DiamondsDataModel
Bhavesh Vaswani
2019-10-14
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)## Warning: Computation failed in `stat_binhex()`:
## Package `hexbin` required for `stat_binhex`.
## Please install and try again.
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)## Warning: Computation failed in `stat_binhex()`:
## Package `hexbin` required for `stat_binhex`.
## Please install and try again.
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)## Warning: Computation failed in `stat_binhex()`:
## Package `hexbin` required for `stat_binhex`.
## Please install and try again.
Add residuals and plot
diamonds2 <- diamonds2 %>%
add_residuals(mod_diamond, "lresid")
ggplot(diamonds2, aes(lcarat, lresid)) +
geom_hex(bins = 50)## Warning: Computation failed in `stat_binhex()`:
## Package `hexbin` required for `stat_binhex`.
## Please install and try again.
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)## Warning: Computation failed in `stat_binhex()`:
## Package `hexbin` required for `stat_binhex`.
## Please install and try again.
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?
The visualized analysis shows counts of diamond cuts. The bright vertical strips represent higher count. They represent preffered weight as useful by the jewel maker in order to cut specific weight for diamonds.
Question #2
If log(price) = a_0 + a_1 * log(carat), what does that say about the relationship between price and carat?
Linear relationship between diamond price & diamond carat can be represented based on the above depicted relationship.
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
diamond_extract <- diamonds %>%
filter(carat <= 2.5) %>%
mutate(lprice = log2(price), lcarat = log2(carat))
diamondmod <- lm(lprice ~ lcarat + color + clarity + cut, data = diamond_extract)
diamond_extract <- diamond_extract %>%
add_residuals(diamondmod ,'lresid')
summary(diamond_extract$lresid)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -1.17388 -0.12437 -0.00094 0.00000 0.11920 2.78322diamond_extract2<- diamond_extract %>% filter(lresid > quantile(lresid)[[3]] | lresid < quantile(lresid)[[1]] )
table(diamond_extract2$cut)##
## Fair Good Very Good Premium Ideal
## 780 2562 6020 7048 10497table(diamond_extract2$clarity)##
## I1 SI2 SI1 VS2 VS1 VVS2 VVS1 IF
## 391 5032 6898 5879 3810 2395 1686 816diamond_extract2 %>% ggplot(aes(clarity,price)) + geom_boxplot() + facet_grid(~cut)
Graph plainly depicts low carat diamonds show high residuals.
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
diamondmod2 <- lm(lprice ~ lcarat + color + cut + clarity, diamond_extract)
dia_variable <- diamond_extract %>% add_predictions(diamondmod2)
ggplot(dia_variable, aes(lprice, pred)) + geom_point() + geom_abline(slope=1, color="red")
#Summarizing the model
summary(diamondmod2)##
## Call:
## lm(formula = lprice ~ lcarat + color + cut + clarity, data = diamond_extract)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.17388 -0.12437 -0.00094 0.11920 2.78322
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.206978 0.001693 7211.806 < 2e-16 ***
## lcarat 1.886239 0.001124 1677.809 < 2e-16 ***
## color.L -0.633998 0.002910 -217.872 < 2e-16 ***
## color.Q -0.137580 0.002676 -51.409 < 2e-16 ***
## color.C -0.022072 0.002503 -8.819 < 2e-16 ***
## color^4 0.016570 0.002297 7.213 5.54e-13 ***
## color^5 -0.002828 0.002169 -1.304 0.192
## color^6 0.003533 0.001971 1.793 0.073 .
## cut.L 0.173866 0.003386 51.349 < 2e-16 ***
## cut.Q -0.050346 0.002980 -16.897 < 2e-16 ***
## cut.C 0.019129 0.002583 7.407 1.31e-13 ***
## cut^4 -0.002410 0.002066 -1.166 0.243
## clarity.L 1.308155 0.005179 252.598 < 2e-16 ***
## clarity.Q -0.334090 0.004839 -69.047 < 2e-16 ***
## clarity.C 0.178423 0.004140 43.093 < 2e-16 ***
## clarity^4 -0.088059 0.003298 -26.697 < 2e-16 ***
## clarity^5 0.035885 0.002680 13.389 < 2e-16 ***
## clarity^6 -0.001371 0.002327 -0.589 0.556
## clarity^7 0.048221 0.002051 23.512 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1916 on 53795 degrees of freedom
## Multiple R-squared: 0.9828, Adjusted R-squared: 0.9828
## F-statistic: 1.706e+05 on 18 and 53795 DF, p-value: < 2.2e-16Significant coefficients p-values obtained based on above summary table.