MATH2349 Semester 2, 2018

Assignment 3

Required packages

library(readr)
library(dplyr)
library(tidyr)
library(magrittr)
library(Hmisc)
library(forecast)
library(stringr)
library(lubridate)
library(editrules)

Executive Summary

Two open data sets accidents and weather were joined to create the data frame used for required data preprocessing. Some tidying of the data sets occured before merging. They were filtered to keep only observations for January 2016 to reduce the number of rows as well as the running time. The key variable was created to enable merging the data frames with left join(). Types of variables, data structures and attributes were checked. Data types conversions were performed where necessary. The combined data frame conforms the tidy data principles, so not much was done to tidy it up. Two new variables were mutated from the existing for better understanding of data. Scanning the data for missing values, inconsistencies and obvious errors was performed. Missing values in some numeric variables were removed due to their nature and some were replaced with a mean value. No data inconsistency was found. The numeric variables were scanned for univariate outliers. In some cases the outliers were kept and in some - capped using the Tukey’s method. Data transformation techniques were applied where seemed appropriate.

Data

The accidents data set contains 477732 observations of 29 variables and includes the information about all vehicle collisions in New York City during 2015 and 2016. It was taken from kaggle.com located at https://www.kaggle.com/nypd/vehicle-collisions/home.

The variables are: UNIQUE KEY [integer], DATE [character], TIME [‘hms’ numeric], BOROUGH [character], ZIP CODE [integer], LATITUDE [numeric], LONGITUDE [numeric], LOCATION [character], ON STREET NAME [character], CROSS STREET NAME [character], OFF STREET NAME [character], PERSONS INJURED [integer], PERSONS KILLED [integer], PEDESTRIANS INJURED [integer], PEDESTRIANS KILLED [integer], CYCLISTS INJURED [integer], CYCLISTS KILLED [integer], MOTORISTS INJURED [integer], MOTORISTS KILLED [integer], VEHICLE 1 TYPE [character], VEHICLE 2 TYPE [character], VEHICLE 3 TYPE [character], VEHICLE 4 TYPE [character],VEHICLE 5 TYPE [character], VEHICLE 1 FACTOR [character], VEHICLE 2 FACTOR [character], VEHICLE 3 FACTOR [character], VEHICLE 4 FACTOR [character], VEHICLE 5 FACTOR [character]. Variables like VEHICLE FACTOR refer to the reason this vehicle was involved in an accident. The other variables are self explanatory.

The weather data set contains 5175 observations of 12 variables and includes the information about hourly weather conditions in New York City from January to June 2016. It was taken from kaggle.com located at https://www.kaggle.com/pschale/nyc-taxi-wunderground-weather/home.

The variables are: timestamp [POSIXct], temp [numeric], windspeed [numeric], humidity [numeric], precip [numeric], pressure [numeric], conditions [character], dailyprecip [character], dailysnow [character], fog [integer], rain [integer], snow [integer]. precip and dailyprecip variables refer to precipitation during last hour in inches and the total precipitation during the day respectively. Variables fog, rain and snow: if 1 - current conditions include fog, rain or snow, else 0. The other variables are self explanatory.

accidents <- read_csv("accidents.csv")

Parsed with column specification:
cols(
  .default = col_character(),
  `UNIQUE KEY` = col_integer(),
  TIME = col_time(format = ""),
  `ZIP CODE` = col_integer(),
  LATITUDE = col_double(),
  LONGITUDE = col_double(),
  `PERSONS INJURED` = col_integer(),
  `PERSONS KILLED` = col_integer(),
  `PEDESTRIANS INJURED` = col_integer(),
  `PEDESTRIANS KILLED` = col_integer(),
  `CYCLISTS INJURED` = col_integer(),
  `CYCLISTS KILLED` = col_integer(),
  `MOTORISTS INJURED` = col_integer(),
  `MOTORISTS KILLED` = col_integer()
)
See spec(...) for full column specifications.

head(accidents)

weather <- read_csv("weatherdata.csv")

Parsed with column specification:
cols(
  timestamp = col_datetime(format = ""),
  temp = col_double(),
  windspeed = col_double(),
  humidity = col_double(),
  precip = col_double(),
  pressure = col_double(),
  conditions = col_character(),
  dailyprecip = col_character(),
  dailysnow = col_character(),
  fog = col_integer(),
  rain = col_integer(),
  snow = col_integer()
)

head(weather)

accidents$DATE <- mdy(accidents$DATE)
accidents <- accidents %>% mutate(., year = year(accidents$DATE), 
                                     month = month(accidents$DATE), 
                                     day = day(accidents$DATE), 
                                     hour = hour(accidents$TIME))
accidents <- accidents %>% filter(., year == 2016 & month == 1)
accidents <- accidents %>% unite(key, month, day, hour, sep = "-")
accidents <- accidents[c(1:3, 5, 12:19, 31)]
head(accidents)

weather <- weather %>% mutate(month = month(timestamp), 
                              day = day(timestamp), 
                              hour = hour(timestamp))
weather <-  weather %>% filter(., month == 1)
weather <- weather %>% unite(key, month, day, hour, sep = "-")
tidy_weather <- weather %>% filter(., minute(timestamp) == 51)
head(tidy_weather)

combined <- left_join(accidents, tidy_weather, by = "key")
head(combined)

accidents and weather data sets were joined to create a combined data frame which was used for further processing. Left join was used to match the observations from the weather data frame to the accidents data frame and keep all observations in the latter. Key variable key was mutated to merge the data sets, it was created by uniting month number, day of the month and hour.

Some tidying of the initial data sets was performed before they were merged. The steps were as follows:

• DATE variable was converted from character to a date type with the use of mdy() function.

• Four additional variables were created (year, month, day, hour) by extracting elements from the DATE and TIME variables.

• The accidents data frame was filtered to keep only observations for January 2016, the same was done to the weather data frame. The accidents data was also subset to keep only required variables.

• After analysing the weather data frame, it was found that it contained several observations for the same hour in the day which created duplicates when joined to accidents data. So, only observations for 51st minute of every hour in a day were kept in a tidy_weather data frame (e.g. 2016-01-01 00:51:00, 2016-01-01 01:51:00, etc.), as this was an hourly pattern in the data.

After all tidying and filtering, the combined data frame contains 18101 observations of 25 variables.

Understand

combined <- combined %>% mutate(., `UNIQUE KEY` = as.character(`UNIQUE KEY`),
                                   `ZIP CODE` = as.character(`ZIP CODE`))
combined$dailyprecip[which(combined$dailyprecip == "T")] <- "0.00"
combined$dailysnow[which(combined$dailysnow == "T")] <- "0.00"
combined <- combined %>% mutate(precip = as.numeric(precip),
                                dailyprecip = as.numeric(dailyprecip),
                                dailysnow = as.numeric(dailysnow))
combined <- combined %>% mutate(fog = factor(fog, levels = c("0","1"), labels = c("No","Yes")), 
                                rain = factor(rain, levels = c("0","1"), labels = c("No","Yes")),
                                snow = factor(snow, levels = c("0","1"), labels = c("No","Yes")))
head(combined$fog)

[1] No No No No No No
Levels: No Yes

head(combined$rain)

[1] No No No No No No
Levels: No Yes

head(combined$snow)

[1] No No No No No No
Levels: No Yes

str(combined)

Classes ‘tbl_df’, ‘tbl’ and 'data.frame':   18101 obs. of  25 variables:
 $ UNIQUE KEY         : chr  "3374565" "3511927" "3363408" "3364610" ...
 $ DATE               : Date, format: "2016-01-01" ...
 $ TIME               : 'hms' num  00:01:00 00:01:00 00:01:00 00:05:00 ...
  ..- attr(*, "units")= chr "secs"
 $ ZIP CODE           : chr  "10022" "11235" "10035" "10035" ...
 $ PERSONS INJURED    : int  0 1 1 2 0 0 0 0 0 1 ...
 $ PERSONS KILLED     : int  0 0 0 0 0 0 0 0 0 0 ...
 $ PEDESTRIANS INJURED: int  0 0 1 0 0 0 0 0 0 1 ...
 $ PEDESTRIANS KILLED : int  0 0 0 0 0 0 0 0 0 0 ...
 $ CYCLISTS INJURED   : int  0 3 0 0 0 0 0 0 0 0 ...
 $ CYCLISTS KILLED    : int  0 0 0 0 0 0 0 0 0 0 ...
 $ MOTORISTS INJURED  : int  0 0 0 2 0 0 0 0 0 0 ...
 $ MOTORISTS KILLED   : int  0 0 0 0 0 0 0 0 0 0 ...
 $ key                : chr  "1-1-0" "1-1-0" "1-1-0" "1-1-0" ...
 $ timestamp          : POSIXct, format: "2016-01-01 00:51:00" ...
 $ temp               : num  42.1 42.1 42.1 42.1 42.1 42.1 42.1 42.1 42.1 42.1 ...
 $ windspeed          : num  4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 ...
 $ humidity           : num  51 51 51 51 51 51 51 51 51 51 ...
 $ precip             : num  0 0 0 0 0 0 0 0 0 0 ...
 $ pressure           : num  30.1 30.1 30.1 30.1 30.1 ...
 $ conditions         : chr  "Overcast" "Overcast" "Overcast" "Overcast" ...
 $ dailyprecip        : num  0 0 0 0 0 0 0 0 0 0 ...
 $ dailysnow          : num  0 0 0 0 0 0 0 0 0 0 ...
 $ fog                : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...
 $ rain               : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...
 $ snow               : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...

attributes(combined)

$names
 [1] "UNIQUE KEY"          "DATE"               
 [3] "TIME"                "ZIP CODE"           
 [5] "PERSONS INJURED"     "PERSONS KILLED"     
 [7] "PEDESTRIANS INJURED" "PEDESTRIANS KILLED" 
 [9] "CYCLISTS INJURED"    "CYCLISTS KILLED"    
[11] "MOTORISTS INJURED"   "MOTORISTS KILLED"   
[13] "key"                 "timestamp"          
[15] "temp"                "windspeed"          
[17] "humidity"            "precip"             
[19] "pressure"            "conditions"         
[21] "dailyprecip"         "dailysnow"          
[23] "fog"                 "rain"               
[25] "snow"               

$class
[1] "tbl_df"     "tbl"        "data.frame"

$row.names
   [1]    1    2    3    4    5    6    7    8    9   10   11   12
  [13]   13   14   15   16   17   18   19   20   21   22   23   24
  [25]   25   26   27   28   29   30   31   32   33   34   35   36
  [37]   37   38   39   40   41   42   43   44   45   46   47   48
  [49]   49   50   51   52   53   54   55   56   57   58   59   60
  [61]   61   62   63   64   65   66   67   68   69   70   71   72
  [73]   73   74   75   76   77   78   79   80   81   82   83   84
  [85]   85   86   87   88   89   90   91   92   93   94   95   96
  [97]   97   98   99  100  101  102  103  104  105  106  107  108
 [109]  109  110  111  112  113  114  115  116  117  118  119  120
 [121]  121  122  123  124  125  126  127  128  129  130  131  132
 [133]  133  134  135  136  137  138  139  140  141  142  143  144
 [145]  145  146  147  148  149  150  151  152  153  154  155  156
 [157]  157  158  159  160  161  162  163  164  165  166  167  168
 [169]  169  170  171  172  173  174  175  176  177  178  179  180
 [181]  181  182  183  184  185  186  187  188  189  190  191  192
 [193]  193  194  195  196  197  198  199  200  201  202  203  204
 [205]  205  206  207  208  209  210  211  212  213  214  215  216
 [217]  217  218  219  220  221  222  223  224  225  226  227  228
 [229]  229  230  231  232  233  234  235  236  237  238  239  240
 [241]  241  242  243  244  245  246  247  248  249  250  251  252
 [253]  253  254  255  256  257  258  259  260  261  262  263  264
 [265]  265  266  267  268  269  270  271  272  273  274  275  276
 [277]  277  278  279  280  281  282  283  284  285  286  287  288
 [289]  289  290  291  292  293  294  295  296  297  298  299  300
 [301]  301  302  303  304  305  306  307  308  309  310  311  312
 [313]  313  314  315  316  317  318  319  320  321  322  323  324
 [325]  325  326  327  328  329  330  331  332  333  334  335  336
 [337]  337  338  339  340  341  342  343  344  345  346  347  348
 [349]  349  350  351  352  353  354  355  356  357  358  359  360
 [361]  361  362  363  364  365  366  367  368  369  370  371  372
 [373]  373  374  375  376  377  378  379  380  381  382  383  384
 [385]  385  386  387  388  389  390  391  392  393  394  395  396
 [397]  397  398  399  400  401  402  403  404  405  406  407  408
 [409]  409  410  411  412  413  414  415  416  417  418  419  420
 [421]  421  422  423  424  425  426  427  428  429  430  431  432
 [433]  433  434  435  436  437  438  439  440  441  442  443  444
 [445]  445  446  447  448  449  450  451  452  453  454  455  456
 [457]  457  458  459  460  461  462  463  464  465  466  467  468
 [469]  469  470  471  472  473  474  475  476  477  478  479  480
 [481]  481  482  483  484  485  486  487  488  489  490  491  492
 [493]  493  494  495  496  497  498  499  500  501  502  503  504
 [505]  505  506  507  508  509  510  511  512  513  514  515  516
 [517]  517  518  519  520  521  522  523  524  525  526  527  528
 [529]  529  530  531  532  533  534  535  536  537  538  539  540
 [541]  541  542  543  544  545  546  547  548  549  550  551  552
 [553]  553  554  555  556  557  558  559  560  561  562  563  564
 [565]  565  566  567  568  569  570  571  572  573  574  575  576
 [577]  577  578  579  580  581  582  583  584  585  586  587  588
 [589]  589  590  591  592  593  594  595  596  597  598  599  600
 [601]  601  602  603  604  605  606  607  608  609  610  611  612
 [613]  613  614  615  616  617  618  619  620  621  622  623  624
 [625]  625  626  627  628  629  630  631  632  633  634  635  636
 [637]  637  638  639  640  641  642  643  644  645  646  647  648
 [649]  649  650  651  652  653  654  655  656  657  658  659  660
 [661]  661  662  663  664  665  666  667  668  669  670  671  672
 [673]  673  674  675  676  677  678  679  680  681  682  683  684
 [685]  685  686  687  688  689  690  691  692  693  694  695  696
 [697]  697  698  699  700  701  702  703  704  705  706  707  708
 [709]  709  710  711  712  713  714  715  716  717  718  719  720
 [721]  721  722  723  724  725  726  727  728  729  730  731  732
 [733]  733  734  735  736  737  738  739  740  741  742  743  744
 [745]  745  746  747  748  749  750  751  752  753  754  755  756
 [757]  757  758  759  760  761  762  763  764  765  766  767  768
 [769]  769  770  771  772  773  774  775  776  777  778  779  780
 [781]  781  782  783  784  785  786  787  788  789  790  791  792
 [793]  793  794  795  796  797  798  799  800  801  802  803  804
 [805]  805  806  807  808  809  810  811  812  813  814  815  816
 [817]  817  818  819  820  821  822  823  824  825  826  827  828
 [829]  829  830  831  832  833  834  835  836  837  838  839  840
 [841]  841  842  843  844  845  846  847  848  849  850  851  852
 [853]  853  854  855  856  857  858  859  860  861  862  863  864
 [865]  865  866  867  868  869  870  871  872  873  874  875  876
 [877]  877  878  879  880  881  882  883  884  885  886  887  888
 [889]  889  890  891  892  893  894  895  896  897  898  899  900
 [901]  901  902  903  904  905  906  907  908  909  910  911  912
 [913]  913  914  915  916  917  918  919  920  921  922  923  924
 [925]  925  926  927  928  929  930  931  932  933  934  935  936
 [937]  937  938  939  940  941  942  943  944  945  946  947  948
 [949]  949  950  951  952  953  954  955  956  957  958  959  960
 [961]  961  962  963  964  965  966  967  968  969  970  971  972
 [973]  973  974  975  976  977  978  979  980  981  982  983  984
 [985]  985  986  987  988  989  990  991  992  993  994  995  996
 [997]  997  998  999 1000
 [ reached getOption("max.print") -- omitted 17101 entries ]

The steps taken in this section:

• Integer variables UNIQUE KEY and ZIP CODE were converted to a character type.

• Variables dailyprecip and dailysnow were read as characters because of, what seems to be, a data entry error, they had an unexplainable “T” character in several observations. They was replaced with a 0.00 value. These variables, as well as the variable precip, were converted to a numeric type.

• Integer variables fog, rain and snow were converted to factors and labeled.

• Structure and attributes of combined data frame were checked.

Tidy & Manipulate Data I

In this section DATE and TIME variables from combined data frame were united to create a DATETIME varible. DATETIME was converted to a date(POSIXct) type. Overall, as some tidying up has been done before joining data sets, merged data conforms the tidy data principles (each variable forms a column, each observation forms a row and each type of observational unit forms a table).

combined <- combined %>% unite(DATETIME,DATE,TIME, sep = " ")
combined$DATETIME <- ymd_hms(combined$DATETIME)
head(combined)

Tidy & Manipulate Data II

Two new variables PEOPLE_INJURED and PEOPLE_KILLED were created from the existing variables for better understanding of the data. Subset was done to drop the unnecessary columns.

combined <- combined %>% mutate(`PEOPLE_INJURED` = `PERSONS INJURED`+`PEDESTRIANS INJURED`+`CYCLISTS INJURED`+`MOTORISTS INJURED`,
                                `PEOPLE_KILLED` = `PERSONS KILLED`+`PEDESTRIANS KILLED`+`CYCLISTS KILLED`+`MOTORISTS KILLED`)
combined_1 <- combined[,-(4:13)]
head(combined_1)

Scan I

The steps taken in this section are as follows:

• The combined_1 data frame was scanned for missing values using functions colSums(is.na()). Only missing values in numeric variables were considered.

• Based on the output of the previous step, it was found variables temp, humidity, precip, conditions, dailypercip, dailysnow, fog, rain and snow have the same number of missing values. After checking the locations of these missing values, it was found they occured in the same observations. These missing values, therefore, were introduced in the process of left_join().

• The missing values mentioned above were removed by subsetting.

• There were also missing values in varaibles windspeed and pressure, they were replaced with the mean value.

• Lastly, inconsisitencies were checked using violatedEdits() under the rule we set, and no violations were found in the data set.

colSums(is.na(combined_1))

    UNIQUE KEY       DATETIME       ZIP CODE           temp 
             0              0           4148             77 
     windspeed       humidity         precip       pressure 
          2859             77             77            336 
    conditions    dailyprecip      dailysnow            fog 
            77             77             77             77 
          rain           snow PEOPLE_INJURED  PEOPLE_KILLED 
            77             77              0              0 

which(is.na(combined_1$humidity))

 [1] 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722
[14] 1723 1724 1725 1726 1727 1728 1852 1853 1854 1855 1856 1857 1858
[27] 1859 1860 1861 1862 1863 2262 2263 4178 4179 4180 4181 4182 4183
[40] 4184 4185 4186 4187 4188 4189 4190 4191 4192 4193 4194 4195 4196
[53] 4197 4198 4199 4200 4201 4202 4203 4204 4205 4206 4207 4208 4209
[66] 4210 4211 4212 4213 4214 4215 4216 4217 4218 4219 4220 4221

which(is.na(combined_1$dailyprecip))

 [1] 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722
[14] 1723 1724 1725 1726 1727 1728 1852 1853 1854 1855 1856 1857 1858
[27] 1859 1860 1861 1862 1863 2262 2263 4178 4179 4180 4181 4182 4183
[40] 4184 4185 4186 4187 4188 4189 4190 4191 4192 4193 4194 4195 4196
[53] 4197 4198 4199 4200 4201 4202 4203 4204 4205 4206 4207 4208 4209
[66] 4210 4211 4212 4213 4214 4215 4216 4217 4218 4219 4220 4221

which(is.na(combined_1$temp))

 [1] 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722
[14] 1723 1724 1725 1726 1727 1728 1852 1853 1854 1855 1856 1857 1858
[27] 1859 1860 1861 1862 1863 2262 2263 4178 4179 4180 4181 4182 4183
[40] 4184 4185 4186 4187 4188 4189 4190 4191 4192 4193 4194 4195 4196
[53] 4197 4198 4199 4200 4201 4202 4203 4204 4205 4206 4207 4208 4209
[66] 4210 4211 4212 4213 4214 4215 4216 4217 4218 4219 4220 4221

combined_2 <- combined_1[-(which(is.na(combined_1$temp))),]
colSums(is.na(combined_2))

    UNIQUE KEY       DATETIME       ZIP CODE           temp 
             0              0           4131              0 
     windspeed       humidity         precip       pressure 
          2782              0              0            259 
    conditions    dailyprecip      dailysnow            fog 
             0              0              0              0 
          rain           snow PEOPLE_INJURED  PEOPLE_KILLED 
             0              0              0              0 

combined_2$windspeed[is.na(combined_2$windspeed)] <- mean(combined_2$windspeed, na.rm = T)
combined_2$pressure[is.na(combined_2$pressure)] <- mean(combined_2$pressure, na.rm = T)
colSums(is.na(combined_2))

    UNIQUE KEY       DATETIME       ZIP CODE           temp 
             0              0           4131              0 
     windspeed       humidity         precip       pressure 
             0              0              0              0 
    conditions    dailyprecip      dailysnow            fog 
             0              0              0              0 
          rain           snow PEOPLE_INJURED  PEOPLE_KILLED 
             0              0              0              0 

(rule1 <- editset(c("windspeed >= 0", "humidity >= 0", "humidity <= 100", "precip >= 0", "pressure >=0", "dailyprecip >= 0", "dailysnow >= 0", "PEOPLE_INJURED >= 0", "PEOPLE_KILLED >=0")))

Edit set:
num1 : 0 <= windspeed
num2 : 0 <= humidity
num3 : humidity <= 100
num4 : 0 <= precip
num5 : 0 <= pressure
num6 : 0 <= dailyprecip
num7 : 0 <= dailysnow
num8 : 0 <= PEOPLE_INJURED
num9 : 0 <= PEOPLE_KILLED 

violated <- violatedEdits(rule1, combined_2)
summary(violated)

No violations detected, 0 checks evaluated to NA

NULL

Scan II

The steps taken in this section are as follows:

• Boxplot of numeric variables were created side by side for scanning univariate ourliers.

• Outliers in variables windspeed, humidity and pressure were capped using the Tukey’s method.

• Outliers in variables precip, dailyprecip, dailysnow, PEOPLE INJURED and PEOPLE KILLED were kept, they occur only because most of the observations in these variables are zeros.

• Boxplots of the capped variables were made to check if capping successfully removed the outliers.

par(mfrow=c(2,5)) 
combined_2$temp %>% boxplot(main = "Temperature")
combined_2$windspeed %>% boxplot(main = "Windspeed")

combined_2$humidity %>% boxplot(main = "Humidity")
combined_2$precip %>% boxplot(main = "Precipitation")

combined_2$pressure %>% boxplot(main = "Pressure")
combined_2$dailyprecip %>% boxplot(main = "Daily Precipitation")

combined_2$dailysnow %>% boxplot(main = "Daily Snow")
combined_2$PEOPLE_INJURED %>% boxplot(main = "People Injured")

combined_2$PEOPLE_KILLED %>% boxplot(main = "People Killed")
cap <- function(x){
    quantiles <- quantile( x, c(.05, 0.25, 0.75, .95 ) )
    x[ x < quantiles[2] - 1.5*IQR(x) ] <- quantiles[1]
    x[ x > quantiles[3] + 1.5*IQR(x) ] <- quantiles[4]
    x
}
combined_2$windspeed <- combined_2$windspeed %>% cap()
combined_2$humidity <- combined_2$humidity %>% cap()
combined_2$pressure <- combined_2$pressure %>% cap()
par(mfrow=c(1,3)) 

combined_2$windspeed %>% boxplot(main = "Windspeed")
combined_2$humidity %>% boxplot(main = "Humidity")

combined_2$pressure %>% boxplot(main = "Pressure")

Transform

In this section square root transformation was applied for the windspeed variable to reduce slight right skewness in its distribution. Histograms were made to visualise the effect of data transformation.

Z-score transformation was applied for variables humidity and temp, as their values have significantly greater range than the other variables. The resulting transformed data values have a zero mean and standard deviation equals to one.

transformed <- combined_2
hist(combined_2$windspeed,
     breaks = 5,
     main = "Histogram of Windspeed",
     xlab = "Windspeed")

transformed$windspeed <- sqrt(combined_2$windspeed)
hist(transformed$windspeed, breaks = 5,
                            main = "Histogram of Transformed Windspeed",
                            xlab = "Square Root of Windspeed")

hist(combined_2$humidity,
     main = "Histogram of Humidity",
     xlab = "Humidity")

transformed$humidity <- scale(combined_2$humidity, center = T, scale = T)
hist(transformed$humidity,
     main = "Histogram of Standardised Humidity", 
     xlab = "z-score Humidity")

hist(combined_2$temp,
     main = "Histogram of Temperature",
     xlab = "Temperature")

transformed$temp <- scale(combined_2$temp, center = T, scale = T)
hist(transformed$temp,
     main = "Histogram of Standardised Temperature", 
     xlab = "z-score Temperature")

head(combined_2)

head(transformed)