Exploration of Diamond Pricing
Paul Foley
Explore how a diamonds features affect diamond price.
Diamond Features
- Carat
- Cut
- Color
- Clarity
- Depth
- Table
- x, y, z (Volume)
Feature Summary
## carat cut color clarity
## Min. :0.2000 Fair : 1610 D: 6775 SI1 :13065
## 1st Qu.:0.4000 Good : 4906 E: 9797 VS2 :12258
## Median :0.7000 Very Good:12082 F: 9542 SI2 : 9194
## Mean :0.7979 Premium :13791 G:11292 VS1 : 8171
## 3rd Qu.:1.0400 Ideal :21551 H: 8304 VVS2 : 5066
## Max. :5.0100 I: 5422 VVS1 : 3655
## J: 2808 (Other): 2531
## depth table price x
## Min. :43.00 Min. :43.00 Min. : 326 Min. : 0.000
## 1st Qu.:61.00 1st Qu.:56.00 1st Qu.: 950 1st Qu.: 4.710
## Median :61.80 Median :57.00 Median : 2401 Median : 5.700
## Mean :61.75 Mean :57.46 Mean : 3933 Mean : 5.731
## 3rd Qu.:62.50 3rd Qu.:59.00 3rd Qu.: 5324 3rd Qu.: 6.540
## Max. :79.00 Max. :95.00 Max. :18823 Max. :10.740
##
## y z
## Min. : 0.000 Min. : 0.000
## 1st Qu.: 4.720 1st Qu.: 2.910
## Median : 5.710 Median : 3.530
## Mean : 5.735 Mean : 3.539
## 3rd Qu.: 6.540 3rd Qu.: 4.040
## Max. :58.900 Max. :31.800
## Price Exploration
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 326 950 2401 3933 5324 18823
Price by Cut Exploration
## diamonds$cut: Fair
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 337 2050 3282 4359 5206 18574
## --------------------------------------------------------
## diamonds$cut: Good
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 327 1145 3050 3929 5028 18788
## --------------------------------------------------------
## diamonds$cut: Very Good
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 336 912 2648 3982 5373 18818
## --------------------------------------------------------
## diamonds$cut: Premium
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 326 1046 3185 4584 6296 18823
## --------------------------------------------------------
## diamonds$cut: Ideal
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 326 878 1810 3458 4678 18806
Price By Carat Exploration
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1051 2478 3495 4008 4950 17829
Price By Color Exploration
## diamonds$color: D
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 357 911 1838 3170 4214 18693
## --------------------------------------------------------
## diamonds$color: E
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 326 882 1739 3077 4003 18731
## --------------------------------------------------------
## diamonds$color: F
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 342 982 2344 3725 4868 18791
## --------------------------------------------------------
## diamonds$color: G
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 354 931 2242 3999 6048 18818
## --------------------------------------------------------
## diamonds$color: H
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 337 984 3460 4487 5980 18803
## --------------------------------------------------------
## diamonds$color: I
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 334 1120 3730 5092 7202 18823
## --------------------------------------------------------
## diamonds$color: J
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 335 1860 4234 5324 7695 18710
Price By Clarity Exploration
Price By x, y, z (Volume) Exploration
##
## Pearson's product-moment correlation
##
## data: price and x
## t = 440.16, df = 53938, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8825835 0.8862594
## sample estimates:
## cor
## 0.8844352##
## Pearson's product-moment correlation
##
## data: price and y
## t = 401.14, df = 53938, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8632867 0.8675241
## sample estimates:
## cor
## 0.8654209##
## Pearson's product-moment correlation
##
## data: price and z
## t = 393.6, df = 53938, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8590541 0.8634131
## sample estimates:
## cor
## 0.8612494
Correlation - Price Vs. Volume
##
## Pearson's product-moment correlation
##
## data: volume_df$price and volume_df$volume
## t = 485.41, df = 53930, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.9004947 0.9036387
## sample estimates:
## cor
## 0.9020786
Price By Depth Exploration
##
## Pearson's product-moment correlation
##
## data: price and depth
## t = -2.473, df = 53938, p-value = 0.0134
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.019084756 -0.002208537
## sample estimates:
## cor
## -0.0106474
Price by Table Exploration
Building the Linear Model for Price
##
## Calls:
## m1: lm(formula = I(log(price)) ~ I(carat^(1/3)), data = diamonds)
## m2: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat, data = diamonds)
## m3: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut, data = diamonds)
## m4: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut + color,
## data = diamonds)
## m5: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut + color +
## clarity, data = diamonds)
##
## =============================================================================
## m1 m2 m3 m4 m5
## -----------------------------------------------------------------------------
## (Intercept) 2.821*** 1.039*** 0.874*** 0.932*** 0.415***
## (0.006) (0.019) (0.019) (0.017) (0.010)
## I(carat^(1/3)) 5.558*** 8.568*** 8.703*** 8.438*** 9.144***
## (0.007) (0.032) (0.031) (0.028) (0.016)
## carat -1.137*** -1.163*** -0.992*** -1.093***
## (0.012) (0.011) (0.010) (0.006)
## cut: .L 0.224*** 0.224*** 0.120***
## (0.004) (0.004) (0.002)
## cut: .Q -0.062*** -0.062*** -0.031***
## (0.004) (0.003) (0.002)
## cut: .C 0.051*** 0.052*** 0.014***
## (0.003) (0.003) (0.002)
## cut: ^4 0.018*** 0.018*** -0.002
## (0.003) (0.002) (0.001)
## color: .L -0.373*** -0.441***
## (0.003) (0.002)
## color: .Q -0.129*** -0.093***
## (0.003) (0.002)
## color: .C 0.001 -0.013***
## (0.003) (0.002)
## color: ^4 0.029*** 0.012***
## (0.003) (0.002)
## color: ^5 -0.016*** -0.003*
## (0.003) (0.001)
## color: ^6 -0.023*** 0.001
## (0.002) (0.001)
## clarity: .L 0.907***
## (0.003)
## clarity: .Q -0.240***
## (0.003)
## clarity: .C 0.131***
## (0.003)
## clarity: ^4 -0.063***
## (0.002)
## clarity: ^5 0.026***
## (0.002)
## clarity: ^6 -0.002
## (0.002)
## clarity: ^7 0.032***
## (0.001)
## -----------------------------------------------------------------------------
## R-squared 0.924 0.935 0.939 0.951 0.984
## adj. R-squared 0.924 0.935 0.939 0.951 0.984
## sigma 0.280 0.259 0.250 0.224 0.129
## F 652012.063 387489.366 138654.523 87959.467 173791.084
## p 0.000 0.000 0.000 0.000 0.000
## Log-likelihood -7962.499 -3631.319 -1837.416 4235.240 34091.272
## Deviance 4242.831 3613.360 3380.837 2699.212 892.214
## AIC 15930.999 7270.637 3690.832 -8442.481 -68140.544
## BIC 15957.685 7306.220 3761.997 -8317.942 -67953.736
## N 53940 53940 53940 53940 53940
## =============================================================================Prediction
Diamond Features:
- Carat = 1.00
- Cut = “Very Good”
- Color = “I”
- Clarity=“VS1”
Price Perdiction:
## fit lwr upr
## 1 4537.822 3526.389 5839.352