IS 607: PROJECT
MUSA T. GANIYU
April 28, 2016
ABSTRACT:
The project analysis is done on three (3) different datasets from different sources. The first dataset if from the University of California, Irvine website on Air Quality, the second dataset was extracted as an .xls file from World Bank website for the year 1961-1999, while the third dataset was base on incident rate of leukemia in US States and was extracted from cancer.gov website.
Analyses was done on all the three datasets to determine if the is linear relationship between them. I found out that the Air Quality has some of it variables that are way beyond the acceptable threnshold, I checked for interaction between those variables and benzene. I compared the result with the Leukemia incident rate in the 49 US States and the result is amazing.
We would randomly select observations to avoid bias.
We would do some of the analysis on three(3) different programs; R, MySQL and MongoDB.
AIM AND OBJECTIVE:
- I am motivated by the serious impacts of the Air Quality throughout the whole world. Lots of adults, children are prone or exposed to the various categories of air throughout the globe. I thought it would be good to do an analysis to see the level of impact and to offer solutions.
Load Libraries:
- Please, kindly install the package(s) first if you don’t already have it and load their respective libraries.
options(warn = -1)
suppressMessages(library(xlsx))
library(xlsxjars)
library(rJava)
library(devtools)
suppressMessages(library(RMySQL))
library(DBI)
suppressMessages(library(plotly))
suppressWarnings(library(rmongodb))
library(knitr)
library(mongolite)
suppressMessages(library(RCurl))
suppressMessages(library(plyr))
suppressMessages(library(ggplot2))We will be using the Air Quality dataset from the University of California, Irvine website:
http://archive.ics.uci.edu/ml/datasets/Air+Quality#
** It is a .xlsx dataset that I downloaded into my local computer.**
- Kindly download from here:
https://github.com/mascotinme/MSDA-IS607/blob/master/cckp_historical_data_0.xls
airqu <- read.xlsx2("C:/Users/mayowa/Documents/GitHub/MSDA-IS607/AirQualityUCI.xlsx", sheetName = "AirQualityUCI", header=TRUE, colClasses=NA)
dim(airqu)## [1] 9471 15kable(head(airqu))| Date | Time | CO.GT. | PT08.S1.CO. | NMHC.GT. | C6H6.GT. | PT08.S2.NMHC. | NOx.GT. | PT08.S3.NOx. | NO2.GT. | PT08.S4.NO2. | PT08.S5.O3. | T | RH | AH |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2004-03-10 | 1899-12-30 18:00:00 | 2.6 | 1360.00 | 150 | 11.881723 | 1045.50 | 166 | 1056.25 | 113 | 1692.00 | 1267.50 | 13.600 | 48.875 | 0.7577538 |
| 2004-03-10 | 1899-12-30 19:00:00 | 2.0 | 1292.25 | 112 | 9.397165 | 954.75 | 103 | 1173.75 | 92 | 1558.75 | 972.25 | 13.300 | 47.700 | 0.7254874 |
| 2004-03-10 | 1899-12-30 20:00:00 | 2.2 | 1402.00 | 88 | 8.997817 | 939.25 | 131 | 1140.00 | 114 | 1554.50 | 1074.00 | 11.900 | 53.975 | 0.7502391 |
| 2004-03-10 | 1899-12-30 21:00:00 | 2.2 | 1375.50 | 80 | 9.228796 | 948.25 | 172 | 1092.00 | 122 | 1583.75 | 1203.25 | 11.000 | 60.000 | 0.7867125 |
| 2004-03-10 | 1899-12-30 22:00:00 | 1.6 | 1272.25 | 51 | 6.518224 | 835.50 | 131 | 1205.00 | 116 | 1490.00 | 1110.00 | 11.150 | 59.575 | 0.7887942 |
| 2004-03-10 | 1899-12-30 23:00:00 | 1.2 | 1197.00 | 38 | 4.741012 | 750.25 | 89 | 1336.50 | 96 | 1393.00 | 949.25 | 11.175 | 59.175 | 0.7847717 |
kable(tail(airqu))| Date | Time | CO.GT. | PT08.S1.CO. | NMHC.GT. | C6H6.GT. | PT08.S2.NMHC. | NOx.GT. | PT08.S3.NOx. | NO2.GT. | PT08.S4.NO2. | PT08.S5.O3. | T | RH | AH | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 9466 | NA | NA | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 9467 | NA | NA | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 9468 | NA | NA | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 9469 | NA | NA | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 9470 | NA | NA | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 9471 | NA | NA | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
names(airqu)## [1] "Date" "Time" "CO.GT." "PT08.S1.CO."
## [5] "NMHC.GT." "C6H6.GT." "PT08.S2.NMHC." "NOx.GT."
## [9] "PT08.S3.NOx." "NO2.GT." "PT08.S4.NO2." "PT08.S5.O3."
## [13] "T" "RH" "AH"str(airqu)## 'data.frame': 9471 obs. of 15 variables:
## $ Date :Class 'POSIXct' atomic [1:9471] 1.08e+09 1.08e+09 1.08e+09 1.08e+09 1.08e+09 ...
## .. ..- attr(*, "tzone")= chr "GMT"
## $ Time :Class 'POSIXct' atomic [1:9471] -2.21e+09 -2.21e+09 -2.21e+09 -2.21e+09 -2.21e+09 ...
## .. ..- attr(*, "tzone")= chr "GMT"
## $ CO.GT. : num 2.6 2 2.2 2.2 1.6 1.2 1.2 1 0.9 0.6 ...
## $ PT08.S1.CO. : num 1360 1292 1402 1376 1272 ...
## $ NMHC.GT. : num 150 112 88 80 51 38 31 31 24 19 ...
## $ C6H6.GT. : num 11.88 9.4 9 9.23 6.52 ...
## $ PT08.S2.NMHC.: num 1046 955 939 948 836 ...
## $ NOx.GT. : num 166 103 131 172 131 89 62 62 45 -200 ...
## $ PT08.S3.NOx. : num 1056 1174 1140 1092 1205 ...
## $ NO2.GT. : num 113 92 114 122 116 96 77 76 60 -200 ...
## $ PT08.S4.NO2. : num 1692 1559 1554 1584 1490 ...
## $ PT08.S5.O3. : num 1268 972 1074 1203 1110 ...
## $ T : num 13.6 13.3 11.9 11 11.2 ...
## $ RH : num 48.9 47.7 54 60 59.6 ...
## $ AH : num 0.758 0.725 0.75 0.787 0.789 ...class(airqu)## [1] "data.frame"
- We notice that there are alot of NA’s in the dataset, we therefore thought it would be appropriate (for easy analysis) to replace the missing values or NA with Zero(o)
- We also notice that the column names is ambiguous, we therefore change it to a reasonable column names.
airqu$NMHC.GT.[is.na(airqu$NMHC.GT.)] <- 0.0000
airqu$CO.GT.[is.na(airqu$CO.GT.)] <- 0.0000
airqu$PT08.S1.CO.[is.na(airqu$PT08.S1.CO.)] <- 0.0000
airqu$C6H6.GT.[is.na(airqu$C6H6.GT.)] <- 0.0000
airqu$PT08.S2.NMHC.[is.na(airqu$PT08.S2.NMHC.)] <- 0.0000
airqu$NOx.GT.[is.na(airqu$NOx.GT.)] <- 0.0000
airqu$PT08.S3.NOx.[is.na(airqu$PT08.S3.NOx.)] <- 0.0000
airqu$NO2.GT.[is.na(airqu$NO2.GT.)] <- 0.0000
airqu$PT08.S4.NO2.[is.na(airqu$PT08.S4.NO2.)] <- 0.0000
airqu$PT08.S5.O3.[is.na(airqu$PT08.S5.O3.)] <- 0.0000
airqu$T[is.na(airqu$T)] <- 0.0000
airqu$RH[is.na(airqu$RH)] <- 0.0000
airqu$AH[is.na(airqu$AH)] <- 0.0000
kable(head(airqu))| Date | Time | CO.GT. | PT08.S1.CO. | NMHC.GT. | C6H6.GT. | PT08.S2.NMHC. | NOx.GT. | PT08.S3.NOx. | NO2.GT. | PT08.S4.NO2. | PT08.S5.O3. | T | RH | AH |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2004-03-10 | 1899-12-30 18:00:00 | 2.6 | 1360.00 | 150 | 11.881723 | 1045.50 | 166 | 1056.25 | 113 | 1692.00 | 1267.50 | 13.600 | 48.875 | 0.7577538 |
| 2004-03-10 | 1899-12-30 19:00:00 | 2.0 | 1292.25 | 112 | 9.397165 | 954.75 | 103 | 1173.75 | 92 | 1558.75 | 972.25 | 13.300 | 47.700 | 0.7254874 |
| 2004-03-10 | 1899-12-30 20:00:00 | 2.2 | 1402.00 | 88 | 8.997817 | 939.25 | 131 | 1140.00 | 114 | 1554.50 | 1074.00 | 11.900 | 53.975 | 0.7502391 |
| 2004-03-10 | 1899-12-30 21:00:00 | 2.2 | 1375.50 | 80 | 9.228796 | 948.25 | 172 | 1092.00 | 122 | 1583.75 | 1203.25 | 11.000 | 60.000 | 0.7867125 |
| 2004-03-10 | 1899-12-30 22:00:00 | 1.6 | 1272.25 | 51 | 6.518224 | 835.50 | 131 | 1205.00 | 116 | 1490.00 | 1110.00 | 11.150 | 59.575 | 0.7887942 |
| 2004-03-10 | 1899-12-30 23:00:00 | 1.2 | 1197.00 | 38 | 4.741012 | 750.25 | 89 | 1336.50 | 96 | 1393.00 | 949.25 | 11.175 | 59.175 | 0.7847717 |
colnames(airqu)[1] <- "date"
colnames(airqu)[2] <- "time"
colnames(airqu)[3] <- "co"
colnames(airqu)[4] <- "tin_oxide"
colnames(airqu)[5] <- "hydrocarbon"
colnames(airqu)[6] <- "benzene"
colnames(airqu)[7] <- "titania"
colnames(airqu)[8] <- "nitroge_oxide"
colnames(airqu)[9] <- "tungsten-oxide"
colnames(airqu)[10] <- "no2"
colnames(airqu)[11] <- "tungsten_oxide_o2"
colnames(airqu)[12] <- "indium_oxide"
colnames(airqu)[13] <- "temp_ac"
colnames(airqu)[14] <- "rh"
colnames(airqu)[15] <- "ah"
kable(head(airqu))| date | time | co | tin_oxide | hydrocarbon | benzene | titania | nitroge_oxide | tungsten-oxide | no2 | tungsten_oxide_o2 | indium_oxide | temp_ac | rh | ah |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2004-03-10 | 1899-12-30 18:00:00 | 2.6 | 1360.00 | 150 | 11.881723 | 1045.50 | 166 | 1056.25 | 113 | 1692.00 | 1267.50 | 13.600 | 48.875 | 0.7577538 |
| 2004-03-10 | 1899-12-30 19:00:00 | 2.0 | 1292.25 | 112 | 9.397165 | 954.75 | 103 | 1173.75 | 92 | 1558.75 | 972.25 | 13.300 | 47.700 | 0.7254874 |
| 2004-03-10 | 1899-12-30 20:00:00 | 2.2 | 1402.00 | 88 | 8.997817 | 939.25 | 131 | 1140.00 | 114 | 1554.50 | 1074.00 | 11.900 | 53.975 | 0.7502391 |
| 2004-03-10 | 1899-12-30 21:00:00 | 2.2 | 1375.50 | 80 | 9.228796 | 948.25 | 172 | 1092.00 | 122 | 1583.75 | 1203.25 | 11.000 | 60.000 | 0.7867125 |
| 2004-03-10 | 1899-12-30 22:00:00 | 1.6 | 1272.25 | 51 | 6.518224 | 835.50 | 131 | 1205.00 | 116 | 1490.00 | 1110.00 | 11.150 | 59.575 | 0.7887942 |
| 2004-03-10 | 1899-12-30 23:00:00 | 1.2 | 1197.00 | 38 | 4.741012 | 750.25 | 89 | 1336.50 | 96 | 1393.00 | 949.25 | 11.175 | 59.175 | 0.7847717 |
We will now connect R with MySql database.
mysql = dbConnect(MySQL(), user='root', password='oracle', dbname='world', host='localhost') # This connects the R with MySQL. Note that the login entities may be different from your login details, kindly adjust as neccesary.We would like to view the list of database(s) which are already in MySQL database.
class(mysql)## [1] "MySQLConnection"
## attr(,"package")
## [1] "RMySQL"dbListTables(mysql)## [1] "airqu" "airqualityuci" "city" "country"
## [5] "countrylanguage" "flights"Dropping and adding of table if they already exist to give access to the new table to be created.
dbSendQuery(mysql, 'drop table if exists airqu')## <MySQLResult:0,0,1>dbWriteTable(conn=mysql, name='airqu', value=airqu)## [1] TRUEdbListFields(mysql, 'airqualityuci')## [1] "row_names" "Date" "Time"
## [4] "co" "tin_oxide" "hydrocarbon"
## [7] "benzene" "titania" "nitroge_oxide"
## [10] "tungsten.oxide" "no2" "tungsten_oxide_o2"
## [13] "indium_oxide" "temp_ac" "rh"
## [16] "ah"We can now read and access the newly created table in R from MySQL directly.
airqualityuci <- dbReadTable(conn=mysql, name='airqu')
write.table(airqualityuci, file = "airqualityuci.csv",row.names=FALSE, na="",col.names=TRUE, sep=",")Attribute Information :
- Date: Date (DD/MM/YYYY)
Time: Time (HH.MM.SS)
co: True hourly averaged concentration CO in mg/m^3
tin_oxide: PT08.S1 (tin oxide) hourly averaged sensor response (nominally CO targeted)
hydrocarbon: True hourly averaged overall Non Metanic HydroCarbons concentration in microg/m^3 (reference analyzer)
benzene: True hourly averaged Benzene concentration in microg/m^3 (reference analyzer)
titania: PT08.S2 (titania) hourly averaged sensor response (nominally NMHC targeted)
nitroge_oxide: True hourly averaged NOx concentration in ppb (reference analyzer)
tungsten_oxide: PT08.S3 (tungsten oxide) hourly averaged sensor response (nominally NOx targeted)
no2: True hourly averaged NO2 concentration in microg/m^3 (reference analyzer)
tungsten_oxide2: PT08.S4 (tungsten oxide) hourly averaged sensor response (nominally NO2 targeted)
indium_oxide: PT08.S5 (indium oxide) hourly averaged sensor response (nominally O3 targeted)
temp_ac: Temperature in °C
rh: Relative Humidity (%)
ah: AH Absolute Humidit
** we are going to randomly sample 900 (Less than 10%) observations from the total dataset.**
airqualityuci <- airqualityuci[sample(nrow(airqualityuci), 900), ]
dim(airqualityuci)## [1] 900 15str(airqualityuci)## 'data.frame': 900 obs. of 15 variables:
## $ date : chr "1094083200" "1101427200" "1100217600" "1096416000" ...
## $ time : chr "-2209161600" "-2209129200" "-2209161600" "-2209158000" ...
## $ co : num 2 5.8 1.2 0.9 2.5 0.5 0.7 4 1.5 2.7 ...
## $ tin_oxide : num 1060 1521 932 872 1171 ...
## $ hydrocarbon : num -200 -200 -200 -200 -200 -200 -200 -200 -200 -200 ...
## $ benzene : num 11.41 26.63 4.53 4.14 12.98 ...
## $ titania : num 1029 1470 740 718 1083 ...
## $ nitroge_oxide : num 242 960 167 106 390 ...
## $ tungsten.oxide : num 622 456 926 980 694 ...
## $ no2 : num 126 149 92 71 96 50.7 78.4 127 103 126 ...
## $ tungsten_oxide_o2: num 1663 1857 1180 1223 1758 ...
## $ indium_oxide : num 1210 1726 774 872 1276 ...
## $ temp_ac : num 24.3 10.6 12.9 16.3 22.9 ...
## $ rh : num 44.7 72.7 69.9 56.8 59.1 ...
## $ ah : num 1.343 0.927 1.037 1.047 1.633 ...summary(airqualityuci)## date time co tin_oxide
## Length:900 Length:900 Min. :-200.00 Min. :-200.0
## Class :character Class :character 1st Qu.: 0.50 1st Qu.: 909.6
## Mode :character Mode :character Median : 1.40 Median :1049.5
## Mean : -36.97 Mean :1030.8
## 3rd Qu.: 2.40 3rd Qu.:1204.8
## Max. : 10.20 Max. :1982.2
## hydrocarbon benzene titania nitroge_oxide
## Min. :-200.0 Min. :-200.000 Min. :-200.0 Min. :-200.0
## 1st Qu.:-200.0 1st Qu.: 3.856 1st Qu.: 702.7 1st Qu.: 44.0
## Median :-200.0 Median : 7.701 Median : 886.8 Median : 132.1
## Mean :-164.4 Mean : 1.465 Mean : 875.1 Mean : 160.8
## 3rd Qu.:-200.0 3rd Qu.: 13.237 3rd Qu.:1091.6 3rd Qu.: 265.1
## Max. : 880.0 Max. : 49.492 Max. :1958.8 Max. :1369.0
## tungsten.oxide no2 tungsten_oxide_o2 indium_oxide
## Min. :-200.0 Min. :-200.00 Min. :-200 Min. :-200.0
## 1st Qu.: 651.9 1st Qu.: 49.75 1st Qu.:1169 1st Qu.: 663.9
## Median : 806.9 Median : 92.00 Median :1436 Median : 933.6
## Mean : 802.7 Mean : 54.35 Mean :1374 Mean : 952.1
## 3rd Qu.: 966.2 3rd Qu.: 129.15 3rd Qu.:1649 3rd Qu.:1219.4
## Max. :2047.0 Max. : 288.00 Max. :2536 Max. :2385.5
## temp_ac rh ah
## Min. :-200.000 Min. :-200.00 Min. :-200.0000
## 1st Qu.: 11.238 1st Qu.: 34.05 1st Qu.: 0.7186
## Median : 16.350 Median : 48.40 Median : 0.9729
## Mean : 9.823 Mean : 39.58 Mean : -6.7912
## 3rd Qu.: 24.431 3rd Qu.: 63.20 3rd Qu.: 1.2935
## Max. : 44.350 Max. : 86.53 Max. : 2.2310What recommendations has the federal government made to protect human health?
….EPA estimates that 10 ppb benzene in drinking water that is consumed regularly or exposure to 0.4 ppb in air over a lifetime could cause a risk of one additional cancer case for every 100,000 exposed persons……
- The underlisted output displays the date, time of benzene with ppb greater than the safely regulated ppb for benzene.
mysqlquery <- dbGetQuery(mysql, "SELECT Date, Time, benzene
FROM airqu
WHERE benzene IN (SELECT benzene
FROM airqu
WHERE benzene > 10)")
kable(head(mysqlquery))| Date | Time | benzene |
|---|---|---|
| 1078876800 | -2209096800 | 11.88172 |
| 1078963200 | -2209111200 | 11.53901 |
| 1078963200 | -2209100400 | 11.15158 |
| 1078963200 | -2209096800 | 20.79922 |
| 1078963200 | -2209093200 | 27.35981 |
| 1078963200 | -2209089600 | 24.01776 |
No wonder! The EPA has classified benzene as a Group A, known human carcinogen!
MONGODB —A NO-SQL
- use this query from your cmd shell:
mongoimport –db world –collection airqualityuci –type csv –file“c:.csv” –headerline
- Adjust the file location accordingly
mongo_conn <- mongo.create() # createing a MongoDB connection
mongo.is.connected(mongo_conn) # checking if the mongo is connected## [1] TRUEif(mongo.is.connected(mongo_conn) == TRUE) {
mongo.get.databases(mongo_conn)
}## [1] "database" "flights" "hockey" "world"if(mongo.is.connected(mongo_conn) == TRUE) {
db <- "world"
mongo.get.database.collections(mongo_conn, db)
}## character(0)mongo_conn = mongo(collection = "airqualityuci", db = "world")
mongo_conn$insert(airqualityuci) # Insert the airqualityuci into mongodb collection##
Complete! Processed total of 900 rows.## [1] TRUEplot(airqualityuci$temp_ac, airqualityuci$benzene, main = "Scatter Plot", xlab = "Temperature", ylab = "Benzene")
abline(lm(airqualityuci$temp_ac~airqualityuci$benzene), col = "blue");
cor(airqualityuci$temp_ac, airqualityuci$benzene)## [1] 0.9713017temp_co <- lm(temp_ac ~ benzene, data=airqualityuci)
summary.lm(temp_co)##
## Call:
## lm(formula = temp_ac ~ benzene, data = airqualityuci)
##
## Residuals:
## Min 1Q Median 3Q Max
## -45.602 -5.712 -0.020 6.493 27.833
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.330640 0.342555 24.32 <2e-16 ***
## benzene 1.018777 0.008325 122.37 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.27 on 898 degrees of freedom
## Multiple R-squared: 0.9434, Adjusted R-squared: 0.9434
## F-statistic: 1.498e+04 on 1 and 898 DF, p-value: < 2.2e-16plot(x=temp_co$residuals, y=temp_co$benzene)
abline(h = 0, lty = 3, col = "blue")
hist(temp_co$residuals)
airqual <- subset(airqualityuci, select=c(co, tin_oxide, hydrocarbon, benzene, titania, nitroge_oxide, tungsten.oxide, no2, tungsten_oxide_o2, indium_oxide, temp_ac, rh, ah ))
plot(airqual)
We are going to do a Multiple Linear Regression model. But, we will want to choose the best model for our prediction.
\({ Y }\quad =\quad { B }_{ 0 }\quad +\quad { B }_{ 1 }{ X }_{ 1 }\quad +\quad { B }_{ 2 }{ X }_{ 2 }\quad +\quad\) ………+\(\quad { B }_{ n }{ X }_{ n }\quad\) +\(\quad { e}\\\)
SETTING UP HYPOTHESIS: # 1
Null Hypothesis: The population parameters(means) are the same
\(H_o:\) \(\mu_1\) = \(\mu_2\) = \(\mu_3\)…..= \(\mu_n\)
Alternative Hythesis: Not \(H_o\)
\(H_a:\) Not \(H_o\) : \(\mu_1\) \(\neq\) \(\mu_2\) \(\neq\) \(\mu_3\)…..\(\neq\) \(\mu_n\)
Rejection:
Reject \(H_o\) (Null Hypothesis) if the calculated value (P-Value) is less that the tabulated value(Table value = 0.05 ), otherwise do not reject \(H_o\)
- Underlisted are the best variables for the model, and analysis would be made on them.
modelselection <- lm(temp_ac ~ tin_oxide+hydrocarbon+benzene+titania+nitroge_oxide+tungsten.oxide+no2+tungsten_oxide_o2+indium_oxide+co+rh+ah, data=airqual)
stepwise <- step(modelselection, direction = "both") # Model Selection using both FORWARD AND BACKWARD selection.## Start: AIC=2001.43
## temp_ac ~ tin_oxide + hydrocarbon + benzene + titania + nitroge_oxide +
## tungsten.oxide + no2 + tungsten_oxide_o2 + indium_oxide +
## co + rh + ah
##
## Df Sum of Sq RSS AIC
## - tin_oxide 1 9.1 8090.4 2000.4
## - co 1 17.6 8098.9 2001.4
## <none> 8081.3 2001.4
## - titania 1 202.6 8284.0 2021.7
## - no2 1 292.0 8373.4 2031.4
## - nitroge_oxide 1 371.1 8452.4 2039.8
## - indium_oxide 1 532.7 8614.0 2056.9
## - tungsten.oxide 1 732.2 8813.5 2077.5
## - hydrocarbon 1 1219.3 9300.7 2125.9
## - benzene 1 2427.0 10508.4 2235.8
## - ah 1 13361.4 21442.8 2877.7
## - tungsten_oxide_o2 1 14312.4 22393.7 2916.7
## - rh 1 15167.0 23248.3 2950.4
##
## Step: AIC=2000.44
## temp_ac ~ hydrocarbon + benzene + titania + nitroge_oxide + tungsten.oxide +
## no2 + tungsten_oxide_o2 + indium_oxide + co + rh + ah
##
## Df Sum of Sq RSS AIC
## <none> 8090.4 2000.4
## - co 1 18.2 8108.7 2000.5
## + tin_oxide 1 9.1 8081.3 2001.4
## - titania 1 281.7 8372.1 2029.2
## - no2 1 289.1 8379.6 2030.0
## - nitroge_oxide 1 371.6 8462.0 2038.8
## - indium_oxide 1 571.1 8661.6 2059.8
## - tungsten.oxide 1 723.7 8814.1 2075.5
## - hydrocarbon 1 1231.7 9322.1 2126.0
## - benzene 1 2537.2 10627.7 2243.9
## - ah 1 13690.5 21780.9 2889.8
## - tungsten_oxide_o2 1 14502.7 22593.1 2922.7
## - rh 1 17193.7 25284.1 3024.0summary(stepwise)##
## Call:
## lm(formula = temp_ac ~ hydrocarbon + benzene + titania + nitroge_oxide +
## tungsten.oxide + no2 + tungsten_oxide_o2 + indium_oxide +
## co + rh + ah, data = airqual)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.0612 -1.9755 0.1464 1.8602 12.1700
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.8150246 1.1167344 2.521 0.0119 *
## hydrocarbon -0.0103517 0.0008903 -11.627 < 2e-16 ***
## benzene -1.0401703 0.0623307 -16.688 < 2e-16 ***
## titania 0.0112008 0.0020145 5.560 3.57e-08 ***
## nitroge_oxide 0.0066334 0.0010387 6.386 2.74e-10 ***
## tungsten.oxide -0.0049917 0.0005601 -8.912 < 2e-16 ***
## no2 -0.0105469 0.0018722 -5.633 2.37e-08 ***
## tungsten_oxide_o2 0.0247435 0.0006202 39.897 < 2e-16 ***
## indium_oxide -0.0053875 0.0006805 -7.917 7.21e-15 ***
## co 0.0026057 0.0018412 1.415 0.1574
## rh -0.3096226 0.0071273 -43.442 < 2e-16 ***
## ah 2.3536728 0.0607178 38.764 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.018 on 888 degrees of freedom
## Multiple R-squared: 0.9952, Adjusted R-squared: 0.9951
## F-statistic: 1.663e+04 on 11 and 888 DF, p-value: < 2.2e-16- We will like to further test by using another statistical tool called Analysis of Variance (ANOVA)
ANALYSIS OF VARIANCE (ANOVA)
anova(stepwise, test= "F")## Analysis of Variance Table
##
## Response: temp_ac
## Df Sum Sq Mean Sq F value Pr(>F)
## hydrocarbon 1 1728 1728 1.8968e+02 <2e-16 ***
## benzene 1 1579793 1579793 1.7340e+05 <2e-16 ***
## titania 1 17270 17270 1.8955e+03 <2e-16 ***
## nitroge_oxide 1 15927 15927 1.7481e+03 <2e-16 ***
## tungsten.oxide 1 1071 1071 1.1752e+02 <2e-16 ***
## no2 1 9132 9132 1.0023e+03 <2e-16 ***
## tungsten_oxide_o2 1 12744 12744 1.3987e+03 <2e-16 ***
## indium_oxide 1 5798 5798 6.3636e+02 <2e-16 ***
## co 1 15 15 1.6648e+00 0.1973
## rh 1 8991 8991 9.8684e+02 <2e-16 ***
## ah 1 13690 13690 1.5027e+03 <2e-16 ***
## Residuals 888 8090 9
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1confint(stepwise)## 2.5 % 97.5 %
## (Intercept) 0.623277993 5.006771200
## hydrocarbon -0.012099085 -0.008604343
## benzene -1.162503038 -0.917837527
## titania 0.007247048 0.015154553
## nitroge_oxide 0.004594774 0.008672034
## tungsten.oxide -0.006090906 -0.003892402
## no2 -0.014221378 -0.006872474
## tungsten_oxide_o2 0.023526332 0.025960701
## indium_oxide -0.006722946 -0.004051988
## co -0.001007918 0.006219285
## rh -0.323611008 -0.295634221
## ah 2.234505597 2.472840022The Error Term or Residual
- We are going to check the distribution of the residuals with normal dataset distribution to determine the stochastics difference between the expected value and the observed value.
residual_temp = data.frame(Fitted = fitted(stepwise),
Residuals = resid(stepwise), Treatment = airqual$temp_ac)
residual_benzene = data.frame(Fitted = fitted(stepwise),
Residuals = resid(stepwise), Treatment = airqual$benzene)
ggplot(residual_temp, aes(Fitted, Residuals, colour = Treatment)) + geom_point()
ggplot(residual_benzene, aes(Fitted, Residuals, colour = Treatment)) + geom_point()
Decision & Conclusion:
From the above multiple regression analysis and ANOVA, we found that the P-value is actually low compare to the Table value (0.05), we therefor reject \(H_o\) (Null hypothesis) and conclude that there is/are difference(s) between the variables.
SECOND DATASET WAS EXTRACTED FROM THE WORLD BANK WEBSITE AS A .XLS FILE
This dataset contains historical temperature extracted from the Climate Research Unit (Mitchell et al, 2003), aggregated to the country and basin levels. The dataset time is from 1961-1999.
Country_temperatureCRU: mean monthly and annual temperatures by country for the period 1961-1999. Values are in degrees Celsius.
http://databank.worldbank.org/data/download/catalog/cckp_historical_data_0.xls
we will like to compare the dataset with the above airquality analysis.
suppressMessages(library(dplyr))
dataset2 <- read.xlsx("C:/Users/mayowa/Documents/cckp_historical_data_0.xls", sheetIndex=4,
startRow=NULL, endRow=179, colIndex=NULL,
as.data.frame=TRUE, header=TRUE,
keepFormulas=FALSE)
str(dataset2)## 'data.frame': 178 obs. of 14 variables:
## $ ISO_3DIGIT : Factor w/ 178 levels "AFG","AGO","ALB",..: 1 2 3 4 5 6 7 8 9 10 ...
## $ Jan_Temp : num 0.0731 22.5822 2.0231 18.4275 20.8035 ...
## $ Feb_temp : num 2.11 22.68 3.22 19.43 19.9 ...
## $ Mar_temp : num 7.6 22.78 6.04 22.61 17.51 ...
## $ Apr_Temp : num 13.37 22.35 9.92 26.58 14.05 ...
## $ May_temp : num 18.2 20.7 14.4 30.6 10.6 ...
## $ Jun_Temp : num 23.2 18.37 17.93 32.46 7.66 ...
## $ July_Temp : num 25.26 17.95 20.54 33.8 7.42 ...
## $ Aug_Temp : num 23.77 19.9 20.48 33.55 9.02 ...
## $ Sept_temp : num 19 22.2 17.2 31.7 11.5 ...
## $ Oct_temp : num 13 23.2 12.3 28.3 14.7 ...
## $ Nov_Temp : num 7 22.79 7.58 24.06 17.54 ...
## $ Dec_temp : num 2.43 22.61 3.65 20.28 19.83 ...
## $ Annual_temp: num 12.9 21.5 11.3 26.8 14.2 ...kable(summary(dataset2))| ISO_3DIGIT | Jan_Temp | Feb_temp | Mar_temp | Apr_Temp | May_temp | Jun_Temp | July_Temp | Aug_Temp | Sept_temp | Oct_temp | Nov_Temp | Dec_temp | Annual_temp | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AFG : 1 | Min. :-26.9967 | Min. :-24.725 | Min. :-18.717 | Min. :-14.249 | Min. :-6.319 | Min. : 0.07677 | Min. : 2.02 | Min. : 2.583 | Min. :-2.336 | Min. :-8.36 | Min. :-17.638 | Min. :-24.074 | Min. :-9.143 | |
| AGO : 1 | 1st Qu.: 0.1473 | 1st Qu.: 2.092 | 1st Qu.: 5.265 | 1st Qu.: 9.689 | 1st Qu.:14.050 | 1st Qu.:16.36776 | 1st Qu.:18.05 | 1st Qu.:18.455 | 1st Qu.:15.333 | 1st Qu.:10.85 | 1st Qu.: 5.953 | 1st Qu.: 2.041 | 1st Qu.:10.091 | |
| ALB : 1 | Median : 19.2529 | Median : 20.492 | Median : 21.995 | Median : 22.028 | Median :21.907 | Median :22.99741 | Median :22.98 | Median :23.314 | Median :22.598 | Median :22.49 | Median : 21.282 | Median : 20.043 | Median :21.582 | |
| ARE : 1 | Mean : 12.8916 | Mean : 13.879 | Mean : 15.935 | Mean : 18.241 | Mean :20.160 | Mean :21.34465 | Mean :22.01 | Mean :21.941 | Mean :20.757 | Mean :18.70 | Mean : 15.992 | Mean : 13.729 | Mean :17.965 | |
| ARG : 1 | 3rd Qu.: 24.2336 | 3rd Qu.: 24.821 | 3rd Qu.: 25.333 | 3rd Qu.: 25.633 | 3rd Qu.:25.898 | 3rd Qu.:26.01320 | 3rd Qu.:26.05 | 3rd Qu.:26.057 | 3rd Qu.:25.772 | 3rd Qu.:25.32 | 3rd Qu.: 24.545 | 3rd Qu.: 23.983 | 3rd Qu.:25.046 | |
| ARM : 1 | Max. : 27.7845 | Max. : 29.088 | Max. : 30.629 | Max. : 32.055 | Max. :33.062 | Max. :34.72038 | Max. :36.25 | Max. :35.878 | Max. :32.778 | Max. :29.55 | Max. : 27.473 | Max. : 27.302 | Max. :28.300 | |
| (Other):172 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
we are going to sample 178 observations from the 1st dataset to match with the second dataset to avoid bias.
SETTING UP HYPOTHESIS: # 2
Null Hypothesis: There is no difference between means temperature in dataset 1 and dataset 2
\(H_o:\) \(\mu_1\) = \(\mu_2\) = \(\mu_3\)…..= \(\mu_n\)
Alternative Hythesis:
\(H_a:\) Not \(H_o:\) \(\mu_1\) \(\neq\) \(\mu_2\) \(\neq\) \(\mu_3\)…..\(\neq\) \(\mu_n\)
Rejection:
Reject \(H_o\) (Null Hypothesis) if the calculated value (P-Value) is less that the tabulated value(Table value = 0.05 ), otherwise do not reject \(H_o\)
Decision:
We therefore Accept \(H_o\), since calculated calculated value (P-Value) is greater than the tabulated value(Table value = 0.05 )
sample1 <- airqual[sample(nrow(airqual), 178), ]
dim(sample1)## [1] 178 13temp_2 <- lm(sample1$temp_ac ~ dataset2$Annual_temp)
summary.lm(temp_2)##
## Call:
## lm(formula = sample1$temp_ac ~ dataset2$Annual_temp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -213.093 0.661 5.772 13.928 28.177
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 17.4049 7.0242 2.478 0.0142 *
## dataset2$Annual_temp -0.3337 0.3526 -0.946 0.3453
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 40.48 on 176 degrees of freedom
## Multiple R-squared: 0.005061, Adjusted R-squared: -0.0005919
## F-statistic: 0.8953 on 1 and 176 DF, p-value: 0.3453cor.test(sample1$temp_ac, dataset2$Annual_temp, method = c("pearson", "kendall", "spearman"),
exact = NULL, conf.level = 0.95, continuity = FALSE)##
## Pearson's product-moment correlation
##
## data: sample1$temp_ac and dataset2$Annual_temp
## t = -0.9462, df = 176, p-value = 0.3453
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.21596693 0.07674566
## sample estimates:
## cor
## -0.0711421anova(temp_2)## Analysis of Variance Table
##
## Response: sample1$temp_ac
## Df Sum Sq Mean Sq F value Pr(>F)
## dataset2$Annual_temp 1 1467 1466.9 0.8953 0.3453
## Residuals 176 288371 1638.5DATASET THREE(3)
- The dataset is a Leukemia incident rate collected from the Center for Diseases Control and Prevention Website for 49 US States…..
** Data Source:**
SETTING UP HYPOTHESIS: # 3
Null Hypothesis: There is no relationship between benzene in dataset 1 and and the average incident in dataset 3
\(H_o:\) \(\mu_1\) = \(\mu_2\) = \(\mu_3\)…..= \(\mu_n\)
Alternative Hythesis:
\(H_a:\) Not \(H_o:\) \(\mu_1\) \(\neq\) \(\mu_2\) \(\neq\) \(\mu_3\)…..\(\neq\) \(\mu_n\)
Rejection:
Reject \(H_o\) (Null Hypothesis) if the calculated value (P-Value) is less than the tabulated value(Table value = 0.05 ), otherwise do not reject \(H_o\)
library(plyr)
incd <- read.csv("https://raw.githubusercontent.com/mascotinme/MSDA-IS607/master/incd.csv", sep = ",", header = TRUE, skip = 8)
str(incd)## 'data.frame': 75 obs. of 10 variables:
## $ State : Factor w/ 71 levels "","# Data do not include cases diagnosed in other states for those states in which the data exchange agreement specifically prohib"| __truncated__,..: 64 70 41 37 29 33 50 52 44 34 ...
## $ FIPS : int 0 55000 27000 23000 16000 19000 36000 38000 30000 20000 ...
## $ Age.Adjusted.Incidence.Rate......cases.per.100.000: Factor w/ 35 levels "","¶¶ ","10.2",..: 17 35 34 33 32 31 30 29 28 27 ...
## $ Lower.95..Confidence.Interval : Factor w/ 35 levels "","¶¶","10","10.4",..: 22 34 33 32 30 31 32 26 27 29 ...
## $ Upper.95..Confidence.Interval : Factor w/ 36 levels ""," ¶¶","11",..: 15 36 34 35 32 30 28 33 31 29 ...
## $ Average.Annual.Count : Factor w/ 53 levels "","¶¶","1005",..: 30 4 52 20 19 35 27 6 14 31 ...
## $ Recent.Trend : Factor w/ 5 levels "","¶¶","falling",..: 5 5 5 5 5 5 5 5 5 5 ...
## $ Recent.5.Year.Trend.....in.Incidence.Rates : Factor w/ 38 levels "","-0.1","-0.3",..: 15 2 32 17 6 15 26 12 33 28 ...
## $ Lower.95..Confidence.Interval.1 : Factor w/ 43 levels "","-0.1","-0.3",..: 7 22 16 34 10 3 20 35 19 2 ...
## $ Upper.95..Confidence.Interval.1 : Factor w/ 43 levels "","-0.1","¶¶",..: 7 25 43 40 38 5 37 8 12 29 ...# Rename the column names for easy accesibility
incd$Average.Annual.Count <- as.numeric(incd$Average.Annual.Count)
names(incd) <- c("state", "FIPS", "adj_age_100000", "lower_Adj_CI", "upper_Adj_CI", "avg_annual_count", "Recent.Trend", "5years_rate", "Lower_5Yrs_CI", "upper_5Yrs_CI")
# We are going to seperate the rows(Stable, Rising and Falling)
str(incd)## 'data.frame': 75 obs. of 10 variables:
## $ state : Factor w/ 71 levels "","# Data do not include cases diagnosed in other states for those states in which the data exchange agreement specifically prohib"| __truncated__,..: 64 70 41 37 29 33 50 52 44 34 ...
## $ FIPS : int 0 55000 27000 23000 16000 19000 36000 38000 30000 20000 ...
## $ adj_age_100000 : Factor w/ 35 levels "","¶¶ ","10.2",..: 17 35 34 33 32 31 30 29 28 27 ...
## $ lower_Adj_CI : Factor w/ 35 levels "","¶¶","10","10.4",..: 22 34 33 32 30 31 32 26 27 29 ...
## $ upper_Adj_CI : Factor w/ 36 levels ""," ¶¶","11",..: 15 36 34 35 32 30 28 33 31 29 ...
## $ avg_annual_count: num 30 4 52 20 19 35 27 6 14 31 ...
## $ Recent.Trend : Factor w/ 5 levels "","¶¶","falling",..: 5 5 5 5 5 5 5 5 5 5 ...
## $ 5years_rate : Factor w/ 38 levels "","-0.1","-0.3",..: 15 2 32 17 6 15 26 12 33 28 ...
## $ Lower_5Yrs_CI : Factor w/ 43 levels "","-0.1","-0.3",..: 7 22 16 34 10 3 20 35 19 2 ...
## $ upper_5Yrs_CI : Factor w/ 43 levels "","-0.1","¶¶",..: 7 25 43 40 38 5 37 8 12 29 ...kable(head(incd))| state | FIPS | adj_age_100000 | lower_Adj_CI | upper_Adj_CI | avg_annual_count | Recent.Trend | 5years_rate | Lower_5Yrs_CI | upper_5Yrs_CI |
|---|---|---|---|---|---|---|---|---|---|
| US (SEER+NPCR)(1,10) | 0 | 13.2 | 13.1 | 13.2 | 30 | stable | 0 | -1.3 | 1.2 |
| Wisconsin(6,10) | 55000 | 16.5 | 16.1 | 17 | 4 | stable | -0.1 | -3.6 | 3.6 |
| Minnesota(6,10) | 27000 | 16 | 15.5 | 16.4 | 52 | stable | 3.4 | -2.7 | 9.8 |
| Maine(6,10) | 23000 | 15.7 | 14.8 | 16.6 | 20 | stable | 0.3 | -8 | 9.2 |
| Idaho(6,10) | 16000 | 15.3 | 14.4 | 16.2 | 19 | stable | -1.7 | -10.4 | 7.7 |
| Iowa(3,8) | 19000 | 15.2 | 14.6 | 15.8 | 35 | stable | 0 | -0.3 | 0.3 |
stable <- subset(incd, incd$Recent.Trend == "stable")
rising <- subset(incd, incd$Recent.Trend == "rising")
falling <- subset(incd, incd$Recent.Trend == "falling")
kable(head(stable))| state | FIPS | adj_age_100000 | lower_Adj_CI | upper_Adj_CI | avg_annual_count | Recent.Trend | 5years_rate | Lower_5Yrs_CI | upper_5Yrs_CI |
|---|---|---|---|---|---|---|---|---|---|
| US (SEER+NPCR)(1,10) | 0 | 13.2 | 13.1 | 13.2 | 30 | stable | 0 | -1.3 | 1.2 |
| Wisconsin(6,10) | 55000 | 16.5 | 16.1 | 17 | 4 | stable | -0.1 | -3.6 | 3.6 |
| Minnesota(6,10) | 27000 | 16 | 15.5 | 16.4 | 52 | stable | 3.4 | -2.7 | 9.8 |
| Maine(6,10) | 23000 | 15.7 | 14.8 | 16.6 | 20 | stable | 0.3 | -8 | 9.2 |
| Idaho(6,10) | 16000 | 15.3 | 14.4 | 16.2 | 19 | stable | -1.7 | -10.4 | 7.7 |
| Iowa(3,8) | 19000 | 15.2 | 14.6 | 15.8 | 35 | stable | 0 | -0.3 | 0.3 |
kable(head(rising))| state | FIPS | adj_age_100000 | lower_Adj_CI | upper_Adj_CI | avg_annual_count | Recent.Trend | 5years_rate | Lower_5Yrs_CI | upper_5Yrs_CI | |
|---|---|---|---|---|---|---|---|---|---|---|
| 12 | Connecticut(3,8) | 9000 | 14.7 | 14.2 | 15.2 | 38 | rising | 0.8 | 0.4 | 1.2 |
| 14 | New Jersey(3,8) | 34000 | 14.2 | 13.9 | 14.6 | 9 | rising | 0.4 | 0.1 | 0.6 |
| 24 | Utah(3,8) | 49000 | 13.3 | 12.6 | 14 | 26 | rising | 0.8 | 0.3 | 1.4 |
| 29 | Tennessee(6,10) | 47000 | 13.1 | 12.7 | 13.5 | 50 | rising | 2.6 | 0.1 | 5.2 |
| 34 | Missouri(6,10) | 29000 | 12.7 | 12.3 | 13.1 | 47 | rising | 2.4 | 0.3 | 4.6 |
| 43 | Hawaii(3,8) | 15000 | 12 | 11.2 | 12.8 | 16 | rising | 1.6 | 0.6 | 2.5 |
kable(head(falling))| state | FIPS | adj_age_100000 | lower_Adj_CI | upper_Adj_CI | avg_annual_count | Recent.Trend | 5years_rate | Lower_5Yrs_CI | upper_5Yrs_CI | |
|---|---|---|---|---|---|---|---|---|---|---|
| 37 | California(3,9) | 6000 | 12.5 | 12.4 | 12.7 | 32 | falling | -1.7 | -3.4 | -0.1 |
require(ggplot2)
ggplot(stable, col = "red", aes(x =state, y=round(avg_annual_count,2))) +
geom_bar(stat="identity",position="dodge") +
xlab("States") +
ylab("Average Annual counts") +
ggtitle("Average Annual Stable Leukemia Counts per US States")
ggplot(rising, col = "blue", aes(x =state, y=round(avg_annual_count,2))) +
geom_bar(stat="identity",position="dodge") +
xlab("States") +
ylab("Average Annual counts") +
ggtitle("Average Annual Rising Leukemia Counts per US States")
sample_all1 <- sample1[sample(nrow(sample1), 45), ]
sample_all2 <- dataset2[sample(nrow(dataset2), 45), ]
sample_all3 <- incd[sample(nrow(incd), 45), ]
allsamples <- data.frame(c(sample_all1, sample_all2, sample_all3))
all_dataset_subset <- allsamples[, c("avg_annual_count", "Annual_temp" , "co", "benzene")]
str(all_dataset_subset)## 'data.frame': 45 obs. of 4 variables:
## $ avg_annual_count: num 1 1 36 3 17 30 13 21 1 1 ...
## $ Annual_temp : num 25.06 25.8 26.82 5.03 -9.14 ...
## $ co : num 4.6 -200 0.5 1.1 1.5 1.1 -200 1 1.9 2.3 ...
## $ benzene : num 24.24 1.37 4.09 3.46 7.62 ...linearmodel <- lm(all_dataset_subset$avg_annual_count ~(all_dataset_subset$co + all_dataset_subset$benzene))
linearmodel##
## Call:
## lm(formula = all_dataset_subset$avg_annual_count ~ (all_dataset_subset$co +
## all_dataset_subset$benzene))
##
## Coefficients:
## (Intercept) all_dataset_subset$co
## 21.08803 0.03006
## all_dataset_subset$benzene
## 0.05977anova(linearmodel)## Analysis of Variance Table
##
## Response: all_dataset_subset$avg_annual_count
## Df Sum Sq Mean Sq F value Pr(>F)
## all_dataset_subset$co 1 193.6 193.63 0.6415 0.4277
## all_dataset_subset$benzene 1 306.3 306.35 1.0149 0.3195
## Residuals 42 12677.8 301.85Decision:
We therefore Reject \(H_o\), since calculated calculated value (P-Value) is greater than the tabulated value(Table value = 0.05 )
GENERAL CONCLUSION:
Based on the above analyzes done on the three datasets, we therefore conclude that there are strong relationships between the carbon-monoxide (co), Temperature (temp_ac) and Benzene. Though, the datasets might not be enough to be able to determine the actual causes, and links between the variables, we are strongly confident that a reduction in the exposure to their atmospheric condition (particularly Benzene) may aid in reducing leukemia in the United States and the World at large.
Note: The analysis is not exclusive as some other contributing factor(s) may also needs to be accessed.
REFERENCES: