Initial Visualization

install.packages("hexbin")
## Installing package into '/home/rstudio-user/R/x86_64-pc-linux-gnu-library/3.6'
## (as 'lib' is unspecified)
library(hexbin)
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?

#  Answer question 1
# Answer: the bright strips are indicating the count of the diamonds. it seems that particular carat diamonds are popular or common or we can say have good demand in the market.

Question #2

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

#  Answer question 2

# Answer 2: itseems that relationship between Carat Size and price have an exponential relationship but price of the diamond is dependent on the Carat size.

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

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

mod_diamond <- lm(lprice ~ lcarat, data = diamonds2)

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

summary(diamonds2$lresid)
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## -1.964068 -0.245488 -0.008442  0.000000  0.239301  1.934855
diamond_extract <- diamonds2 %>% filter(lresid > quantile(lresid)[[3]] | lresid < quantile(lresid)[[1]] )
table(diamond_extract$cut)
## 
##      Fair      Good Very Good   Premium     Ideal 
##       317      1651      5515      6477     12946
diamond_extract %>% 
  ggplot(aes(clarity,price))+
  geom_boxplot()+
  facet_grid(~cut)

# we can see the ideal and premium diamonds clarity wise, they are price less than the good and very good one. it seems there is a pricing error.

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

#i do not select the Model to decide to buy a diamond or not because the predictions accross the categroies like bad good and premium are almost equally priced (predicted).