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data(algae, package="DMwR2")
algae

#Central Tendency Measures: mean, median, and mode
mean(algae$a1)

[1] 16.9235

median(algae$a1)

[1] 6.95

median(algae$a1, na.rm=TRUE)

[1] 6.95

mean(algae$NO3)

[1] NA

mean(algae$NO3, na.rm=TRUE)

[1] 3.282389

median(algae$NO3, na.rm=TRUE)

[1] 2.675

installed.packages("modes")

     Package LibPath Version Priority Depends Imports LinkingTo Suggests Enhances License License_is_FOSS License_restricts_use
     OS_type Archs MD5sum NeedsCompilation Built

library("modes")

Error in library("modes") : there is no package called ‘modes’

library(DMwR2)
centralValue(algae$a1)

[1] 6.95

centralValue(algae$speed)

[1] "high"

#statistics of spread
var(algae$a1)

[1] 455.7532

sd(algae$a1)

[1] 21.34838

range(algae$a1)

[1]  0.0 89.8

max(algae$a1)

[1] 89.8

min(algae$a1)

[1] 0

IQR(algae$a1)

[1] 23.3

quantile(algae$a1)

   0%   25%   50%   75%  100% 
 0.00  1.50  6.95 24.80 89.80 

quantile(algae$a1, probs=c(0.2, 0.8))

  20%   80% 
 1.20 32.18 

# find NAs
nas <- apply(algae, 1, function(r) sum(is.na(r)))

cat("The dataset contains ", sum(nas), "NA values. \n")

The dataset contains  33 NA values. 

cat("The dataset contains ", sum(!complete.cases(algae)), "(out of ", nrow(algae) ,") incomplete rows. \n")

The dataset contains  16 (out of  200 ) incomplete rows. 

#ways to obtain summaries over the entire dataset
summary(algae)

    season       size       speed         mxPH            mnO2              Cl               NO3              NH4          
 autumn:40   large :45   high  :84   Min.   :5.600   Min.   : 1.500   Min.   :  0.222   Min.   : 0.050   Min.   :    5.00  
 spring:53   medium:84   low   :33   1st Qu.:7.700   1st Qu.: 7.725   1st Qu.: 10.981   1st Qu.: 1.296   1st Qu.:   38.33  
 summer:45   small :71   medium:83   Median :8.060   Median : 9.800   Median : 32.730   Median : 2.675   Median :  103.17  
 winter:62                           Mean   :8.012   Mean   : 9.118   Mean   : 43.636   Mean   : 3.282   Mean   :  501.30  
                                     3rd Qu.:8.400   3rd Qu.:10.800   3rd Qu.: 57.824   3rd Qu.: 4.446   3rd Qu.:  226.95  
                                     Max.   :9.700   Max.   :13.400   Max.   :391.500   Max.   :45.650   Max.   :24064.00  
                                     NA's   :1       NA's   :2        NA's   :10        NA's   :2        NA's   :2         
      oPO4             PO4              Chla               a1              a2               a3               a4        
 Min.   :  1.00   Min.   :  1.00   Min.   :  0.200   Min.   : 0.00   Min.   : 0.000   Min.   : 0.000   Min.   : 0.000  
 1st Qu.: 15.70   1st Qu.: 41.38   1st Qu.:  2.000   1st Qu.: 1.50   1st Qu.: 0.000   1st Qu.: 0.000   1st Qu.: 0.000  
 Median : 40.15   Median :103.29   Median :  5.475   Median : 6.95   Median : 3.000   Median : 1.550   Median : 0.000  
 Mean   : 73.59   Mean   :137.88   Mean   : 13.971   Mean   :16.92   Mean   : 7.458   Mean   : 4.309   Mean   : 1.992  
 3rd Qu.: 99.33   3rd Qu.:213.75   3rd Qu.: 18.308   3rd Qu.:24.80   3rd Qu.:11.375   3rd Qu.: 4.925   3rd Qu.: 2.400  
 Max.   :564.60   Max.   :771.60   Max.   :110.456   Max.   :89.80   Max.   :72.600   Max.   :42.800   Max.   :44.600  
 NA's   :2        NA's   :2        NA's   :12                                                                          
       a5               a6               a7        
 Min.   : 0.000   Min.   : 0.000   Min.   : 0.000  
 1st Qu.: 0.000   1st Qu.: 0.000   1st Qu.: 0.000  
 Median : 1.900   Median : 0.000   Median : 1.000  
 Mean   : 5.064   Mean   : 5.964   Mean   : 2.495  
 3rd Qu.: 7.500   3rd Qu.: 6.925   3rd Qu.: 2.400  
 Max.   :44.400   Max.   :77.600   Max.   :31.600  
                                                   

library(Hmisc)
data(iris)
describe(iris)

iris 

 5  Variables      150  Observations
----------------------------------------------------------------------------------------------------------------------------------
Sepal.Length 
       n  missing distinct     Info     Mean      Gmd      .05      .10      .25      .50      .75      .90      .95 
     150        0       35    0.998    5.843   0.9462    4.600    4.800    5.100    5.800    6.400    6.900    7.255 

lowest : 4.3 4.4 4.5 4.6 4.7, highest: 7.3 7.4 7.6 7.7 7.9
----------------------------------------------------------------------------------------------------------------------------------
Sepal.Width 
       n  missing distinct     Info     Mean      Gmd      .05      .10      .25      .50      .75      .90      .95 
     150        0       23    0.992    3.057   0.4872    2.345    2.500    2.800    3.000    3.300    3.610    3.800 

lowest : 2.0 2.2 2.3 2.4 2.5, highest: 3.9 4.0 4.1 4.2 4.4
----------------------------------------------------------------------------------------------------------------------------------
Petal.Length 
       n  missing distinct     Info     Mean      Gmd      .05      .10      .25      .50      .75      .90      .95 
     150        0       43    0.998    3.758    1.979     1.30     1.40     1.60     4.35     5.10     5.80     6.10 

lowest : 1.0 1.1 1.2 1.3 1.4, highest: 6.3 6.4 6.6 6.7 6.9
----------------------------------------------------------------------------------------------------------------------------------
Petal.Width 
       n  missing distinct     Info     Mean      Gmd      .05      .10      .25      .50      .75      .90      .95 
     150        0       22     0.99    1.199   0.8676      0.2      0.2      0.3      1.3      1.8      2.2      2.3 

lowest : 0.1 0.2 0.3 0.4 0.5, highest: 2.1 2.2 2.3 2.4 2.5
----------------------------------------------------------------------------------------------------------------------------------
Species 
       n  missing distinct 
     150        0        3 
                                           
Value          setosa versicolor  virginica
Frequency          50         50         50
Proportion      0.333      0.333      0.333
----------------------------------------------------------------------------------------------------------------------------------

library(dplyr) 
alg <- as_tibble(algae) #the book converted algae to alg, but
identical(alg, algae) #they are identical, so below we use just algae.

[1] TRUE

summarise(algae, avgNO3=mean(NO3, na.rm=TRUE), medA1=median(a1))

select(algae, mxPH:Cl) %>%  summarise_all(list(mean, median), na.rm=TRUE  )

group_by(algae, season, size) %>%
summarise(nobs=n(), mA7=median(a7))

`summarise()` regrouping output by 'season' (override with `.groups` argument)

select(algae, a1:a7) %>% summarise_all(funs(var))

select(algae, a1:a7) %>% summarise_all(c("min", "max"))

data(iris)
group_by(iris, Species) %>% summarise(var=var(Sepal.Length))

`summarise()` ungrouping output (override with `.groups` argument)

# base R’s aggregate() can be helpful for summary functions that don’t return a scalar 
group_by(iris, Species) %>% summarise(var=quantile(Sepal.Length))

`summarise()` regrouping output by 'Species' (override with `.groups` argument)

aggregate(x=iris$Sepal.Length, by=list(Species=iris$Species), FUN="quantile")

NA

aggregate(x=iris[-5], by=list(Species=iris$Species), FUN="quantile")

NA
NA

#base R’s by (). By() applies to data frames
by(data=iris[,1:4], INDICES=iris$Species, FUN=summary)

iris$Species: setosa
  Sepal.Length    Sepal.Width     Petal.Length    Petal.Width   
 Min.   :4.300   Min.   :2.300   Min.   :1.000   Min.   :0.100  
 1st Qu.:4.800   1st Qu.:3.200   1st Qu.:1.400   1st Qu.:0.200  
 Median :5.000   Median :3.400   Median :1.500   Median :0.200  
 Mean   :5.006   Mean   :3.428   Mean   :1.462   Mean   :0.246  
 3rd Qu.:5.200   3rd Qu.:3.675   3rd Qu.:1.575   3rd Qu.:0.300  
 Max.   :5.800   Max.   :4.400   Max.   :1.900   Max.   :0.600  
------------------------------------------------------------------------------------------------- 
iris$Species: versicolor
  Sepal.Length    Sepal.Width     Petal.Length   Petal.Width   
 Min.   :4.900   Min.   :2.000   Min.   :3.00   Min.   :1.000  
 1st Qu.:5.600   1st Qu.:2.525   1st Qu.:4.00   1st Qu.:1.200  
 Median :5.900   Median :2.800   Median :4.35   Median :1.300  
 Mean   :5.936   Mean   :2.770   Mean   :4.26   Mean   :1.326  
 3rd Qu.:6.300   3rd Qu.:3.000   3rd Qu.:4.60   3rd Qu.:1.500  
 Max.   :7.000   Max.   :3.400   Max.   :5.10   Max.   :1.800  
------------------------------------------------------------------------------------------------- 
iris$Species: virginica
  Sepal.Length    Sepal.Width     Petal.Length    Petal.Width   
 Min.   :4.900   Min.   :2.200   Min.   :4.500   Min.   :1.400  
 1st Qu.:6.225   1st Qu.:2.800   1st Qu.:5.100   1st Qu.:1.800  
 Median :6.500   Median :3.000   Median :5.550   Median :2.000  
 Mean   :6.588   Mean   :2.974   Mean   :5.552   Mean   :2.026  
 3rd Qu.:6.900   3rd Qu.:3.175   3rd Qu.:5.875   3rd Qu.:2.300  
 Max.   :7.900   Max.   :3.800   Max.   :6.900   Max.   :2.500  

while (!is.null(dev.list())) dev.off() #close the device

library(ggplot2)
data(algae, package="DMwR2")
freqOcc <- table(algae$season)
barplot(freqOcc, main="Frequency of the Seasons")

ggplot(algae, aes(x=season)) + geom_bar() + ggtitle("Frequency of the Seasons")

theme_update(plot.title = element_text(hjust=0.5))
ggplot(algae, aes(x=season)) + geom_bar() + ggtitle("Frequency of the Seasons")

ggplot(algae, aes(x=season, color=season)) + geom_bar() + ggtitle("Frequency of the Seasons")

ggplot(algae, aes(x=season, fill=season)) + geom_bar() + ggtitle("Frequency of the Seasons")

#continuous variables
hist(algae$mxPH, xlab = "Maximal pH")

ggplot(algae, aes(x=mxPH)) + geom_histogram() + xlab("Maximal pH")

NA
NA

boxplot(algae$mxPH, ylab="Maximal pH")

ggplot(algae, aes(y=mxPH)) + geom_boxplot() + ylab("Maximal pH") + theme(axis.text.x = element_blank())

boxplot(mxPH ~ season, algae, ylab="Maximal pH", xlab="Seasons")

ggplot(algae, aes(x=season, y=mxPH)) + geom_boxplot() + ylab("Maximal pH") + xlab("Seasons")

ggplot(algae, aes(x=a1)) + geom_histogram() + facet_grid(size~speed)

ggplot(algae, aes(x=a1)) + geom_histogram() + facet_grid(.~speed)

ggplot(algae, aes(x=speed, y=a1)) + geom_boxplot() + facet_grid(size~season)

#scatter plots
plot(algae$a1, algae$a2, main="Relationships btw a1 and a2")

ggplot(algae, aes(x=a1, y=a2)) + geom_point() + ggtitle("Relationship btw a1 and a2")

plot(algae$a1, algae$a2, col=algae$season, main="Relationships btw a1 and a2")

ggplot(algae, aes(x=a1, y=a2, color=season)) + geom_point() + ggtitle("Relationship btw a1 and a2")

ggplot(algae, aes(x=a1, y=a2)) + geom_point()+ggtitle("Relationship btw a1 and a2") + facet_grid(.~season)

ggplot(algae, aes(x=a1, y=a2)) + geom_point() + ggtitle("Relationship btw a1 and a2") + facet_wrap(~season)

pairs(algae[, 12:16])

install.packages("GGally")

Error in install.packages : Updating loaded packages

library(GGally)
ggpairs(algae, columns=12:16)
install.packages("GGally")

WARNING: Rtools is required to build R packages but is not currently installed. Please download and install the appropriate version of Rtools before proceeding:

https://cran.rstudio.com/bin/windows/Rtools/

Warning in install.packages :
  package ‘GGally’ is in use and will not be installed

ggpairs(algae, columns=2:5)

#what types of plots are shown and why?
#sine plot, histogram plot, bar plot, box plot, scatter plot
#for size and speed columns the bar plot and the box plot have been applied because these vectors represent discreet variable and the box plot have been used to represent Five-number summary of a distribution, Minimum, Q1, Median, Q3, Maximum
# for mxPH and mnO2 sine plot, histogram plot, and scatter plot have been used which represent continuous variable and sine plot provides information regarding Median, mean and mode of symmetric, positively and negatively skewed data and scatter plot Provides a first look at bivariate numerical data to see clusters of points, outliers, etc

algae

h <- c(3.5, 2.6, 4.0, 3.2, 4.5, 3.3 ) #height values 

length(h)

[1] 6

w <- c(13.5, 12.6, 14.0, 13.2, 14.5, 13.3 ) #weight values 

length(w)

[1] 6

qqplot(h, w) #h and w values are sorted, paired, and then plotted. 
abline(lsfit(h,w)) #fit a line using the least square

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#HW2
x <- c(13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30,
33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70)

result.mean <-  mean(x,na.rm = TRUE)
print(result.mean)

[1] 29.96296

result.median <-  median(x,na.rm = TRUE)
print(result.median)

[1] 25

min(x)

[1] 13

max(x)

[1] 70

mid_rangr=(min(x)+max(x))/2
print(mid_rangr)

[1] 41.5

quantile(x)

  0%  25%  50%  75% 100% 
13.0 20.5 25.0 35.0 70.0 

summary(x)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  13.00   20.50   25.00   29.96   35.00   70.00 

boxplot(x, ylab="age value")

age <- c(23, 23, 27, 27, 39, 41, 47, 49, 50, 52, 54, 54, 56, 57, 58, 58, 60, 61)

fat <- c(9.5, 26.5, 7.8, 17.8, 31.4, 25.9, 27.4, 27.2, 31.2, 34.6, 42.5, 28.8, 33.4, 30.2, 34.1, 32.9, 41.2, 35.7)

result.mean <-  mean(age,na.rm = TRUE)
print(result.mean)

[1] 46.44444

result.mean <-  mean(fat,na.rm = TRUE)
print(result.mean)

[1] 28.78333

result.median <-  median(age,na.rm = TRUE)
print(result.median)

[1] 51

result.median <-  median(fat,na.rm = TRUE)
print(result.median)

[1] 30.7

sd(age)

[1] 13.21862

sd(fat)

[1] 9.254395

boxplot(age, ylab="age value")

boxplot(fat, ylab="%fat value")

plot(fat, age, main="Relationships btw age and %fat")

qqplot(fat, age) 

qqplot(fat, age)  
abline(lsfit(fat,age)) 

x1<-c(1.5,1.7)
x2<-c(2,1.9)
x3<-c(1.6,1.8)
x4<-c(1.2,1.5)
x5<-c(1.5,1)

x6<-c(1.4,1.6)

sqrt(sum((x1-x6)^2))

[1] 0.1414214

sqrt(sum((x2-x6)^2))

[1] 0.6708204

sqrt(sum((x3-x6)^2))

[1] 0.2828427

sqrt(sum((x4-x6)^2))

[1] 0.2236068

sqrt(sum((x5-x6)^2))

[1] 0.6082763