The purpose of this study was to discuss the procedures for establishing indices for physical senility from simple physical fitness tests through linear regression analysis. The fluctuation of residuals obtained from the various regression analyses and the statistical procedures for dealing with the variables when the assumptions concerning the residuals were contradicted, were discussed. In this study, 168 females (mean age 37.7, SD 11.3, range 20 to 65years) who were registered with one occupational insurance organization were examined. They each underwent tests to establish readings for seven variables, including five physical fitness tests: standing trunk flexion (FLEX), sit-ups in 30seconds (SIT-UP), vertical jump (VERT), repetitious side step in 20seconds (SIDE), and step test (STEP-ME). Two blood pressure readings while at rest were also taken (SBP, DBP). The results can be summarized as follows. In the forward stepwise regression analysis, the order of entered variables was VERT (R=0.637), SIT-UP (R=0.673), DBP (R=0.696), FLEX (R=0.704), and SIDE (R=0.717). The equation is y=61.38-0.569×(VERT)-0.513×(SITUP)+0.183×(DBP)+0.283×(FLEX)-0.328×(SIDE). Minimum AIC estimates (MAICE) were achieved for this equation. The correlation coefficient between residuals and predicted value was 0.345 (p<0.05). To satisfy the assumptions of the standard regression model, the researchers worked with transformed variables instead of working with original variables. The transformations of the raw data into logarithms and into reciprocals is described. According to the rules of variable elimination using ridge regression analysis, SBP and STEP-ME were eliminated from the set of seven variables. However, an examination of the residuals indicated that there were no advantages with using these transformations compared to the general linear model using raw data. The ratio of the predicted age for each client obtained from the predictive equation and chronological age is regarded as a marker of aging. Therefore, it is necessary for researchers to examine what kind of life styles result in such individual differences.
Upper case are ; Age, NOS ; Physical Fitness ; predictive ; Diastolic blood pressure

The measurements of body composition of standing body height (HT), body weight (WT), percent body fat (FAT), lean body mass (LBM), and bone stiffness (BONE) by an ultrasound apparatus were performed in 38 male subjects (age range: 19-74 yr) who live in a hilly region. Analysis of variance (ANOVA) and analysis of covariance (ANCOVA) were applied to these anthropometric measurements with the degree of being engaged in agricultural work set as a factor and age of years as a covariate. When each mean value of variables measured in this study were compared to the standard values of the Japanese, the subjects were shorter and lesser in body fat. The correlation coefficients between age and anthropometric measurements of HT, WT, BONE, and LBM except FAT were. The relation between age and BONE showed the upside-down of V letter with the peak at 40 years of age. ANOVA resulted in that the effect of the degree of being engaged in agricultural work was not significant in any anthropometric variable except HT. As a result of ANCOVA, the effect of the degree of being engaged in agricultural work of any variable was not significant except HT. However, the probability of F-value of each variable in ANCOVA became higher than the probability in ANOVA. The significance of F values of ANOVA of BONE, LBM, and WT were lowered after ANOCOVA was applied. The reason is probably then the substantiality of body composition was not enough in the younger generation.

Forty-two anthropometric measurements were evaluated to determine total body water and percent fat of 71 adult males under 19-77 years of age. Deuterium oxid (D₂O) dilution method was used to determine total body water. A step-wise multiple regression analysis of the data indicated that total body water and percent fat could be predicted from body surface area. Twenty-seven additional boys were tested to increase the sample size. Using the data from these 98 subjects, a step-wise multiple regression analysis gave an equation which yielded a multiple R=0.963 between the predicted total body water and the actual total body water as determined by D₂O dilution method. The standard error of estimate was 1.92 water units and 4.55 percent fat units, respectively. These results indicate that the equation obtained provide an accurate method of body composition estimation when used on a population of Japanese men.

In this paper, a predictive equation for TBW (Total Body Water) from various anthropometric measurements was established. Fifty-seven healthy adult males, aged 19 to 54 years old, volunteered as subjects in this experiment.
Ten anthropometric measurements were taken for each subject such as standing height (HT), body weight (WT), breadth of humerus and femurs (B1, B2), girth of upper arm and calf (G1, G2), and skinfold thickness of triceps, subscaplar, suprailliac and abdomen (S1, S2, S3, S4) along with the amount of ingested deutrium oxide (D₂O) .
Total body water was quantitied by the analysis of dilution of orally ingested D₂O in urine. The method of forward stepwise regression analysis was adopted to establish the predictive equation. The stopping rule to select the variables was F statistics (F=2.0) . Furthermore, some criteria such as AIC (Akaike's an information criterion), Mallows' Cp, Schwarz's criterion, R* (adjusted for degree of freedom R) were derived as the regression equation was constructed at each step. These criteria contributed to selecting the best and most valid equation of all equations possible. The results obatained was summarized as follows.
1) Firstly, descriptive statistics were derived for all subjects. Mean (±S. D, ) of TBW was 34.85 (±5.38) l. Skewness and kurtosis were not significant. Multico-linearlity was suggested by correlation matrix (10×10) of all independent variables.
2) Six variables were entered into the equation such as sequences WT, S4, HT, G2, S1, B1. The multiple correlation coefficient (R) and standard error of estimates (SEE) of this equation were 0.961 and 1.568, respectively. It was derived as follows:
Y=-34.56+0.170×HT+0.231×WT+0.567×G2+1.37×B1-0.167×S1-0.086×S4
3) Since the analysis of residuals suggested that abnormal values were contained in this sample, the next regression analysis was adopted after deleted the results of 7 subjects whose standardized residuals were over 1.5. Consequently, the regression equation composited from WT, S4, S2, HT, S1 was evaluated as the best equation according to Cp and Schwarz criterion. AIC selected the equation which added S3 as the 6 th variables. The multiple regression equation established at this stage was described as follows, and R and SEE were 0.9857, 0.940, respectively.
Y=8.10+0.4573×WT-0.0839×S4-0.0951×S2+0.1089×HT-0.1368×S1
4) The specific problem was not obtained from statistics of residuals. However, the co-ordinates of eis (standardized residuals) and predicted value suggested a specific changing pattern. The low possibility of existing multico-linearlity was determined from the eigen value of correlation matrix between independent variables.

A comparative study was conducted between two independent methods to estimate body fat in a total population of 27 Japanese females (aged 20-40) . The two methods dealt with different body component parameters. Body fat was estimated (1) in terms of skinfolds according to the formula of Nagamine and Suzuki ('64), who used triceps and subscapular skinfolds, and (2) in terms of total body water based on the analysis of the dilution of orally ingested deuterium oxide (D₂O) in urine. The estimate of the percent body fat by each of the two methods showed significant difference. The skinfold estimate of percent body fat was significantly lower than the D₂O estimate. The best combination of four variables for predicting total body water was found to be humerus breadth, femur breadth, abdomen skinfold and body weight. The prediction equation based on humerus breadth, femur breadth, abdomen skinfold and body weight proved to be accurate for estimating total body water (R =.903 ; SEE=1.276) than the combination of skinfolds (r=.706) . Multiple regression equation was applied to the estimation of the total body water from these anthropometric measurements. Thus, the equation based on humerus breadth, femur breadth, abdomen skinfold and body weight could be instead of skinfolds to accurately estimate the criterion percent body fat.

In this paper, it was aimed to establish a multiple regression equation to predict total body water (TBW) from several anthropometric measurement.
Total body water was determined by the analysis of the dilution of orally ingested deuterium oxide (D₂O) in urine of 27 Japanese females in 20-39 yrs. old, who vol-unteerly participated in this experiment.
The anthropometric measurements were taken for each subject on standing height, body weight and a total of 8 body sites, including 4 skinfold thickness, 2 diameters, and 2 circumferences of limbs on the same day.
The method of forward stepwise regression analysis was adopted to establish the regression equation. The rule of stopping to select the variables was F-statistics (F enter=1.8, F remove=1.7) .
The results obtained were as follows.
1) The mean value of TBW was 25.3 (l), which was less than the value of the American adolescent males reported by Schutte (1980) .
2) Entered variables in this equation were body weight (WT), femur breadth (B1), humerus breadth (B2), abdomen skinfold thickness (S4) and the other variables contributed little.
3) The regression equation obtained were as follows. y=8.70+0.189xWT+1.79xB2-0.092xS4+1.84xB1
4) The multiple correlation coefficient and standard error of estimates of this regression equation were 0.908, 1.271 (l), respectively.
5) An analysis of residuals by means of plotting of standardized residuals and predicted value showed that the defficiency of this equation was little recognized.
We must pay most effort to establish the predictve equation on the samples which have been selected from populations defined on the basis of factors such as age, sex, or race alone or in combination.