str(diamonds)

## tibble [53,940 × 10] (S3: tbl_df/tbl/data.frame)
##  $ carat  : num [1:53940] 0.23 0.21 0.23 0.29 0.31 0.24 0.24 0.26 0.22 0.23 ...
##  $ cut    : Ord.factor w/ 5 levels "Fair"<"Good"<..: 5 4 2 4 2 3 3 3 1 3 ...
##  $ color  : Ord.factor w/ 7 levels "D"<"E"<"F"<"G"<..: 2 2 2 6 7 7 6 5 2 5 ...
##  $ clarity: Ord.factor w/ 8 levels "I1"<"SI2"<"SI1"<..: 2 3 5 4 2 6 7 3 4 5 ...
##  $ depth  : num [1:53940] 61.5 59.8 56.9 62.4 63.3 62.8 62.3 61.9 65.1 59.4 ...
##  $ table  : num [1:53940] 55 61 65 58 58 57 57 55 61 61 ...
##  $ price  : int [1:53940] 326 326 327 334 335 336 336 337 337 338 ...
##  $ x      : num [1:53940] 3.95 3.89 4.05 4.2 4.34 3.94 3.95 4.07 3.87 4 ...
##  $ y      : num [1:53940] 3.98 3.84 4.07 4.23 4.35 3.96 3.98 4.11 3.78 4.05 ...
##  $ z      : num [1:53940] 2.43 2.31 2.31 2.63 2.75 2.48 2.47 2.53 2.49 2.39 ...

summary(diamonds)

##      carat               cut        color        clarity          depth      
##  Min.   :0.2000   Fair     : 1610   D: 6775   SI1    :13065   Min.   :43.00  
##  1st Qu.:0.4000   Good     : 4906   E: 9797   VS2    :12258   1st Qu.:61.00  
##  Median :0.7000   Very Good:12082   F: 9542   SI2    : 9194   Median :61.80  
##  Mean   :0.7979   Premium  :13791   G:11292   VS1    : 8171   Mean   :61.75  
##  3rd Qu.:1.0400   Ideal    :21551   H: 8304   VVS2   : 5066   3rd Qu.:62.50  
##  Max.   :5.0100                     I: 5422   VVS1   : 3655   Max.   :79.00  
##                                     J: 2808   (Other): 2531                  
##      table           price             x                y         
##  Min.   :43.00   Min.   :  326   Min.   : 0.000   Min.   : 0.000  
##  1st Qu.:56.00   1st Qu.:  950   1st Qu.: 4.710   1st Qu.: 4.720  
##  Median :57.00   Median : 2401   Median : 5.700   Median : 5.710  
##  Mean   :57.46   Mean   : 3933   Mean   : 5.731   Mean   : 5.735  
##  3rd Qu.:59.00   3rd Qu.: 5324   3rd Qu.: 6.540   3rd Qu.: 6.540  
##  Max.   :95.00   Max.   :18823   Max.   :10.740   Max.   :58.900  
##                                                                   
##        z         
##  Min.   : 0.000  
##  1st Qu.: 2.910  
##  Median : 3.530  
##  Mean   : 3.539  
##  3rd Qu.: 4.040  
##  Max.   :31.800  
## 

The diamonds dataset includes over 50,000 entries with attributes like carat, cut, color, clarity, and price. It’s ideal for visualizing relationships between features and pricing.

ggplot(diamonds, aes(x = carat, y = price)) +
  geom_point(alpha = 0.3, color = "darkgreen") +
  geom_smooth(method = "lm", se = FALSE, color = "black") +
  labs(title = "Price vs. Carat",
       x = "Carat",
       y = "Price (USD)")

## `geom_smooth()` using formula = 'y ~ x'

As carat increases, price rises sharply — suggesting a strong positive correlation.

ggplot(diamonds, aes(x = cut, y = price)) +
  geom_boxplot(fill = "lightblue") +
  labs(title = "Diamond Prices by Cut",
       x = "Cut Quality",
       y = "Price (USD)")

Diamonds with better cut tend to cost more on average, but variation is high for each cut group.

plot_ly(data = diamonds %>% sample_n(1000),
        x = ~carat,
        y = ~price,
        z = ~as.numeric(clarity),
        type = "scatter3d",
        mode = "markers",
        color = ~clarity,
        marker = list(size = 3)) %>%
  layout(title = "3D Scatter: Carat, Price, Clarity")

Higher clarity generally aligns with higher prices, but carat still plays the dominant role.

\[ \\text{Corr}(X, Y) = \\frac{\\text{Cov}(X, Y)}{\\sigma_X \\cdot \\sigma_Y} \]

The Pearson correlation coefficient measures linear association between two variables — useful here for carat and price.

\[ \\hat{y} = \\beta_0 + \\beta_1 x \]

A simple linear regression model is often used to predict price based on features like carat.

cor(diamonds$carat, diamonds$price)

## [1] 0.9215913

This R command calculates the correlation between carat and price — expect a strong positive value.