Midterm

Setup

library(forecast)

## Registered S3 method overwritten by 'quantmod':
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##   as.zoo.data.frame zoo

library(Amelia)

## Loading required package: Rcpp

## ## 
## ## Amelia II: Multiple Imputation
## ## (Version 1.7.6, built: 2019-11-24)
## ## Copyright (C) 2005-2020 James Honaker, Gary King and Matthew Blackwell
## ## Refer to http://gking.harvard.edu/amelia/ for more information
## ##

library(psych)
library(ResourceSelection)

## ResourceSelection 0.3-5   2019-07-22

library(ggplot2)

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## The following objects are masked from 'package:psych':
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library(dplyr)

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## The following objects are masked from 'package:base':
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library(xts)

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library(tidyverse)

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## ✓ tidyr   1.1.0     ✓ stringr 1.4.0
## ✓ readr   1.3.1     ✓ forcats 0.5.0

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library(lubridate)

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## Attaching package: 'lubridate'

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library(tseries)
library(TTR)
library(knitr)

Data setup

air_visit_data$visit_date=as.Date(air_visit_data$visit_date)
date_info$calendar_date=as.Date(date_info$calendar_date)
air_reserve$reserve_date = as.Date(air_reserve$reserve_datetime)
air_reserve$visit_date = as.Date(air_reserve$visit_datetime)
hpg_reserve$reserve_date = as.Date(hpg_reserve$reserve_datetime)
hpg_reserve$visit_date = as.Date(hpg_reserve$visit_datetime)

air_visit_withdates = merge(air_visit_data,date_info,by.x = "visit_date", by.y = "calendar_date")
air_visit_infodates = merge(air_visit_withdates, air_store_info, by = "air_store_id")

hpg_reserve_total = merge(hpg_reserve, hpg_store_info, by = "hpg_store_id")

air_visit_infodates$visit_month = month(air_visit_infodates$visit_date)
air_visit_infodates$visit_day = wday(air_visit_infodates$visit_date)

hpg_reserve_total$visit_month = month(hpg_reserve_total$visit_date)
hpg_reserve_total$visit_day = wday(hpg_reserve_total$visit_date)

Data investigation

summary(air_reserve)

##  air_store_id       visit_datetime     reserve_datetime   reserve_visitors 
##  Length:92378       Length:92378       Length:92378       Min.   :  1.000  
##  Class :character   Class :character   Class :character   1st Qu.:  2.000  
##  Mode  :character   Mode  :character   Mode  :character   Median :  3.000  
##                                                           Mean   :  4.482  
##                                                           3rd Qu.:  5.000  
##                                                           Max.   :100.000  
##   reserve_date          visit_date        
##  Min.   :2016-01-01   Min.   :2016-01-01  
##  1st Qu.:2016-11-07   1st Qu.:2016-11-15  
##  Median :2016-12-27   Median :2017-01-05  
##  Mean   :2016-11-26   Mean   :2016-12-04  
##  3rd Qu.:2017-02-26   3rd Qu.:2017-03-03  
##  Max.   :2017-04-22   Max.   :2017-05-31

summary(hpg_reserve_total)

##  hpg_store_id       visit_datetime     reserve_datetime   reserve_visitors 
##  Length:871308      Length:871308      Length:871308      Min.   :  1.000  
##  Class :character   Class :character   Class :character   1st Qu.:  2.000  
##  Mode  :character   Mode  :character   Mode  :character   Median :  3.000  
##                                                           Mean   :  5.335  
##                                                           3rd Qu.:  6.000  
##                                                           Max.   :100.000  
##   reserve_date          visit_date         hpg_genre_name    
##  Min.   :2016-01-01   Min.   :2016-01-01   Length:871308     
##  1st Qu.:2016-06-30   1st Qu.:2016-07-08   Class :character  
##  Median :2016-11-21   Median :2016-12-02   Mode  :character  
##  Mean   :2016-10-14   Mean   :2016-10-21                     
##  3rd Qu.:2017-02-03   3rd Qu.:2017-02-10                     
##  Max.   :2017-04-22   Max.   :2017-05-31                     
##  hpg_area_name         latitude       longitude      visit_month    
##  Length:871308      Min.   :33.31   Min.   :130.3   Min.   : 1.000  
##  Class :character   1st Qu.:34.69   1st Qu.:135.5   1st Qu.: 3.000  
##  Mode  :character   Median :35.65   Median :139.4   Median : 4.000  
##                     Mean   :35.86   Mean   :137.5   Mean   : 5.961  
##                     3rd Qu.:35.70   3rd Qu.:139.7   3rd Qu.:10.000  
##                     Max.   :43.77   Max.   :143.7   Max.   :12.000  
##    visit_day    
##  Min.   :1.000  
##  1st Qu.:3.000  
##  Median :5.000  
##  Mean   :4.786  
##  3rd Qu.:6.000  
##  Max.   :7.000

summary(air_visit_infodates)

##  air_store_id         visit_date            visitors      day_of_week       
##  Length:252108      Min.   :2016-01-01   Min.   :  1.00   Length:252108     
##  Class :character   1st Qu.:2016-07-23   1st Qu.:  9.00   Class :character  
##  Mode  :character   Median :2016-10-23   Median : 17.00   Mode  :character  
##                     Mean   :2016-10-12   Mean   : 20.97                     
##                     3rd Qu.:2017-01-24   3rd Qu.: 29.00                     
##                     Max.   :2017-04-22   Max.   :877.00                     
##   holiday_flg      air_genre_name     air_area_name         latitude    
##  Min.   :0.00000   Length:252108      Length:252108      Min.   :33.21  
##  1st Qu.:0.00000   Class :character   Class :character   1st Qu.:34.69  
##  Median :0.00000   Mode  :character   Mode  :character   Median :35.66  
##  Mean   :0.05067                                         Mean   :35.61  
##  3rd Qu.:0.00000                                         3rd Qu.:35.69  
##  Max.   :1.00000                                         Max.   :44.02  
##    longitude      visit_month       visit_day    
##  Min.   :130.2   Min.   : 1.000   Min.   :1.000  
##  1st Qu.:135.3   1st Qu.: 3.000   1st Qu.:3.000  
##  Median :139.7   Median : 7.000   Median :4.000  
##  Mean   :137.4   Mean   : 6.208   Mean   :4.187  
##  3rd Qu.:139.8   3rd Qu.:10.000   3rd Qu.:6.000  
##  Max.   :144.3   Max.   :12.000   Max.   :7.000

missmap(air_reserve)

missmap(hpg_reserve_total)

missmap(air_visit_infodates)

EDA

describe(air_visit_infodates[,3])

##    vars      n  mean    sd median trimmed   mad min max range skew kurtosis
## X1    1 252108 20.97 16.76     17   18.82 13.34   1 877   876 3.31    74.26
##      se
## X1 0.03

 #time series plot of visits
aggregateVists = aggregate(air_visit_infodates["visitors"], by=air_visit_infodates["visit_date"], sum)
dates <- seq(as.Date("2016-01-01"),length=NROW(aggregateVists),by="days")
tsVisits = ts(aggregateVists, start = 2016, frequency = 365)
tsVisits = tsVisits[,-1]
autoplot(tsVisits, main = "Sum of Visits by Date", ylab = "Visits (sum of all restaurants)")

#histogram of visits
bins = seq(0, 24000, by=2400)
h = hist(aggregateVists$visitors, breaks = bins, plot=FALSE)
h$counts=round(h$counts/sum(h$counts), 3)*100
 plot(h, labels = TRUE, col = 5, main = "Relative Frequency Histogram of Visits", xlab = "Total Number of Visits to a Restaurant", ylab = "Frequency (%)", xaxt = "n")
 axis(1, at = seq(0, 24000, by = 3000), las = 1)

 #boxplot of visits
air_visit_infodates$day_of_week <- factor(air_visit_infodates$day_of_week, levels= c("Sunday", "Monday", 
    "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"))

boxplot(air_visit_infodates$visitors~air_visit_infodates$day_of_week, ylab = "Visits", xlab = "Day of Week", main = "Visits to All Restaurants by Day of the Week", outline = FALSE)

boxplot(air_visit_infodates$visitors~air_visit_infodates$visit_month, ylab = "Visits", xlab = "Month", main = "Visits to All Restaurants by Month", outline = FALSE)

More EDA

airGenres = aggregate(air_visit_withdates["visitors"], by=air_visit_infodates["air_genre_name"], sum)
ggplot(data=airGenres, aes(y=air_genre_name, x=visitors, fill = air_genre_name)) +
  geom_bar(stat='identity')+ theme(legend.position = 'none')

airArea = aggregate(air_visit_withdates["visitors"], by=air_visit_infodates["air_area_name"], sum)

airArea = airArea[order(-airArea$visitors),]
airArea = head(airArea, n = 20)
ggplot(data=airArea, aes(y=air_area_name, x=visitors, fill = air_area_name)) +
  geom_bar(stat='identity') + theme(legend.position = 'none')

data for prediction

testData = subset(air_visit_infodates, visit_date >= as.Date("2017-03-18"))
trainData = subset(air_visit_infodates, visit_date < as.Date("2017-03-18"))

testDataTS = ts(testData[,3], frequency = 7)

uniqueData = unique(trainData$air_store_id)

Model 1: Seasonal Naive

accData = data.frame(matrix(ncol = 7, nrow =0))
colnames(accData)=c("ME","RMSE", "MAE", "MPE", "MAPE", "MASE", "ACF1")


testAccuracy = data.frame(matrix(ncol = 8, nrow =0))
colnames(testAccuracy)=c("ME","RMSE", "MAE", "MPE", "MAPE", "MASE", "ACF1", "Theil's U")

for (i in 1:15) {
  randVal = sample(1:NROW(uniqueData), 1)
  getAirID = uniqueData[randVal]
  testDataFilter = filter(testData, air_store_id == getAirID)
  
  filterData = filter(trainData, air_store_id == getAirID)
  filterTS = ts(filterData, frequency = 7)
  filterTS[,3] = log(filterTS[,3])
  modeldata1 = snaive(filterTS[,3], h=NROW(testDataFilter))
  
  acc = accuracy(modeldata1)
  accData[nrow(accData) + 1,] = acc

  testacc = data.frame(accuracy(modeldata1,testDataTS))
  testacc = testacc[-1,]
  testAccuracy = rbind(testAccuracy, testacc)
}


printAcc = data.frame(matrix(ncol = 1, nrow =8))
rownames(printAcc)=c("ME","RMSE", "MAE", "MPE", "MAPE", "MASE", "ACF1", "Theil's U")
colnames(printAcc) = "Mean"
for (i in 1:NROW(printAcc)) {
  printAcc[i,] = mean(testAccuracy[,i])
}

kable(printAcc, "simple")

	Mean
ME	23.7764296
RMSE	27.0785020
MAE	23.8508807
MPE	74.8268154
MAPE	79.8831795
MASE	35.8236287
ACF1	0.1250411
Theil's U	1.2747822

Model 2: Holt Winters

accData2 = data.frame(matrix(ncol = 7, nrow =0))
colnames(accData2)=c("ME","RMSE", "MAE", "MPE", "MAPE", "MASE", "ACF1")

testAccuracy = data.frame(matrix(ncol = 8, nrow =0))
colnames(testAccuracy)=c("ME","RMSE", "MAE", "MPE", "MAPE", "MASE", "ACF1", "Theil's U")

for (i in 1:15) {
  randVal = sample(1:NROW(uniqueData), 15)
  getAirID = uniqueData[randVal]
  testDataFilter = filter(testData, air_store_id == getAirID)

  filterData = filter(trainData, air_store_id == getAirID)
  filterTS = ts(filterData[,3], frequency = 7)
  filterTS = log(filterTS)
  modelData = hw(filterTS, h = NROW(testDataFilter))
  
  acc = accuracy(modelData)
  accData2[nrow(accData2) + 1,] = acc

  testacc = data.frame(accuracy(modelData,testDataTS))
  testacc = testacc[-1,]
  testAccuracy = rbind(testAccuracy, testacc)

}

## Warning in air_store_id == getAirID: longer object length is not a multiple of
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printAcc = data.frame(matrix(ncol = 1, nrow =8))
rownames(printAcc)=c("ME","RMSE", "MAE", "MPE", "MAPE", "MASE", "ACF1", "Theil's U")
colnames(printAcc) = "Mean"
for (i in 1:NROW(printAcc)) {
  printAcc[i,] = mean(testAccuracy[,i])
}

kable(printAcc, "simple")

	Mean
ME	20.566314
RMSE	25.073962
MAE	20.616436
MPE	77.621547
MAPE	80.127675
MASE	25.726933
ACF1	0.205317
Theil's U	1.182569

Model 3: ARIMA

accData3 = data.frame(matrix(ncol = 7, nrow =0))
colnames(accData3)=c("ME","RMSE", "MAE", "MPE", "MAPE", "MASE", "ACF1")

testAccuracy = data.frame(matrix(ncol = 8, nrow =0))
colnames(testAccuracy)=c("ME","RMSE", "MAE", "MPE", "MAPE", "MASE", "ACF1", "Theil's U")

for (i in 1:15) {
  randVal = sample(1:NROW(uniqueData), 15)
  getAirID = uniqueData[randVal]
  testDataFilter = filter(testData, air_store_id == getAirID)

  filterData = filter(trainData, air_store_id == getAirID)
  filterTS = ts(filterData, frequency = 7)
  adf = adf.test(filterTS[,3], alternative = "stationary")

  modelData = auto.arima(filterTS[,3],seasonal = TRUE)
  fc = forecast(modelData, h = NROW(testDataFilter))
  
  
  acc = accuracy(fc)
  accData3[nrow(accData3) + 1,] = acc
  
  testacc = data.frame(accuracy(fc,testDataTS))
  testacc = testacc[-1,]
  testAccuracy = rbind(testAccuracy, testacc)
}

## Warning in air_store_id == getAirID: longer object length is not a multiple of
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## Warning in adf.test(filterTS[, 3], alternative = "stationary"): p-value smaller
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## Warning in adf.test(filterTS[, 3], alternative = "stationary"): p-value smaller
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## Warning in adf.test(filterTS[, 3], alternative = "stationary"): p-value smaller
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## Warning in air_store_id == getAirID: longer object length is not a multiple of
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## Warning in adf.test(filterTS[, 3], alternative = "stationary"): p-value smaller
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## Warning in air_store_id == getAirID: longer object length is not a multiple of
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printAcc = data.frame(matrix(ncol = 1, nrow =8))
rownames(printAcc)=c("ME","RMSE", "MAE", "MPE", "MAPE", "MASE", "ACF1", "Theil's U")
colnames(printAcc) = "Mean"
for (i in 1:NROW(printAcc)) {
  printAcc[i,] = mean(testAccuracy[,i])
}

kable(printAcc, "simple")

	Mean
ME	3.5491204
RMSE	16.5597264
MAE	13.7582514
MPE	-61.9083941
MAPE	104.3864122
MASE	1.0575576
ACF1	0.1979226
Theil's U	0.9707378

Forecasting

uniqueSubmit = unique(sample_submission$air_store_id)

df = data.frame(matrix(ncol = 6, nrow =0))
colnames(df)=c("Point.Forecast","Lo.80", "Hi.80", "Lo.95", "Hi.95", "air_store_id")

for (i in 1:NROW(uniqueSubmit)) {
  getAirID = uniqueSubmit[i]
  filterData = filter(air_visit_infodates, air_store_id == getAirID)
  filterTS = ts(filterData, frequency = 7)
  filterTS[,3] = log(filterTS[,3])
  modelData = auto.arima(filterTS[,3],seasonal = TRUE)
  fc = forecast(modelData, h = 39, lambda = 0)
  frameFC = data.frame(fc)
  frameFC$air_store_id = getAirID
  df = rbind(df, frameFC)
}

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
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## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

## Warning in InvBoxCox(pred$pred, lambda, biasadj, pred$se^2): biasadj information
## not found, defaulting to FALSE.

sample_submission = sample_submission[,-c(2:3)]

for (i in 1:nrow(sample_submission)) {
  sample_submission[i,]$visitors = df[i,]$Point.Forecast
}

write.csv(sample_submission, "~/Desktop/midtermForecasts.csv", row.names=FALSE)