This classic dataset contains the prices and other attributes of almost 54,000 diamonds. And the contents of this data set are as follows 1- Price: Price in US dollars ($326–$18,823) 2- Carat: weight of the diamond (0.2–5.01) 3- Cut: quality of the cut (Fair, Good, Very Good, Premium, Ideal) 4- Color: diamond colour, from J (worst) to D (best) 5- Clarity: a measurement of how clear the diamond is (I1 (worst), SI2, SI1, VS2, VS1, VVS2, VVS1, IF (best)) 6- x length in mm (0–10.74) 7- y width in mm (0–58.9) 8- z depth in mm (0–31.8) 9- depth total depth percentage = z / mean(x, y) = 2 * z / (x + y) (43–79) 10- table width of top of diamond relative to widest point (43–95)
So We’ll study the effect of these factors onto the price of a diamond, after this analysis we’ll get to know about which factor have major role in deciding a diamond’s price. Let’s get started
setwd("C:/Users/SAURAB~1/AppData/Local/Temp/Rar$DIa0.525")
diamonds.csv <-read.csv(paste("diamonds.csv",sep = ""))
View(diamonds.csv)For the dimensions of the dataset
dim(diamonds.csv)## [1] 53940 11So there are 53940 rows and 11 columns.
Now firstly we convert the character columns of this dataset into numeric factors so that the analysis becomes easy.
diamonds.csv[, 3:5] <- sapply(diamonds.csv[, 3:5], as.numeric)
View(diamonds.csv)Now let’s find out the some summary statistics of this data set
library(psych)
describe(diamonds.csv)[ ,1:9]## vars n mean sd median trimmed mad min
## X 1 53940 26970.50 15571.28 26970.50 26970.50 19992.86 1.0
## carat 2 53940 0.80 0.47 0.70 0.73 0.47 0.2
## cut 3 53940 3.55 1.03 3.00 3.60 1.48 1.0
## color 4 53940 3.59 1.70 4.00 3.55 1.48 1.0
## clarity 5 53940 4.84 1.72 5.00 4.75 1.48 1.0
## depth 6 53940 61.75 1.43 61.80 61.78 1.04 43.0
## table 7 53940 57.46 2.23 57.00 57.32 1.48 43.0
## price 8 53940 3932.80 3989.44 2401.00 3158.99 2475.94 326.0
## x 9 53940 5.73 1.12 5.70 5.66 1.38 0.0
## y 10 53940 5.73 1.14 5.71 5.66 1.36 0.0
## z 11 53940 3.54 0.71 3.53 3.49 0.85 0.0
## max
## X 53940.00
## carat 5.01
## cut 5.00
## color 7.00
## clarity 8.00
## depth 79.00
## table 95.00
## price 18823.00
## x 10.74
## y 58.90
## z 31.80So these are the summary statistics of all variables,
For summary statistics of prices of diamonds
describe(diamonds.csv$price)## vars n mean sd median trimmed mad min max range skew
## X1 1 53940 3932.8 3989.44 2401 3158.99 2475.94 326 18823 18497 1.62
## kurtosis se
## X1 2.18 17.18So the mean price is 3932.8 and median price is 2401. The prices ranges from 326 to 18823 having standard deviation of 3989.44.
For summary statistics of carats of diamonds
describe(diamonds.csv$carat)## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 53940 0.8 0.47 0.7 0.73 0.47 0.2 5.01 4.81 1.12 1.26
## se
## X1 0So the mean weight is .8 carats and median weight is .7 carats. The weight ranges from .2 to 5.01 carats having standard deviation of .47 .
For summary statistics of depths of diamonds
describe(diamonds.csv$depth)## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 53940 61.75 1.43 61.8 61.78 1.04 43 79 36 -0.08 5.74
## se
## X1 0.01Now drawing one way contingency tables for categorical variables
For cuts of the diamonds
table(diamonds.csv$cut)##
## 1 2 3 4 5
## 1610 4906 21551 13791 12082For color of the diamonds
table(diamonds.csv$color)##
## 1 2 3 4 5 6 7
## 6775 9797 9542 11292 8304 5422 2808For clarity of the diamonds
table(diamonds.csv$clarity)##
## 1 2 3 4 5 6 7 8
## 741 1790 13065 9194 8171 12258 3655 5066For carats of the diamonds
table(diamonds.csv$carat)##
## 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34
## 12 9 5 293 254 212 253 233 198 130 2604 2249 1840 1189 910
## 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49
## 667 572 394 670 398 1299 1382 706 488 212 110 178 99 63 45
## 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64
## 1258 1127 817 709 625 496 492 430 310 282 228 204 135 102 80
## 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79
## 65 48 48 25 26 1981 1294 764 492 322 249 251 251 187 155
## 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94
## 284 200 140 131 64 62 34 31 23 21 1485 570 226 142 59
## 0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09
## 65 103 59 31 23 1558 2242 883 523 475 361 373 342 246 287
## 1.1 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.2 1.21 1.22 1.23 1.24
## 278 308 251 246 207 149 172 110 123 126 645 473 300 279 236
## 1.25 1.26 1.27 1.28 1.29 1.3 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39
## 187 146 134 106 101 122 133 89 87 68 77 50 46 26 36
## 1.4 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.5 1.51 1.52 1.53 1.54
## 50 40 25 19 18 15 18 21 7 11 793 807 381 220 174
## 1.55 1.56 1.57 1.58 1.59 1.6 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69
## 124 109 106 89 89 95 64 61 50 43 32 30 25 19 24
## 1.7 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.8 1.81 1.82 1.83 1.84
## 215 119 57 52 40 50 28 17 12 15 21 9 13 18 4
## 1.85 1.86 1.87 1.88 1.89 1.9 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99
## 3 9 7 4 4 7 12 2 6 3 3 4 4 5 3
## 2 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.1 2.11 2.12 2.13 2.14
## 265 440 177 122 86 67 60 50 41 45 52 43 25 21 48
## 2.15 2.16 2.17 2.18 2.19 2.2 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29
## 22 25 18 31 22 32 23 27 13 16 18 15 12 20 17
## 2.3 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 2.4 2.41 2.42 2.43 2.44
## 21 13 16 9 5 7 8 6 8 7 13 5 8 6 4
## 2.45 2.46 2.47 2.48 2.49 2.5 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59
## 4 3 3 9 3 17 17 9 8 9 3 3 3 3 1
## 2.6 2.61 2.63 2.64 2.65 2.66 2.67 2.68 2.7 2.71 2.72 2.74 2.75 2.77 2.8
## 3 3 3 1 1 3 1 2 1 1 3 3 2 1 2
## 3 3.01 3.02 3.04 3.05 3.11 3.22 3.24 3.4 3.5 3.51 3.65 3.67 4 4.01
## 8 14 1 2 1 1 1 1 1 1 1 1 1 1 2
## 4.13 4.5 5.01
## 1 1 1Now drawing two way contingency tables for categorical variables in the dataset
The table between cut and color
cut_color <-xtabs(~cut+color,data = diamonds.csv)
ftable(cut_color)## color 1 2 3 4 5 6 7
## cut
## 1 163 224 312 314 303 175 119
## 2 662 933 909 871 702 522 307
## 3 2834 3903 3826 4884 3115 2093 896
## 4 1603 2337 2331 2924 2360 1428 808
## 5 1513 2400 2164 2299 1824 1204 678The table between cut and clarity
cut_clarity <-xtabs(~cut+clarity,data = diamonds.csv)
ftable(cut_clarity)## clarity 1 2 3 4 5 6 7 8
## cut
## 1 210 9 408 466 170 261 17 69
## 2 96 71 1560 1081 648 978 186 286
## 3 146 1212 4282 2598 3589 5071 2047 2606
## 4 205 230 3575 2949 1989 3357 616 870
## 5 84 268 3240 2100 1775 2591 789 1235The table between color and clarity
color_clarity <-xtabs(~color+clarity,data = diamonds.csv)
ftable(color_clarity)## clarity 1 2 3 4 5 6 7 8
## color
## 1 42 73 2083 1370 705 1697 252 553
## 2 102 158 2426 1713 1281 2470 656 991
## 3 143 385 2131 1609 1364 2201 734 975
## 4 150 681 1976 1548 2148 2347 999 1443
## 5 162 299 2275 1563 1169 1643 585 608
## 6 92 143 1424 912 962 1169 355 365
## 7 50 51 750 479 542 731 74 131Now drawing box plots of each variable
For carat
boxplot(diamonds.csv$carat)
For cut
boxplot(diamonds.csv$cut)
For color
boxplot(diamonds.csv$color)
For clarity
boxplot(diamonds.csv$color)
For table
boxplot(diamonds.csv$table)
For depth
boxplot(diamonds.csv$table)
For price
boxplot(diamonds.csv$table)
Now drawing histograms for suitable data fields
For distribution of diamond’s weights in carats
library(lattice)
histogram(~carat, data = diamonds.csv,
main = "Distribution of diamond's weight in Carat", xlab="Carats", col='red' )
For distribution of cuts of diamonds
histogram(~cut, data = diamonds.csv,
main = "Distribution of Cuts of diamonds ", xlab="Cuts", col='blue' )
For distribution of colors of diamonds
histogram(~color, data = diamonds.csv,
main = "Distribution of Colors of diamonds ", xlab="Colors", col='blue' )
For distribution of clarity of diamonds
histogram(~clarity, data = diamonds.csv,
main = "Distribution of Clarity of diamonds ", xlab="Clarity", col='green' )
For distribution of colors of diamonds
histogram(~depth, data = diamonds.csv,
main = "Distribution of depths of diamonds ", xlab="Depths", col='skyblue' )
For distribution table of diamonds
histogram(~table, data = diamonds.csv,
main = "Distribution of Tables of diamonds ", xlab="Tables", col='blue' )
For distribution of Prices of diamonds
histogram(~price, data = diamonds.csv,
main = "Distribution of Prices of diamonds ", xlab="Prices", col='red' )
Now some plots to understand data better
For distribution of prices of diamonds with cut
boxplot(price~cut,data = diamonds.csv,main="Distribution of prices of diamonds with cut",xlab="Cut",ylab="Prices")
For distribution of prices of diamonds with weight of diamonds
plot(price~carat,data = diamonds.csv,main="Distribution of prices of diamonds with weight",xlab="Carat",ylab="Prices")
For distribution of prices of diamonds with color of diamonds
boxplot(price~color,data = diamonds.csv,main="Distribution of prices of diamonds with color",xlab="Color",ylab="Prices")
For distribution of prices of diamonds with clarity of diamonds
boxplot(price~clarity,data = diamonds.csv,main="Distribution of prices of diamonds with clarity",xlab="Clarity",ylab="Prices")
For distribution of prices of diamonds with depth of diamonds
plot(price~depth,data = diamonds.csv,main="Distribution of prices of diamonds with depth",xlab="depth",ylab="Prices")
For distribution of prices of diamonds with table of diamonds
boxplot(price~table,data = diamonds.csv,main="Distribution of prices of diamonds with table",xlab="table",ylab="Prices")
For a correlation matrix
cor(diamonds.csv)## X carat cut color clarity
## X 1.00000000 -0.37798348 -0.0233272316 -0.0950979466 0.12513599
## carat -0.37798348 1.00000000 0.0171237362 0.2914367543 -0.21429037
## cut -0.02332723 0.01712374 1.0000000000 0.0003042479 0.02823537
## color -0.09509795 0.29143675 0.0003042479 1.0000000000 -0.02779550
## clarity 0.12513599 -0.21429037 0.0282353656 -0.0277954960 1.00000000
## depth -0.03480023 0.02822431 -0.1942485626 0.0472792348 -0.05308011
## table -0.10083032 0.18161755 0.1503270263 0.0264652011 -0.08822266
## price -0.30687318 0.92159130 0.0398602909 0.1725109282 -0.07153497
## x -0.40544047 0.97509423 0.0223419276 0.2702866854 -0.22572144
## y -0.39584267 0.95172220 0.0275720250 0.2635844027 -0.21761579
## z -0.39920829 0.95338738 0.0020373568 0.2682268757 -0.22426307
## depth table price x y
## X -0.03480023 -0.10083032 -0.30687318 -0.40544047 -0.39584267
## carat 0.02822431 0.18161755 0.92159130 0.97509423 0.95172220
## cut -0.19424856 0.15032703 0.03986029 0.02234193 0.02757203
## color 0.04727923 0.02646520 0.17251093 0.27028669 0.26358440
## clarity -0.05308011 -0.08822266 -0.07153497 -0.22572144 -0.21761579
## depth 1.00000000 -0.29577852 -0.01064740 -0.02528925 -0.02934067
## table -0.29577852 1.00000000 0.12713390 0.19534428 0.18376015
## price -0.01064740 0.12713390 1.00000000 0.88443516 0.86542090
## x -0.02528925 0.19534428 0.88443516 1.00000000 0.97470148
## y -0.02934067 0.18376015 0.86542090 0.97470148 1.00000000
## z 0.09492388 0.15092869 0.86124944 0.97077180 0.95200572
## z
## X -0.399208287
## carat 0.953387381
## cut 0.002037357
## color 0.268226876
## clarity -0.224263069
## depth 0.094923882
## table 0.150928692
## price 0.861249444
## x 0.970771799
## y 0.952005716
## z 1.000000000Now for visualising this let’s create a corrgram
library(corrplot)## corrplot 0.84 loadedcorrplot.mixed(corr=cor(diamonds.csv, use="complete.obs"),lower = "shade" ,
upper="pie", tl.pos="d")
Now for scatterplot of the variables
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitmodel <- ~price+cut+carat+clarity+color+depth+table
scatterplotMatrix(formula = model,
data=diamonds.csv,
main = "Scatter Plot")