library(readxl)
library(dplyr)
## Warning: package 'dplyr' was built under R version 4.3.3
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
portfolio<- read_excel("~/ANU/SEM 4/investment/25_portfolio.xls")
## New names:
## • `` -> `...2`
## • `` -> `...3`
## • `` -> `...4`
## • `` -> `...5`
## • `` -> `...6`
## • `` -> `...7`
## • `` -> `...8`
## • `` -> `...9`
## • `` -> `...10`
## • `` -> `...11`
## • `` -> `...12`
## • `` -> `...13`
## • `` -> `...14`
## • `` -> `...15`
## • `` -> `...16`
## • `` -> `...17`
## • `` -> `...18`
## • `` -> `...19`
## • `` -> `...20`
## • `` -> `...21`
## • `` -> `...22`
## • `` -> `...23`
## • `` -> `...24`
## • `` -> `...25`
## • `` -> `...26`
factors<- read_excel("~/ANU/SEM 4/investment/F-F_Research_Data_Factors.xls")
## New names:
## • `` -> `...2`
## • `` -> `...3`
## • `` -> `...4`
## • `` -> `...5`
portfolio[15, 1] <- "year"
factors[3,1]<-"year"


######################clean data##########
# Drop first 14 rows
port <- portfolio[-c(1:14), ]
# Make row 15 (now first row) the header
colnames(port) <- as.character(unlist(port[1, ]))
port<-port[-1, ] 
#select data
# find first blank row (all NA or "")
blank_row <- which(apply(port, 1, function(x) all(x == "" | is.na(x))))[1]
# keep only rows before it
if (!is.na(blank_row)) {port <- port[1:(blank_row-1), ]}



#Drop first 2 rows 
fact<-factors[-c(1:2), ]
colnames(fact) <- as.character(unlist(fact[1, ]))
fact<-fact[-1, ] 
blank<- which(apply(fact, 1, function(x) all(x == "" | is.na(x))))[1]
# keep only rows before it
if (!is.na(blank)) {fact <- fact[1:(blank-1), ]}


#########select data############
subfact <-fact[,2:5]
combine<-cbind(port,subfact)
complete<-combine%>%filter(year>=199201 & year <=202506)


############Table 2 replicate###################################


adj <- sweep(
  as.data.frame(lapply(complete[ , 2:26], as.numeric)),
  1,
  as.numeric(complete[ , 30]),
  FUN = "-"
)
#mean
colMeans(adj, na.rm = TRUE)
## SMALL.LoBM    ME1.BM2    ME1.BM3    ME1.BM4 SMALL.HiBM    ME2.BM1    ME2.BM2 
##  0.2762970  0.8075734  0.7677405  0.9833308  1.1666520  0.6303139  0.8734393 
##    ME2.BM3    ME2.BM4    ME2.BM5    ME3.BM1    ME3.BM2    ME3.BM3    ME3.BM4 
##  0.8451308  0.8585639  0.9616117  0.6031876  0.8833527  0.7979669  0.8708169 
##    ME3.BM5    ME4.BM1    ME4.BM2    ME4.BM3    ME4.BM4    ME4.BM5   BIG.LoBM 
##  1.0180336  0.7982791  0.8790567  0.7997632  0.9109445  0.8238831  0.8084769 
##    ME5.BM2    ME5.BM3    ME5.BM4   BIG.HiBM 
##  0.7694627  0.7524279  0.5815040  0.8501908
#sd
apply(complete[,2:26], 2, sd, na.rm = TRUE)
## SMALL LoBM    ME1 BM2    ME1 BM3    ME1 BM4 SMALL HiBM    ME2 BM1    ME2 BM2 
##   8.165852   7.083297   5.930591   5.803457   6.292542   7.098609   5.930417 
##    ME2 BM3    ME2 BM4    ME2 BM5    ME3 BM1    ME3 BM2    ME3 BM3    ME3 BM4 
##   5.442208   5.441779   6.436519   6.449446   5.345432   5.013847   5.354154 
##    ME3 BM5    ME4 BM1    ME4 BM2    ME4 BM3    ME4 BM4    ME4 BM5   BIG LoBM 
##   6.120697   5.738091   4.927487   4.935165   5.170598   5.999898   4.511396 
##    ME5 BM2    ME5 BM3    ME5 BM4   BIG HiBM 
##   4.157779   4.320259   5.110153   6.256736
#tstat
apply(complete[ , 2:26], 2, function(x) {
  x <- as.numeric(x)           # force numeric
  m <- mean(x, na.rm = TRUE)
  s <- sd(x, na.rm = TRUE)
  n <- sum(!is.na(x))
  m / (s / sqrt(n))
})
## SMALL LoBM    ME1 BM2    ME1 BM3    ME1 BM4 SMALL HiBM    ME2 BM1    ME2 BM2 
##   1.175701   2.859213   3.280282   4.096969   4.362650   2.352378   3.637731 
##    ME2 BM3    ME2 BM4    ME2 BM5    ME3 BM1    ME3 BM2    ME3 BM3    ME3 BM4 
##   3.859772   3.909569   3.626357   2.504825   4.073016   4.000929   4.019437 
##    ME3 BM5    ME4 BM1    ME4 BM2    ME4 BM3    ME4 BM4    ME4 BM5   BIG LoBM 
##   3.998298   3.497035   4.401005   4.072014   4.317729   3.430003   4.493237 
##    ME5 BM2    ME5 BM3    ME5 BM4   BIG HiBM 
##   4.687247   4.431908   3.076225   3.373505
############Table 4 Replicate############### dependent ~ independent

# Coerce columns to numeric
# predictors
x <- as.numeric(complete[, 27])

# independent matrix
Y <- as.matrix(as.data.frame(lapply(complete[, 2:26], as.numeric)) -
               as.numeric(complete[, 30]))

# run multivariate regression
model4 <- lm(Y ~ x)
summary(model4)  
## Response SMALL.LoBM :
## 
## Call:
## lm(formula = SMALL.LoBM ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -20.802  -2.834  -0.543   2.483  33.245 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.76778    0.27018  -2.842  0.00472 ** 
## x            1.41543    0.06098  23.211  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.342 on 400 degrees of freedom
## Multiple R-squared:  0.5739, Adjusted R-squared:  0.5728 
## F-statistic: 538.8 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME1.BM2 :
## 
## Call:
## lm(formula = ME1.BM2 ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -25.905  -2.643  -0.215   2.019  40.201 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.08205    0.23974  -0.342    0.732    
## x            1.20604    0.05411  22.289   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.74 on 400 degrees of freedom
## Multiple R-squared:  0.554,  Adjusted R-squared:  0.5528 
## F-statistic: 496.8 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME1.BM3 :
## 
## Call:
## lm(formula = ME1.BM3 ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.9844  -2.3981  -0.3016   2.1743  17.3625 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.02837    0.18220  -0.156    0.876    
## x            1.07928    0.04112  26.246   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.602 on 400 degrees of freedom
## Multiple R-squared:  0.6326, Adjusted R-squared:  0.6317 
## F-statistic: 688.8 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME1.BM4 :
## 
## Call:
## lm(formula = ME1.BM4 ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.4485  -2.1914  -0.3365   2.0977  22.9058 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.23599    0.19003   1.242    0.215    
## x            1.01315    0.04289  23.622   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.757 on 400 degrees of freedom
## Multiple R-squared:  0.5825, Adjusted R-squared:  0.5814 
## F-statistic:   558 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response SMALL.HiBM :
## 
## Call:
## lm(formula = SMALL.HiBM ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -14.300  -2.393  -0.273   2.076  40.885 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.39913    0.22072   1.808   0.0713 .  
## x            1.04051    0.04982  20.886   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.364 on 400 degrees of freedom
## Multiple R-squared:  0.5217, Adjusted R-squared:  0.5205 
## F-statistic: 436.2 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME2.BM1 :
## 
## Call:
## lm(formula = ME2.BM1 ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -20.7696  -2.3169  -0.0717   2.3550  27.3126 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.35316    0.20579  -1.716   0.0869 .  
## x            1.33327    0.04645  28.705   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.068 on 400 degrees of freedom
## Multiple R-squared:  0.6732, Adjusted R-squared:  0.6724 
## F-statistic:   824 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME2.BM2 :
## 
## Call:
## lm(formula = ME2.BM2 ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.7064  -1.9485  -0.0707   1.9142  16.0761 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.02955    0.16174   0.183    0.855    
## x            1.14404    0.03650  31.340   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.198 on 400 degrees of freedom
## Multiple R-squared:  0.7106, Adjusted R-squared:  0.7099 
## F-statistic: 982.2 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME2.BM3 :
## 
## Call:
## lm(formula = ME2.BM3 ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.2390 -1.8956 -0.1228  1.6213 10.0483 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.06804    0.14733   0.462    0.644    
## x            1.05348    0.03325  31.682   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.913 on 400 degrees of freedom
## Multiple R-squared:  0.715,  Adjusted R-squared:  0.7143 
## F-statistic:  1004 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME2.BM4 :
## 
## Call:
## lm(formula = ME2.BM4 ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.1867  -1.8537  -0.0924   1.7348  10.8294 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.10753    0.15875   0.677    0.499    
## x            1.01816    0.03583  28.417   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.138 on 400 degrees of freedom
## Multiple R-squared:  0.6687, Adjusted R-squared:  0.6679 
## F-statistic: 807.5 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME2.BM5 :
## 
## Call:
## lm(formula = ME2.BM5 ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -16.5417  -2.1382   0.0075   2.0200  13.1147 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.09822    0.19802   0.496     0.62    
## x            1.17048    0.04469  26.189   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.915 on 400 degrees of freedom
## Multiple R-squared:  0.6316, Adjusted R-squared:  0.6307 
## F-statistic: 685.8 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME3.BM1 :
## 
## Call:
## lm(formula = ME3.BM1 ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -19.5157  -1.7859   0.1243   1.7885  19.3892 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.33085    0.16812  -1.968   0.0498 *  
## x            1.26625    0.03795  33.370   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.324 on 400 degrees of freedom
## Multiple R-squared:  0.7357, Adjusted R-squared:  0.7351 
## F-statistic:  1114 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME3.BM2 :
## 
## Call:
## lm(formula = ME3.BM2 ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.9762 -1.4919 -0.0783  1.4157 12.2804 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.07979    0.12348   0.646    0.519    
## x            1.08938    0.02787  39.089   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.441 on 400 degrees of freedom
## Multiple R-squared:  0.7925, Adjusted R-squared:  0.792 
## F-statistic:  1528 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME3.BM3 :
## 
## Call:
## lm(formula = ME3.BM3 ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.9768 -1.4878 -0.0409  1.3774  8.6714 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.05868    0.12363   0.475    0.635    
## x            1.00224    0.02790  35.917   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.444 on 400 degrees of freedom
## Multiple R-squared:  0.7633, Adjusted R-squared:  0.7627 
## F-statistic:  1290 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME3.BM4 :
## 
## Call:
## lm(formula = ME3.BM4 ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.0233  -1.8183   0.0468   1.5527  11.5176 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.11196    0.14747   0.759    0.448    
## x            1.02877    0.03328  30.909   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.915 on 400 degrees of freedom
## Multiple R-squared:  0.7049, Adjusted R-squared:  0.7041 
## F-statistic: 955.4 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME3.BM5 :
## 
## Call:
## lm(formula = ME3.BM5 ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -16.7185  -2.0170  -0.0857   1.6876  12.6798 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.20168    0.18993   1.062    0.289    
## x            1.10672    0.04287  25.817   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.755 on 400 degrees of freedom
## Multiple R-squared:  0.6249, Adjusted R-squared:  0.624 
## F-statistic: 666.5 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME4.BM1 :
## 
## Call:
## lm(formula = ME4.BM1 ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.5114 -1.3324  0.0719  1.2504 22.5587 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.06946    0.12938  -0.537    0.592    
## x            1.17638    0.02920  40.284   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.558 on 400 degrees of freedom
## Multiple R-squared:  0.8023, Adjusted R-squared:  0.8018 
## F-statistic:  1623 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME4.BM2 :
## 
## Call:
## lm(formula = ME4.BM2 ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.5929 -1.0369 -0.0779  1.0964  8.4035 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.11527    0.09873   1.168    0.244    
## x            1.03545    0.02228  46.465   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.952 on 400 degrees of freedom
## Multiple R-squared:  0.8437, Adjusted R-squared:  0.8433 
## F-statistic:  2159 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME4.BM3 :
## 
## Call:
## lm(formula = ME4.BM3 ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.9438 -1.2769 -0.1226  1.2486 10.7868 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.07112    0.12126   0.587    0.558    
## x            0.98781    0.02737  36.094   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.397 on 400 degrees of freedom
## Multiple R-squared:  0.7651, Adjusted R-squared:  0.7645 
## F-statistic:  1303 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME4.BM4 :
## 
## Call:
## lm(formula = ME4.BM4 ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.8087  -1.4887  -0.0576   1.2992  11.5331 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.16296    0.13475   1.209    0.227    
## x            1.01403    0.03041  33.342   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.664 on 400 degrees of freedom
## Multiple R-squared:  0.7354, Adjusted R-squared:  0.7347 
## F-statistic:  1112 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME4.BM5 :
## 
## Call:
## lm(formula = ME4.BM5 ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.0145  -1.9391  -0.2727   1.9716  12.6705 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.01618    0.18322   0.088     0.93    
## x            1.09499    0.04135  26.480   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.622 on 400 degrees of freedom
## Multiple R-squared:  0.6367, Adjusted R-squared:  0.6358 
## F-statistic: 701.2 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response BIG.LoBM :
## 
## Call:
## lm(formula = BIG.LoBM ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.9022 -1.0598 -0.0036  0.9064  5.2647 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.09203    0.07686   1.197    0.232    
## x            0.97127    0.01735  55.988   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.52 on 400 degrees of freedom
## Multiple R-squared:  0.8868, Adjusted R-squared:  0.8866 
## F-statistic:  3135 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME5.BM2 :
## 
## Call:
## lm(formula = ME5.BM2 ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.2148 -0.8782 -0.0398  0.8027  7.0221 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.12685    0.08398   1.511    0.132    
## x            0.87117    0.01895  45.963   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.66 on 400 degrees of freedom
## Multiple R-squared:  0.8408, Adjusted R-squared:  0.8404 
## F-statistic:  2113 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME5.BM3 :
## 
## Call:
## lm(formula = ME5.BM3 ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.8714  -1.0161   0.0621   1.1178   8.0836 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.12170    0.10939   1.113    0.267    
## x            0.85507    0.02469  34.633   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.163 on 400 degrees of freedom
## Multiple R-squared:  0.7499, Adjusted R-squared:  0.7493 
## F-statistic:  1199 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response ME5.BM4 :
## 
## Call:
## lm(formula = ME5.BM4 ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.4342  -1.3502  -0.0449   1.3892  14.0406 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.11579    0.15150  -0.764    0.445    
## x            0.94530    0.03419  27.646   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.995 on 400 degrees of freedom
## Multiple R-squared:  0.6564, Adjusted R-squared:  0.6556 
## F-statistic: 764.3 on 1 and 400 DF,  p-value: < 2.2e-16
## 
## 
## Response BIG.HiBM :
## 
## Call:
## lm(formula = BIG.HiBM ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -17.6224  -2.1577  -0.2132   2.0856  14.2850 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.03990    0.20251   0.197    0.844    
## x            1.09849    0.04571  24.034   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.004 on 400 degrees of freedom
## Multiple R-squared:  0.5908, Adjusted R-squared:  0.5898 
## F-statistic: 577.6 on 1 and 400 DF,  p-value: < 2.2e-16
############Table 5 Replicate###############

# Dependent matrix (25 cols) for t5,6,10
Y <- as.matrix(as.data.frame(lapply(complete[, 2:26], as.numeric)) -
               as.numeric(complete[, 30]))

# Predictors
X <- data.frame(
  x1 = as.numeric(complete[, 28]),
  x2 = as.numeric(complete[, 29])
)

model5 <- lm(Y ~ x1 + x2, data = X)
summary(model5)     
## Response SMALL.LoBM :
## 
## Call:
## lm(formula = SMALL.LoBM ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -20.9320  -3.1329   0.3738   3.3318  19.2623 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.26245    0.28279   0.928    0.354    
## x1           1.76475    0.09077  19.442  < 2e-16 ***
## x2          -0.35247    0.08715  -4.044  6.3e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.658 on 399 degrees of freedom
## Multiple R-squared:  0.5232, Adjusted R-squared:  0.5208 
## F-statistic: 218.9 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response ME1.BM2 :
## 
## Call:
## lm(formula = ME1.BM2 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -16.4293  -2.7564   0.1913   3.1718  13.5227 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.74738    0.23351   3.201  0.00148 ** 
## x1           1.66596    0.07495  22.227  < 2e-16 ***
## x2          -0.09487    0.07197  -1.318  0.18820    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.672 on 399 degrees of freedom
## Multiple R-squared:  0.5677, Adjusted R-squared:  0.5656 
## F-statistic:   262 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response ME1.BM3 :
## 
## Call:
## lm(formula = ME1.BM3 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -17.0741  -2.3355   0.2722   2.6287  12.5819 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.65960    0.20987   3.143 0.001798 ** 
## x1           1.35110    0.06736  20.057  < 2e-16 ***
## x2           0.22253    0.06468   3.441 0.000642 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.199 on 399 degrees of freedom
## Multiple R-squared:  0.5021, Adjusted R-squared:  0.4996 
## F-statistic: 201.2 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response ME1.BM4 :
## 
## Call:
## lm(formula = ME1.BM4 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -14.8767  -2.1966   0.3407   2.4147  11.0225 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.83008    0.19681   4.218 3.06e-05 ***
## x1           1.35577    0.06317  21.462  < 2e-16 ***
## x2           0.44911    0.06065   7.404 7.89e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.938 on 399 degrees of freedom
## Multiple R-squared:  0.5425, Adjusted R-squared:  0.5402 
## F-statistic: 236.6 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response SMALL.HiBM :
## 
## Call:
## lm(formula = SMALL.HiBM ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.4223  -2.5267   0.2544   2.6441  28.5251 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.97230    0.22566   4.309 2.07e-05 ***
## x1           1.34315    0.07243  18.544  < 2e-16 ***
## x2           0.65956    0.06954   9.484  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.515 on 399 degrees of freedom
## Multiple R-squared:  0.4893, Adjusted R-squared:  0.4867 
## F-statistic: 191.1 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response ME2.BM1 :
## 
## Call:
## lm(formula = ME2.BM1 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -20.9848  -2.7200   0.1944   3.1266  14.5829 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.63539    0.25579   2.484   0.0134 *  
## x1           1.44451    0.08210  17.594  < 2e-16 ***
## x2          -0.37134    0.07883  -4.711 3.42e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.118 on 399 degrees of freedom
## Multiple R-squared:  0.4842, Adjusted R-squared:  0.4816 
## F-statistic: 187.3 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response ME2.BM2 :
## 
## Call:
## lm(formula = ME2.BM2 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -21.2882  -2.6215   0.2921   2.8533  13.6342 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.80167    0.22372   3.583 0.000381 ***
## x1           1.24621    0.07181  17.354  < 2e-16 ***
## x2           0.06402    0.06895   0.929 0.353682    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.476 on 399 degrees of freedom
## Multiple R-squared:  0.4344, Adjusted R-squared:  0.4315 
## F-statistic: 153.2 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response ME2.BM3 :
## 
## Call:
## lm(formula = ME2.BM3 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -16.0418  -2.3676   0.2773   2.6059  14.2628 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.72664    0.21954   3.310  0.00102 ** 
## x1           1.02490    0.07047  14.544  < 2e-16 ***
## x2           0.35281    0.06766   5.214 2.97e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.392 on 399 degrees of freedom
## Multiple R-squared:  0.3536, Adjusted R-squared:  0.3504 
## F-statistic: 109.1 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response ME2.BM4 :
## 
## Call:
## lm(formula = ME2.BM4 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -15.8116  -2.1804   0.3822   2.5919  12.2548 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.70068    0.20837   3.363 0.000846 ***
## x1           1.06552    0.06688  15.931  < 2e-16 ***
## x2           0.54193    0.06422   8.439 5.97e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.169 on 399 degrees of freedom
## Multiple R-squared:  0.417,  Adjusted R-squared:  0.4141 
## F-statistic: 142.7 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response ME2.BM5 :
## 
## Call:
## lm(formula = ME2.BM5 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.7253  -2.6591   0.3494   2.8465  23.0614 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.74917    0.23819   3.145  0.00178 ** 
## x1           1.27234    0.07645  16.642  < 2e-16 ***
## x2           0.76782    0.07341  10.460  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.765 on 399 degrees of freedom
## Multiple R-squared:  0.4555, Adjusted R-squared:  0.4528 
## F-statistic: 166.9 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response ME3.BM1 :
## 
## Call:
## lm(formula = ME3.BM1 ~ x1 + x2, data = X)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -22.128  -2.809   0.212   3.182  14.368 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.63340    0.24954   2.538   0.0115 *  
## x1           1.14189    0.08010  14.256  < 2e-16 ***
## x2          -0.42576    0.07691  -5.536 5.61e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.993 on 399 degrees of freedom
## Multiple R-squared:  0.4053, Adjusted R-squared:  0.4023 
## F-statistic: 135.9 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response ME3.BM2 :
## 
## Call:
## lm(formula = ME3.BM2 ~ x1 + x2, data = X)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -18.399  -2.623   0.271   2.800  12.551 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.81855    0.22889   3.576 0.000392 ***
## x1           0.89516    0.07347  12.184  < 2e-16 ***
## x2           0.11289    0.07054   1.600 0.110315    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.579 on 399 degrees of freedom
## Multiple R-squared:  0.2717, Adjusted R-squared:  0.2681 
## F-statistic: 74.43 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response ME3.BM3 :
## 
## Call:
## lm(formula = ME3.BM3 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -16.2625  -2.7902   0.1884   2.8212  18.5270 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.68975    0.22264   3.098  0.00209 ** 
## x1           0.69810    0.07146   9.769  < 2e-16 ***
## x2           0.37920    0.06861   5.526 5.91e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.454 on 399 degrees of freedom
## Multiple R-squared:  0.216,  Adjusted R-squared:  0.212 
## F-statistic: 54.95 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response ME3.BM4 :
## 
## Call:
## lm(formula = ME3.BM4 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -16.6532  -2.7417   0.3343   2.8564  13.4469 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.71761    0.22806   3.147  0.00178 ** 
## x1           0.77285    0.07320  10.558  < 2e-16 ***
## x2           0.58836    0.07029   8.371 9.76e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.563 on 399 degrees of freedom
## Multiple R-squared:  0.279,  Adjusted R-squared:  0.2754 
## F-statistic: 77.19 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response ME3.BM5 :
## 
## Call:
## lm(formula = ME3.BM5 ~ x1 + x2, data = X)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -17.800  -2.723   0.093   3.301  20.702 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.81233    0.25029   3.246  0.00127 ** 
## x1           0.89098    0.08034  11.091  < 2e-16 ***
## x2           0.82508    0.07714  10.697  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.007 on 399 degrees of freedom
## Multiple R-squared:  0.3347, Adjusted R-squared:  0.3314 
## F-statistic: 100.4 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response ME4.BM1 :
## 
## Call:
## lm(formula = ME4.BM1 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -20.0464  -2.5617   0.0738   2.9343  13.5131 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.83813    0.24106   3.477 0.000563 ***
## x1           0.82765    0.07737  10.697  < 2e-16 ***
## x2          -0.39926    0.07429  -5.374 1.31e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.823 on 399 degrees of freedom
## Multiple R-squared:  0.2988, Adjusted R-squared:  0.2953 
## F-statistic: 85.01 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response ME4.BM2 :
## 
## Call:
## lm(formula = ME4.BM2 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -19.3930  -2.7069   0.3363   2.9746  18.9696 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.81754    0.23172   3.528 0.000467 ***
## x1           0.54237    0.07438   7.292 1.65e-12 ***
## x2           0.18072    0.07141   2.531 0.011771 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.636 on 399 degrees of freedom
## Multiple R-squared:  0.1205, Adjusted R-squared:  0.1161 
## F-statistic: 27.33 on 2 and 399 DF,  p-value: 7.535e-12
## 
## 
## Response ME4.BM3 :
## 
## Call:
## lm(formula = ME4.BM3 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -24.0147  -2.5666   0.3754   2.6818  17.8090 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.69754    0.23078   3.023  0.00267 ** 
## x1           0.45865    0.07407   6.192 1.48e-09 ***
## x2           0.40624    0.07112   5.712 2.19e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.617 on 399 degrees of freedom
## Multiple R-squared:  0.1308, Adjusted R-squared:  0.1264 
## F-statistic: 30.02 on 2 and 399 DF,  p-value: 7.184e-13
## 
## 
## Response ME4.BM4 :
## 
## Call:
## lm(formula = ME4.BM4 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -23.7112  -2.5754   0.3549   2.7636  14.7525 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.78886    0.23604   3.342  0.00091 ***
## x1           0.54935    0.07576   7.251 2.17e-12 ***
## x2           0.48478    0.07275   6.664 8.87e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.722 on 399 degrees of freedom
## Multiple R-squared:  0.1706, Adjusted R-squared:  0.1664 
## F-statistic: 41.02 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response ME4.BM5 :
## 
## Call:
## lm(formula = ME4.BM5 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -25.0212  -2.6510   0.2621   3.3484  16.3492 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.63698    0.26127   2.438   0.0152 *  
## x1           0.61986    0.08386   7.391  8.6e-13 ***
## x2           0.79509    0.08052   9.874  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.227 on 399 degrees of freedom
## Multiple R-squared:  0.2454, Adjusted R-squared:  0.2416 
## F-statistic: 64.89 on 2 and 399 DF,  p-value: < 2.2e-16
## 
## 
## Response BIG.LoBM :
## 
## Call:
## lm(formula = BIG.LoBM ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -16.5293  -2.1324   0.1589   2.7464  12.4966 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.88421    0.21533   4.106 4.88e-05 ***
## x1           0.06994    0.06912   1.012    0.312    
## x2          -0.39904    0.06636  -6.013 4.11e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.308 on 399 degrees of freedom
## Multiple R-squared:  0.09271,    Adjusted R-squared:  0.08817 
## F-statistic: 20.39 on 2 and 399 DF,  p-value: 3.716e-09
## 
## 
## Response ME5.BM2 :
## 
## Call:
## lm(formula = ME5.BM2 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -17.7908  -2.4873   0.4467   2.5879  12.6460 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.75101    0.20739   3.621 0.000331 ***
## x1           0.10926    0.06657   1.641 0.101528    
## x2           0.06700    0.06392   1.048 0.295164    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.149 on 399 degrees of freedom
## Multiple R-squared:  0.008135,   Adjusted R-squared:  0.003164 
## F-statistic: 1.636 on 2 and 399 DF,  p-value: 0.196
## 
## 
## Response ME5.BM3 :
## 
## Call:
## lm(formula = ME5.BM3 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -19.2475  -2.2632   0.5163   2.5847  12.2843 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.68967    0.21105   3.268  0.00118 ** 
## x1           0.11585    0.06774   1.710  0.08800 .  
## x2           0.28904    0.06504   4.444 1.15e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.222 on 399 degrees of freedom
## Multiple R-squared:  0.04905,    Adjusted R-squared:  0.04428 
## F-statistic: 10.29 on 2 and 399 DF,  p-value: 4.389e-05
## 
## 
## Response ME5.BM4 :
## 
## Call:
## lm(formula = ME5.BM4 ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -26.5627  -2.6029   0.3085   2.8396  13.5613 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.45151    0.23472   1.924   0.0551 .  
## x1           0.13091    0.07534   1.738   0.0830 .  
## x2           0.62484    0.07234   8.638   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.696 on 399 degrees of freedom
## Multiple R-squared:  0.1576, Adjusted R-squared:  0.1534 
## F-statistic: 37.32 on 2 and 399 DF,  p-value: 1.389e-15
## 
## 
## Response BIG.HiBM :
## 
## Call:
## lm(formula = BIG.HiBM ~ x1 + x2, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -27.4325  -3.1774   0.4826   3.6815  18.2886 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.69034    0.28826   2.395  0.01709 *  
## x1           0.24901    0.09253   2.691  0.00742 ** 
## x2           0.74727    0.08884   8.411 7.29e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.767 on 399 degrees of freedom
## Multiple R-squared:  0.1531, Adjusted R-squared:  0.1488 
## F-statistic: 36.06 on 2 and 399 DF,  p-value: 4.009e-15
##############Table 6 Replicate######################


# Predictors
XX <- data.frame(
  x1 = as.numeric(complete[, 28]),
  x2 = as.numeric(complete[, 29]),
  x = as.numeric(complete[, 27])
)

model6 <- lm(Y ~ x1 + x2 +x, data = XX)
summary(model6)   
## Response SMALL.LoBM :
## 
## Call:
## lm(formula = SMALL.LoBM ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.4283  -1.6243  -0.1887   1.4230  12.9474 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.58761    0.14435  -4.071 5.66e-05 ***
## x1           1.39887    0.04687  29.843  < 2e-16 ***
## x2          -0.26168    0.04391  -5.960 5.57e-09 ***
## x            1.15155    0.03353  34.345  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.845 on 398 degrees of freedom
## Multiple R-squared:  0.8797, Adjusted R-squared:  0.8788 
## F-statistic: 970.2 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME1.BM2 :
## 
## Call:
## lm(formula = ME1.BM2 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.5880 -1.2961 -0.1523  1.2404 11.6240 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.03295    0.11269   0.292    0.770    
## x1           1.35845    0.03659  37.125   <2e-16 ***
## x2          -0.01857    0.03428  -0.542    0.588    
## x            0.96781    0.02617  36.977   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.221 on 398 degrees of freedom
## Multiple R-squared:  0.9025, Adjusted R-squared:  0.9018 
## F-statistic:  1229 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME1.BM3 :
## 
## Call:
## lm(formula = ME1.BM3 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.0674 -1.0041 -0.1488  0.8588  7.9527 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.01740    0.07950  -0.219    0.827    
## x1           1.05970    0.02581  41.051   <2e-16 ***
## x2           0.29483    0.02418  12.193   <2e-16 ***
## x            0.91710    0.01846  49.668   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.567 on 398 degrees of freedom
## Multiple R-squared:  0.9308, Adjusted R-squared:  0.9303 
## F-statistic:  1785 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME1.BM4 :
## 
## Call:
## lm(formula = ME1.BM4 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.9084 -0.8998 -0.1018  0.8420  5.8728 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.19209    0.07225   2.659  0.00816 ** 
## x1           1.08117    0.02346  46.085  < 2e-16 ***
## x2           0.51725    0.02198  23.537  < 2e-16 ***
## x            0.86425    0.01678  51.503  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.424 on 398 degrees of freedom
## Multiple R-squared:  0.9403, Adjusted R-squared:  0.9399 
## F-statistic:  2090 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response SMALL.HiBM :
## 
## Call:
## lm(formula = SMALL.HiBM ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.7962  -0.9181  -0.1345   0.7977  31.1022 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.29841    0.11739   2.542   0.0114 *  
## x1           1.05309    0.03812  27.627   <2e-16 ***
## x2           0.73153    0.03571  20.487   <2e-16 ***
## x            0.91290    0.02727  33.482   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.314 on 398 degrees of freedom
## Multiple R-squared:  0.8662, Adjusted R-squared:  0.8652 
## F-statistic: 858.8 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME2.BM1 :
## 
## Call:
## lm(formula = ME2.BM1 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.9291 -0.9404 -0.0145  1.1893  6.4237 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.19282    0.09463  -2.038   0.0423 *  
## x1           1.08802    0.03073  35.407   <2e-16 ***
## x2          -0.28289    0.02878  -9.828   <2e-16 ***
## x            1.12195    0.02198  51.045   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.865 on 398 degrees of freedom
## Multiple R-squared:  0.9317, Adjusted R-squared:  0.9311 
## F-statistic:  1808 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME2.BM2 :
## 
## Call:
## lm(formula = ME2.BM2 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.0652 -1.0208 -0.0245  0.8335  6.3494 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.06890    0.07619   0.904    0.366    
## x1           0.93080    0.02474  37.622  < 2e-16 ***
## x2           0.14228    0.02318   6.139 2.01e-09 ***
## x            0.99266    0.01770  56.093  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.502 on 398 degrees of freedom
## Multiple R-squared:  0.9365, Adjusted R-squared:  0.936 
## F-statistic:  1956 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME2.BM3 :
## 
## Call:
## lm(formula = ME2.BM3 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.2630  -0.7766  -0.0768   0.8925   6.3827 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.01737    0.08238   0.211    0.833    
## x1           0.71961    0.02675  26.901   <2e-16 ***
## x2           0.42856    0.02506  17.103   <2e-16 ***
## x            0.96083    0.01913  50.215   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.624 on 398 degrees of freedom
## Multiple R-squared:  0.9119, Adjusted R-squared:  0.9112 
## F-statistic:  1373 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME2.BM4 :
## 
## Call:
## lm(formula = ME2.BM4 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.1901 -0.8048 -0.0186  0.7762  4.8418 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.01338    0.06687    0.20    0.842    
## x1           0.76968    0.02171   35.45   <2e-16 ***
## x2           0.61533    0.02034   30.25   <2e-16 ***
## x            0.93107    0.01553   59.95   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.318 on 398 degrees of freedom
## Multiple R-squared:  0.9419, Adjusted R-squared:  0.9414 
## F-statistic:  2150 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME2.BM5 :
## 
## Call:
## lm(formula = ME2.BM5 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.5211 -0.7402 -0.0942  0.8053 10.2221 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.04316    0.07031  -0.614     0.54    
## x1           0.93130    0.02283  40.790   <2e-16 ***
## x2           0.85244    0.02139  39.858   <2e-16 ***
## x            1.07335    0.01633  65.725   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.386 on 398 degrees of freedom
## Multiple R-squared:  0.9541, Adjusted R-squared:  0.9537 
## F-statistic:  2756 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME3.BM1 :
## 
## Call:
## lm(formula = ME3.BM1 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.7422 -1.2271  0.0439  1.2684  5.6600 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.18033    0.08790  -2.052   0.0409 *  
## x1           0.79165    0.02854  27.737   <2e-16 ***
## x2          -0.33886    0.02674 -12.675   <2e-16 ***
## x            1.10232    0.02042  53.995   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.732 on 398 degrees of freedom
## Multiple R-squared:  0.9286, Adjusted R-squared:  0.928 
## F-statistic:  1724 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME3.BM2 :
## 
## Call:
## lm(formula = ME3.BM2 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.3708 -0.9117 -0.0611  0.9549 10.4615 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.07769    0.08488   0.915    0.361    
## x1           0.57628    0.02756  20.908  < 2e-16 ***
## x2           0.19201    0.02582   7.437 6.38e-13 ***
## x            1.00361    0.01971  50.906  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.673 on 398 degrees of freedom
## Multiple R-squared:  0.903,  Adjusted R-squared:  0.9023 
## F-statistic:  1236 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME3.BM3 :
## 
## Call:
## lm(formula = ME3.BM3 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.7083 -1.0504 -0.0254  0.9692  8.1834 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.02562    0.08637  -0.297    0.767    
## x1           0.39019    0.02805  13.912   <2e-16 ***
## x2           0.45559    0.02627  17.342   <2e-16 ***
## x            0.96908    0.02006  48.306   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.702 on 398 degrees of freedom
## Multiple R-squared:  0.8858, Adjusted R-squared:  0.8849 
## F-statistic:  1029 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME3.BM4 :
## 
## Call:
## lm(formula = ME3.BM4 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.3345 -0.9997 -0.0111  0.9634  7.2486 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.02095    0.08426  -0.249    0.804    
## x1           0.45495    0.02736  16.627   <2e-16 ***
## x2           0.66724    0.02563  26.033   <2e-16 ***
## x            1.00051    0.01957  51.121   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.661 on 398 degrees of freedom
## Multiple R-squared:  0.9047, Adjusted R-squared:  0.904 
## F-statistic:  1259 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME3.BM5 :
## 
## Call:
## lm(formula = ME3.BM5 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -7.169 -1.236 -0.127  1.015  9.164 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.01441    0.10142   0.142    0.887    
## x1           0.54754    0.03293  16.626   <2e-16 ***
## x2           0.91030    0.03085  29.508   <2e-16 ***
## x            1.08092    0.02356  45.886   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.999 on 398 degrees of freedom
## Multiple R-squared:  0.8942, Adjusted R-squared:  0.8934 
## F-statistic:  1122 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME4.BM1 :
## 
## Call:
## lm(formula = ME4.BM1 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.9241 -0.8975  0.0275  0.9220  9.2460 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.05042    0.08359   0.603    0.547    
## x1           0.48860    0.02714  18.002   <2e-16 ***
## x2          -0.31513    0.02542 -12.395   <2e-16 ***
## x            1.06708    0.01941  54.964   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.648 on 398 degrees of freedom
## Multiple R-squared:  0.9184, Adjusted R-squared:  0.9178 
## F-statistic:  1493 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME4.BM2 :
## 
## Call:
## lm(formula = ME4.BM2 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.4640 -0.9476 -0.0343  0.9301  8.1123 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.06665    0.08527   0.782    0.435    
## x1           0.21917    0.02769   7.915 2.48e-14 ***
## x2           0.26091    0.02594  10.059  < 2e-16 ***
## x            1.01720    0.01981  51.359  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.681 on 398 degrees of freedom
## Multiple R-squared:  0.8847, Adjusted R-squared:  0.8838 
## F-statistic:  1018 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME4.BM3 :
## 
## Call:
## lm(formula = ME4.BM3 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.8287 -1.0146 -0.0055  0.9513  7.1312 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.04094    0.09165  -0.447    0.655    
## x1           0.14079    0.02976   4.731 3.11e-06 ***
## x2           0.48511    0.02788  17.401  < 2e-16 ***
## x            1.00038    0.02129  46.995  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.806 on 398 degrees of freedom
## Multiple R-squared:  0.8673, Adjusted R-squared:  0.8663 
## F-statistic: 866.9 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME4.BM4 :
## 
## Call:
## lm(formula = ME4.BM4 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.7579 -1.0506  0.0341  1.1394  7.0510 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.03748    0.09641   0.389    0.698    
## x1           0.22593    0.03131   7.217 2.71e-12 ***
## x2           0.56503    0.02932  19.268  < 2e-16 ***
## x            1.01787    0.02239  45.457  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.9 on 398 degrees of freedom
## Multiple R-squared:  0.866,  Adjusted R-squared:  0.865 
## F-statistic: 857.7 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME4.BM5 :
## 
## Call:
## lm(formula = ME4.BM5 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.9066  -1.3545  -0.0426   1.3840  11.4695 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.18709    0.11165  -1.676   0.0946 .  
## x1           0.26516    0.03625   7.314 1.44e-12 ***
## x2           0.88310    0.03396  26.004  < 2e-16 ***
## x            1.11634    0.02593  43.049  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.201 on 398 degrees of freedom
## Multiple R-squared:  0.8666, Adjusted R-squared:  0.8656 
## F-statistic: 861.8 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response BIG.LoBM :
## 
## Call:
## lm(formula = BIG.LoBM ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.95514 -0.64505  0.05057  0.58600  2.77039 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.15392    0.04804   3.204  0.00146 ** 
## x1          -0.24440    0.01560 -15.668  < 2e-16 ***
## x2          -0.32105    0.01461 -21.972  < 2e-16 ***
## x            0.98931    0.01116  88.669  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9468 on 398 degrees of freedom
## Multiple R-squared:  0.9563, Adjusted R-squared:  0.956 
## F-statistic:  2902 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME5.BM2 :
## 
## Call:
## lm(formula = ME5.BM2 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.9447 -0.9099  0.0282  0.8397  6.1212 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.07678    0.07466   1.028    0.304    
## x1          -0.18095    0.02424  -7.464 5.34e-13 ***
## x2           0.13901    0.02271   6.121 2.23e-09 ***
## x            0.91335    0.01734  52.672  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.472 on 398 degrees of freedom
## Multiple R-squared:  0.8756, Adjusted R-squared:  0.8746 
## F-statistic: 933.4 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME5.BM3 :
## 
## Call:
## lm(formula = ME5.BM3 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.9193 -0.9370 -0.0296  1.0015  7.5613 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.01565    0.08472   0.185    0.854    
## x1          -0.17426    0.02751  -6.334 6.46e-10 ***
## x2           0.36103    0.02577  14.009  < 2e-16 ***
## x            0.91307    0.01968  46.399  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.67 on 398 degrees of freedom
## Multiple R-squared:  0.8516, Adjusted R-squared:  0.8505 
## F-statistic: 761.5 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response ME5.BM4 :
## 
## Call:
## lm(formula = ME5.BM4 ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.6231 -0.8852  0.0857  0.9667  9.2602 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.31162    0.08444  -3.691 0.000255 ***
## x1          -0.19756    0.02742  -7.205 2.92e-12 ***
## x2           0.70634    0.02568  27.501  < 2e-16 ***
## x            1.03379    0.01961  52.713  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.664 on 398 degrees of freedom
## Multiple R-squared:  0.8945, Adjusted R-squared:  0.8937 
## F-statistic:  1124 on 3 and 398 DF,  p-value: < 2.2e-16
## 
## 
## Response BIG.HiBM :
## 
## Call:
## lm(formula = BIG.HiBM ~ x1 + x2 + x, data = XX)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.5668  -1.3081   0.0706   1.5536  10.4264 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.18445    0.14291  -1.291  0.19755    
## x1          -0.12752    0.04640  -2.748  0.00627 ** 
## x2           0.84070    0.04347  19.340  < 2e-16 ***
## x            1.18505    0.03319  35.702  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.817 on 398 degrees of freedom
## Multiple R-squared:  0.7985, Adjusted R-squared:  0.797 
## F-statistic: 525.7 on 3 and 398 DF,  p-value: < 2.2e-16
##############Table 9 DONE##############################

#################Table 10 ##############################

complete$month <- ifelse(substr(complete[[1]], 5, 6) == "01", 1, 0)
model10 <- lm(Y ~ month , data = complete)
summary(model10)  
## Response SMALL.LoBM :
## 
## Call:
## lm(formula = SMALL.LoBM ~ month, data = complete)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -28.503  -5.068   0.346   4.681  35.894 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  0.06504    0.42502   0.153   0.8785  
## month        2.49784    1.46146   1.709   0.0882 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.153 on 400 degrees of freedom
## Multiple R-squared:  0.00725,    Adjusted R-squared:  0.004768 
## F-statistic: 2.921 on 1 and 400 DF,  p-value: 0.0882
## 
## 
## Response ME1.BM2 :
## 
## Call:
## lm(formula = ME1.BM2 ~ month, data = complete)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -22.624  -4.316  -0.007   3.971  42.339 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)   0.7476     0.3698   2.022   0.0439 *
## month         0.7091     1.2716   0.558   0.5774  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.094 on 400 degrees of freedom
## Multiple R-squared:  0.0007768,  Adjusted R-squared:  -0.001721 
## F-statistic: 0.311 on 1 and 400 DF,  p-value: 0.5774
## 
## 
## Response ME1.BM3 :
## 
## Call:
## lm(formula = ME1.BM3 ~ month, data = complete)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -22.700  -3.735   0.169   3.717  19.269 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)   0.7202     0.3097   2.325   0.0205 *
## month         0.5626     1.0649   0.528   0.5976  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.941 on 400 degrees of freedom
## Multiple R-squared:  0.0006973,  Adjusted R-squared:  -0.001801 
## F-statistic: 0.2791 on 1 and 400 DF,  p-value: 0.5976
## 
## 
## Response ME1.BM4 :
## 
## Call:
## lm(formula = ME1.BM4 ~ month, data = complete)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -27.5687  -3.0189   0.0961   3.4222  24.6819 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   0.9523     0.3030   3.143   0.0018 **
## month         0.3665     1.0420   0.352   0.7252   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.813 on 400 degrees of freedom
## Multiple R-squared:  0.0003092,  Adjusted R-squared:  -0.00219 
## F-statistic: 0.1237 on 1 and 400 DF,  p-value: 0.7252
## 
## 
## Response SMALL.HiBM :
## 
## Call:
## lm(formula = SMALL.HiBM ~ month, data = complete)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -28.828  -3.538   0.065   3.517  38.408 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   1.0154     0.3279   3.097  0.00209 **
## month         1.7880     1.1274   1.586  0.11355   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.29 on 400 degrees of freedom
## Multiple R-squared:  0.006249,   Adjusted R-squared:  0.003764 
## F-statistic: 2.515 on 1 and 400 DF,  p-value: 0.1135
## 
## 
## Response ME2.BM1 :
## 
## Call:
## lm(formula = ME2.BM1 ~ month, data = complete)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -26.3940  -4.3421   0.3426   4.4717  29.6082 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  0.631143   0.370995   1.701   0.0897 .
## month       -0.009805   1.275679  -0.008   0.9939  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.117 on 400 degrees of freedom
## Multiple R-squared:  1.477e-07,  Adjusted R-squared:  -0.0025 
## F-statistic: 5.908e-05 on 1 and 400 DF,  p-value: 0.9939
## 
## 
## Response ME2.BM2 :
## 
## Call:
## lm(formula = ME2.BM2 ~ month, data = complete)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -24.4047  -3.3362   0.3758   3.5293  18.0016 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   0.9184     0.3098   2.965  0.00321 **
## month        -0.5319     1.0651  -0.499  0.61780   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.942 on 400 degrees of freedom
## Multiple R-squared:  0.000623,   Adjusted R-squared:  -0.001875 
## F-statistic: 0.2494 on 1 and 400 DF,  p-value: 0.6178
## 
## 
## Response ME2.BM3 :
## 
## Call:
## lm(formula = ME2.BM3 ~ month, data = complete)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -22.7059  -3.0624   0.3871   3.0415  17.4300 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   0.8897     0.2843   3.129  0.00188 **
## month        -0.5273     0.9777  -0.539  0.58997   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.454 on 400 degrees of freedom
## Multiple R-squared:  0.0007266,  Adjusted R-squared:  -0.001772 
## F-statistic: 0.2909 on 1 and 400 DF,  p-value: 0.59
## 
## 
## Response ME2.BM4 :
## 
## Call:
## lm(formula = ME2.BM4 ~ month, data = complete)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -24.6117  -3.1289   0.6258   3.1619  17.7739 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   0.9197     0.2841   3.238  0.00131 **
## month        -0.7226     0.9768  -0.740  0.45983   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.449 on 400 degrees of freedom
## Multiple R-squared:  0.001367,   Adjusted R-squared:  -0.00113 
## F-statistic: 0.5474 on 1 and 400 DF,  p-value: 0.4598
## 
## 
## Response ME2.BM5 :
## 
## Call:
## lm(formula = ME2.BM5 ~ month, data = complete)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -33.106  -3.348   0.430   3.918  24.949 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   1.0134     0.3361   3.015  0.00273 **
## month        -0.6124     1.1558  -0.530  0.59650   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.448 on 400 degrees of freedom
## Multiple R-squared:  0.0007014,  Adjusted R-squared:  -0.001797 
## F-statistic: 0.2808 on 1 and 400 DF,  p-value: 0.5965
## 
## 
## Response ME3.BM1 :
## 
## Call:
## lm(formula = ME3.BM1 ~ month, data = complete)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -23.9424  -3.9679   0.6524   3.8859  21.5581 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)   0.6152     0.3370   1.825   0.0687 .
## month        -0.1423     1.1589  -0.123   0.9023  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.465 on 400 degrees of freedom
## Multiple R-squared:  3.768e-05,  Adjusted R-squared:  -0.002462 
## F-statistic: 0.01507 on 1 and 400 DF,  p-value: 0.9023
## 
## 
## Response ME3.BM2 :
## 
## Call:
## lm(formula = ME3.BM2 ~ month, data = complete)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -23.0163  -3.0695   0.3619   3.3729  17.7977 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.9426     0.2792   3.376 0.000807 ***
## month        -0.7009     0.9600  -0.730 0.465767    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.356 on 400 degrees of freedom
## Multiple R-squared:  0.001331,   Adjusted R-squared:  -0.001166 
## F-statistic: 0.533 on 1 and 400 DF,  p-value: 0.4658
## 
## 
## Response ME3.BM3 :
## 
## Call:
## lm(formula = ME3.BM3 ~ month, data = complete)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -19.1426  -2.9822   0.3466   2.9544  15.8309 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   0.8636     0.2617   3.300  0.00105 **
## month        -0.7758     0.8997  -0.862  0.38905   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.02 on 400 degrees of freedom
## Multiple R-squared:  0.001855,   Adjusted R-squared:  -0.00064 
## F-statistic: 0.7435 on 1 and 400 DF,  p-value: 0.3891
## 
## 
## Response ME3.BM4 :
## 
## Call:
## lm(formula = ME3.BM4 ~ month, data = complete)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -27.5882  -2.8662   0.3083   3.1760  15.7365 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   0.9222     0.2796   3.298  0.00106 **
## month        -0.6080     0.9615  -0.632  0.52752   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.364 on 400 degrees of freedom
## Multiple R-squared:  0.0009987,  Adjusted R-squared:  -0.001499 
## F-statistic: 0.3999 on 1 and 400 DF,  p-value: 0.5275
## 
## 
## Response ME3.BM5 :
## 
## Call:
## lm(formula = ME3.BM5 ~ month, data = complete)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -32.372  -2.872   0.333   3.085  21.855 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   1.0588     0.3195   3.313  0.00101 **
## month        -0.4815     1.0988  -0.438  0.66144   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.13 on 400 degrees of freedom
## Multiple R-squared:  0.0004799,  Adjusted R-squared:  -0.002019 
## F-statistic: 0.1921 on 1 and 400 DF,  p-value: 0.6614
## 
## 
## Response ME4.BM1 :
## 
## Call:
## lm(formula = ME4.BM1 ~ month, data = complete)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -21.1909  -3.0983   0.2838   3.3694  24.5577 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   0.8254     0.2998   2.753  0.00618 **
## month        -0.3204     1.0309  -0.311  0.75611   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.752 on 400 degrees of freedom
## Multiple R-squared:  0.0002414,  Adjusted R-squared:  -0.002258 
## F-statistic: 0.0966 on 1 and 400 DF,  p-value: 0.7561
## 
## 
## Response ME4.BM2 :
## 
## Call:
## lm(formula = ME4.BM2 ~ month, data = complete)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -21.0890  -2.8424   0.2107   3.0833  14.6148 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.9191     0.2573   3.573 0.000397 ***
## month        -0.4739     0.8847  -0.536 0.592473    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.935 on 400 degrees of freedom
## Multiple R-squared:  0.0007169,  Adjusted R-squared:  -0.001781 
## F-statistic: 0.287 on 1 and 400 DF,  p-value: 0.5925
## 
## 
## Response ME4.BM3 :
## 
## Call:
## lm(formula = ME4.BM3 ~ month, data = complete)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -25.9573  -2.7503   0.3423   3.0609  15.9938 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   0.8129     0.2578   3.153  0.00174 **
## month        -0.1558     0.8865  -0.176  0.86058   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.946 on 400 degrees of freedom
## Multiple R-squared:  7.721e-05,  Adjusted R-squared:  -0.002423 
## F-statistic: 0.03089 on 1 and 400 DF,  p-value: 0.8606
## 
## 
## Response ME4.BM4 :
## 
## Call:
## lm(formula = ME4.BM4 ~ month, data = complete)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -33.158  -2.790   0.442   2.830  15.310 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.9551     0.2699   3.539 0.000448 ***
## month        -0.5221     0.9279  -0.563 0.573999    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.177 on 400 degrees of freedom
## Multiple R-squared:  0.0007908,  Adjusted R-squared:  -0.001707 
## F-statistic: 0.3166 on 1 and 400 DF,  p-value: 0.574
## 
## 
## Response ME4.BM5 :
## 
## Call:
## lm(formula = ME4.BM5 ~ month, data = complete)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -33.487  -3.212   0.766   3.416  19.527 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   0.8481     0.3133   2.707  0.00707 **
## month        -0.2867     1.0772  -0.266  0.79022   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.009 on 400 degrees of freedom
## Multiple R-squared:  0.0001771,  Adjusted R-squared:  -0.002322 
## F-statistic: 0.07086 on 1 and 400 DF,  p-value: 0.7902
## 
## 
## Response BIG.LoBM :
## 
## Call:
## lm(formula = BIG.LoBM ~ month, data = complete)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -15.8779  -2.3707   0.1289   2.9092  13.2650 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.8254     0.2355   3.506 0.000507 ***
## month        -0.2005     0.8096  -0.248 0.804553    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.517 on 400 degrees of freedom
## Multiple R-squared:  0.0001533,  Adjusted R-squared:  -0.002346 
## F-statistic: 0.06132 on 1 and 400 DF,  p-value: 0.8046
## 
## 
## Response ME5.BM2 :
## 
## Call:
## lm(formula = ME5.BM2 ~ month, data = complete)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.2260  -2.5727   0.4091   2.5186  12.7526 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.8278     0.2167   3.820 0.000154 ***
## month        -0.6895     0.7451  -0.925 0.355315    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.157 on 400 degrees of freedom
## Multiple R-squared:  0.002136,   Adjusted R-squared:  -0.0003583 
## F-statistic: 0.8564 on 1 and 400 DF,  p-value: 0.3553
## 
## 
## Response ME5.BM3 :
## 
## Call:
## lm(formula = ME5.BM3 ~ month, data = complete)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.9325  -2.3689   0.6151   2.6172  13.4784 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.7728     0.2254   3.428  0.00067 ***
## month        -0.2409     0.7751  -0.311  0.75608    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.324 on 400 degrees of freedom
## Multiple R-squared:  0.0002415,  Adjusted R-squared:  -0.002258 
## F-statistic: 0.09662 on 1 and 400 DF,  p-value: 0.7561
## 
## 
## Response ME5.BM4 :
## 
## Call:
## lm(formula = ME5.BM4 ~ month, data = complete)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -28.241  -2.461   0.448   2.992  15.709 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)   0.6465     0.2661   2.429   0.0156 *
## month        -0.7689     0.9151  -0.840   0.4013  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.105 on 400 degrees of freedom
## Multiple R-squared:  0.001762,   Adjusted R-squared:  -0.0007338 
## F-statistic: 0.706 on 1 and 400 DF,  p-value: 0.4013
## 
## 
## Response BIG.HiBM :
## 
## Call:
## lm(formula = BIG.HiBM ~ month, data = complete)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -29.4142  -3.6556   0.4206   3.7364  21.1529 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)   0.8346     0.3263   2.558   0.0109 *
## month         0.1839     1.1219   0.164   0.8699  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.259 on 400 degrees of freedom
## Multiple R-squared:  6.714e-05,  Adjusted R-squared:  -0.002433 
## F-statistic: 0.02686 on 1 and 400 DF,  p-value: 0.8699