DiamondsDataModel
Kaiyu Shi
2019-05-20
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)
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
)
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 11.4ggplot(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 5.25Question #1
In the plot of lcarat vs. lprice, there are some bright vertical strips. What do they represent?
Those bright strips represent a high density of population is aggregated at some specific weights that are deemed to be the popular choices when people buying diamonds.
Question #2
If log(price) = a_0 + a_1 * log(carat), what does that say about the relationship between price and carat?
The equation describes a linear relationship between log-normalized price and log-normalized carat. log transformation means price and carat doesn’t have a linear relationship naturally. Instead, the percentage change in price is constant given a fixed percentage change in carat (i.e. if carat goes up by a%, price will go always up by b%).
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?
There are no pricing errors, but more expensive diamonds do have higher carats/clarity.
# Use this chunk to place your code for extracting the high and low residuals
diamonds2 <-
diamonds %>%
mutate(lprice = log2(price),
lcarat = log2(carat))
mod1 <- lm(lprice ~ lcarat + color + clarity + cut, data = diamonds2)
bottom <-
diamonds2 %>%
add_residuals(mod1) %>%
arrange(resid) %>%
slice(1:10)
top <-
diamonds2 %>%
add_residuals(mod1) %>%
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 6512 3 -1.46
## 2 10470 2.46 -1.17
## 3 10453 3.05 -1.14
## 4 14220 3.01 -1.12
## 5 9925 3.01 -1.12
## 6 18701 3.51 -1.09
## 7 1262 1.03 -1.04
## 8 8040 3.01 -1.02
## 9 12587 3.5 -0.990
## 10 8044 3 -0.985
## 11 2160 0.34 2.81
## 12 1776 0.290 2.10
## 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 1.31Question #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?
Not a very good one. The predictors are not normalized and the consequence is that the model’s residual error is quite high.
# Use this chunk to place your code for assessing how well the model predicts diamond prices
diamonds2 %>%
add_residuals(mod1) %>%
mutate(resid = 2 ^ abs(resid)) %>%
ggplot(aes(resid)) +
geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.