclusion
, we may derive from the data that equation 3 is the better equation to use with the possible exception of sedentary males for college - age participants . in comparison to other studies ,
the foundation for equation 3 is strong ( 15 , 24 , 32 , 39 ) .
( 39 ) from which equation 3 was derived , demonstrated the equation to be unbiased toward sex and physical activity level with regard to meta - analysis and a laboratory - based portion . in a longitudinal study , gellish et al .
( 15 ) also concluded that sex was not significant factor in predicting hrmax while finding similar mhre to that of equation 3 . since both sexes and physical activity levels of the current investigation favor equation 3 , our data validate the results of other studies concluding that 220 - age and 226  age lacks scientific merit for general use with our sample .
the link between age and hrmax has been demonstrated ( 33 , 38 ) , and the small age range of the subjects in this study ( see table 1 ) allowed for greater emphasis to be placed on sex and training effects .
differences in treadmill protocol alone ( i.e. balke vs bruce ) may elicit differing mhres ( 14 ) , but would have no bearing on the current study as only one protocol was utilized .
we could not assess the effect of bmi on hrmax and the accuracy of the mhre .
the current study was also limited in the number of tests performed on each subject .
gellish and colleagues ( 15 ) excluded initial tests due to lower hrmax associated with a learning curve , but remains unknown as to how it has affected the current study . while it is understood that a young healthy cohort may not be conducive toward examining cardiorespiratory health , our research allows a greater emphasis to be placed on gender and activity level with regard to the use of certain mhres .
hopefully , such research would allow others to contemplate the use of proper mhres in any given setting .
future research may focus on experiments involving the impact of exercise protocol to predict hrmax for active and sedentary men and women .
the small sample size is also a limiting factor as it gives us smaller statistical power .
in addition , understanding the impact of a learning curve and how this may affect observational scores of hrmax when compared to predicted values is of great value .
finally , future research should incorporate higher standards in determining vo2max and rer and also utilize additional measurements such as ratings of perceived exertion , blood lactate , and/or estimated hrmax ( 20 , 39 ) . in conclusion , we found the males and sedentary groups to have higher observed maximal heart rates .
hrmax 
 = 208  ( 0.7  age ) equation overall had the most accuracy when measuring observed hrmax , with the possible exception of males and sedentary groups .
such findings validate the use of the equation in the healthy young college - aged population regardless of sex or training status .
 the purpose of the study was to determine if measured maximal heart rate ( hrmax ) was affected by sex or aerobic training status , and to determine the accuracy of three common clinical age - prediction maximal heart rate regression equations used to predict hrmax : hrmax 
 = 220  age , hrmax 
 = 226  age , and hrmax 
 = 208  ( 0.7  age ) . 
 fifty - two participants in total , 30 of which were in the active group ( 15 m , 15 f ) and 22 subjects in the sedentary group ( 9 m , 13 f ) , within the age range of 1825 years and with a normal bmi ( 18.524.9 kgm2 ) underwent a bruce maximal treadmill exercise protocol . 
 the effect of sex and training status on hrmax was analyzed through a two - way anova , and the effect of sex , aerobic training status , and regression equation on accuracy of the hrmax prediction was assessed with a three - way anova ( =0.05 ) . 
 overall , males had a higher hrmax than females ( 198.3 v. 190.4 beats  
 min1 , p<.001 ) and sedentary individuals had higher measured hrmax than active individuals ( 197.3 v. 191.4 beats  
 min1 , p=.002 ) . 
 furthermore , hrmax 
 = 208  ( 0.7  age)(equation 3 ) calculated the smallest signed and unsigned residuals from the difference between observed hrmax and predicted hrmax values for the significant main effects of equation ( 3 ) , equation  sex ( females  3 ) , and equation  activity level ( active  3 ) . 
 therefore , based on our results , we conclude that hrmax 
 = 208  ( 0.7  age ) has greater accuracy than the other two equations studied for predicting observed values of hrmax in 1825 year olds . 
INTRODUCTION
Methods
Participants
Protocol
Statistical Analysis
RESULTS
DISCUSSION