Initial Visualization

ggplot(diamonds, aes(cut,price)) + geom_boxplot()

ggplot(diamonds, aes(color,price)) + geom_boxplot()

ggplot(diamonds, aes(clarity,price)) + geom_boxplot()

ggplot(diamonds, aes(carat, price)) +
  geom_hex(bins=50)

Subset Data and replot

diamonds2 <- diamonds %>%
  filter(carat <= 2.5)  %>%
  mutate(lprice = log2(price), lcarat = log2(carat))

ggplot(diamonds2, aes(lcarat, lprice)) +
  geom_hex(bins=50)

Simple model and visualization

mod_diamond <- lm(lprice ~ lcarat, data = diamonds2, na.action = na.warn)

grid <- diamonds2 %>%
  data_grid(carat = seq_range(carat, 20)) %>%
  mutate(lcarat = log2(carat)) %>%
  add_predictions(mod_diamond, "lprice") %>%
  mutate(price = 2 ^ lprice)

ggplot(diamonds2, aes(carat, price)) +
  geom_hex(bins = 50) +
  geom_line(data = grid, color = "green", size = 1)

Add residuals and plot

diamonds2 <- diamonds2 %>%
  add_residuals(mod_diamond, "lresid")

ggplot(diamonds2, aes(lcarat, lresid)) +
  geom_hex(bins = 50)

ggplot(diamonds2, aes(cut,lresid)) + geom_boxplot()

ggplot(diamonds2, aes(color,lresid)) + geom_boxplot()

ggplot(diamonds2, aes(clarity,lresid)) + geom_boxplot()

Four parameter model and visualization

mod_diamond2 <- lm(
  lprice ~ lcarat + color + cut + clarity, diamonds2, na.action = na.warn
)

grid <- diamonds2 %>%
  data_grid(cut, .model = mod_diamond2) %>%
  add_predictions(mod_diamond2)
grid
## # A tibble: 5 x 5
##   cut       lcarat color clarity  pred
##   <ord>      <dbl> <chr> <chr>   <dbl>
## 1 Fair      -0.515 G     VS2      11.2
## 2 Good      -0.515 G     VS2      11.3
## 3 Very Good -0.515 G     VS2      11.4
## 4 Premium   -0.515 G     VS2      11.4
## 5 Ideal     -0.515 G     VS2      11.4
ggplot(grid, aes(cut, pred)) +
  geom_point()

Plot residuals of four parameter model

diamonds2 <- diamonds2 %>%
  add_residuals(mod_diamond2, "lresid2")

ggplot(diamonds2, aes(lcarat, lresid2)) +
  geom_hex(bins = 50)

diamonds2 %>%
  filter(abs(lresid2) > 1) %>%
  add_predictions(mod_diamond2) %>%
  mutate(pred = round(2^pred)) %>%
  select(price, pred, carat:table, x:z) %>%
  arrange(price)
## # A tibble: 16 x 11
##    price  pred carat cut       color clarity depth table     x     y     z
##    <int> <dbl> <dbl> <ord>     <ord> <ord>   <dbl> <dbl> <dbl> <dbl> <dbl>
##  1  1013   264 0.25  Fair      F     SI2      54.4    64  4.3   4.23  2.32
##  2  1186   284 0.25  Premium   G     SI2      59      60  5.33  5.28  3.12
##  3  1186   284 0.25  Premium   G     SI2      58.8    60  5.33  5.28  3.12
##  4  1262  2644 1.03  Fair      E     I1       78.2    54  5.72  5.59  4.42
##  5  1415   639 0.35  Fair      G     VS2      65.9    54  5.57  5.53  3.66
##  6  1415   639 0.35  Fair      G     VS2      65.9    54  5.57  5.53  3.66
##  7  1715   576 0.32  Fair      F     VS2      59.6    60  4.42  4.34  2.61
##  8  1776   412 0.290 Fair      F     SI1      55.8    60  4.48  4.41  2.48
##  9  2160   314 0.34  Fair      F     I1       55.8    62  4.72  4.6   2.6 
## 10  2366   774 0.3   Very Good D     VVS2     60.6    58  4.33  4.35  2.63
## 11  3360  1373 0.51  Premium   F     SI1      62.7    62  5.09  4.96  3.15
## 12  3807  1540 0.61  Good      F     SI2      62.5    65  5.36  5.29  3.33
## 13  3920  1705 0.51  Fair      F     VVS2     65.4    60  4.98  4.9   3.23
## 14  4368  1705 0.51  Fair      F     VVS2     60.7    66  5.21  5.11  3.13
## 15 10011  4048 1.01  Fair      D     SI2      64.6    58  6.25  6.2   4.02
## 16 10470 23622 2.46  Premium   E     SI2      59.7    59  8.82  8.76  5.25

Question #1

In the plot of lcarat vs. lprice, there are some bright vertical strips. What do they represent?

# Use this chunk to answer question 1
# The bright blue vertical strips indicate the counts. This indicates that there is a higher count of diamonds, the same weight(carat) but a wide range of prices.

Question #2

If log(price) = a_0 + a_1 * log(carat), what does that say about the relationship between price and carat?

# Use this chunk to answer question 2
# From the above equation, we can say that there exists a linear relationship between carat and price. With every 1% increase/decrease in the carat, there is a respective 1% increase/decrease in the price.

Question #3

Extract the diamonds that have very high and very low residuals. Is there anything unusual about these diamonds? Are they particularly bad or good, or do you think these are pricing errors?

# Use this chunk to place your code for extracting the high and low residuals and answer question 3
mod_di <- lm(
  lprice ~ lcarat + color + cut + clarity, diamonds2
)

bottom <-
  diamonds2 %>% 
  add_residuals(mod_diamond2) %>% 
  arrange(resid) %>% 
  slice(1:10)

top <-
  diamonds2 %>% 
  add_residuals(mod_diamond2) %>% 
  arrange(-resid) %>% 
  slice(1:10)

bind_rows(bottom, top) %>% 
  select(price, carat, resid)
## # A tibble: 20 x 3
##    price carat  resid
##    <int> <dbl>  <dbl>
##  1 10470 2.46  -1.17 
##  2  1262 1.03  -1.07 
##  3  2845 1.27  -0.971
##  4  3105 1.52  -0.942
##  5  3105 1.52  -0.942
##  6  7862 1.8   -0.847
##  7  6010 1.59  -0.787
##  8  3780 1.5   -0.787
##  9  7226 2.3   -0.783
## 10 12071 2.5   -0.729
## 11  2160 0.34   2.78 
## 12  1776 0.290  2.11 
## 13  1186 0.25   2.06 
## 14  1186 0.25   2.06 
## 15  1013 0.25   1.94 
## 16  2366 0.3    1.61 
## 17  1715 0.32   1.57 
## 18  4368 0.51   1.36 
## 19 10011 1.01   1.31 
## 20  3807 0.61   1.31

From the above code, we can see that there is no abnormality between the residue and the price. The diamonds with low residue have a higher purity and higher prices except for a couple of residues, the prices are outliered.

Question #4

Does the final model, mod_diamonds2, do a good job of predicting diamond prices? Would you trust it to tell you how much to spend if you were buying a diamond and why?

# Use this chunk to place your code for assessing how well the model predicts diamond prices and answer question 4
d2 <- diamonds2 %>% 
    add_predictions(mod_diamond) %>% 
    mutate(pred = round(2 ^ pred),
           err = pred - price)


d2 %>% 
  add_residuals(mod_diamond) %>% 
  mutate(resid = 2 ^ abs(resid)) %>% 
  ggplot(aes(resid)) +
  geom_histogram(color="lightblue",fill="darkblue")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

par(mfrow=c(2,2))
plot(mod_diamond2)

This model does a fairly good job at predicting the diamond prices but it does not look very reliable with some of the data points on the graph. I would not completely rely on the model to buy diamonds.