ANLY 505 - DiamondsDataModel
Week 3
Anvesh Raavi
2020-02-22
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 11.4ggplot(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?
#Vertical strips represent diamon cutters prefer certain weights which are in high demandQuestion #2
If log(price) = a_0 + a_1 * log(carat), what does that say about the relationship between price and carat?
# It suggests positive correlation between price and caratQuestion #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?
diamonds2 <- diamonds %>%
filter(carat <= 2.5) %>%
mutate(lprice = log2(price), lcarat = log2(carat))
mod_diamond <- lm(lprice ~ lcarat + color + clarity + cut, data = diamonds2)
diamonds2 <- diamonds2 %>%
add_residuals(mod_diamond,'lresid')
summary(diamonds2$lresid)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -1.17388 -0.12437 -0.00094 0.00000 0.11920 2.78322diamonds3 <- diamonds2 %>% filter(lresid > quantile(lresid)[[3]] | lresid < quantile(lresid)[[1]] )
table(diamonds3$cut)##
## Fair Good Very Good Premium Ideal
## 780 2562 6020 7048 10497table(diamonds3$clarity)##
## I1 SI2 SI1 VS2 VS1 VVS2 VVS1 IF
## 391 5032 6898 5879 3810 2395 1686 816diamonds3 %>%
ggplot(aes(clarity,price))+
geom_boxplot()+
facet_grid(~cut)
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 1.31# high residuals occur mostly in low carat dimonds, while low residuals occur in high carat dimonds.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?
mod_diamond2 <- lm(
lprice ~ lcarat + color + cut + clarity, diamonds2
)
diamonds4 <- diamonds2 %>%
add_predictions(mod_diamond2)
ggplot(diamonds4, aes(lprice, pred)) +
geom_point() +
geom_abline(slope=1, color="red")
summary(mod_diamond2)##
## Call:
## lm(formula = lprice ~ lcarat + color + cut + clarity, data = diamonds2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.45867 -0.12459 -0.00033 0.12033 2.81005
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.200915 0.001685 7242.225 < 2e-16 ***
## lcarat 1.883718 0.001129 1668.750 < 2e-16 ***
## color.L -0.634174 0.002925 -216.828 < 2e-16 ***
## color.Q -0.137955 0.002687 -51.335 < 2e-16 ***
## color.C -0.021328 0.002515 -8.481 < 2e-16 ***
## color^4 0.017098 0.002310 7.403 1.35e-13 ***
## color^5 -0.003176 0.002182 -1.455 0.146
## color^6 0.003450 0.001984 1.739 0.082 .
## cut.L 0.174154 0.003396 51.284 < 2e-16 ***
## cut.Q -0.050660 0.002989 -16.950 < 2e-16 ***
## cut.C 0.019446 0.002595 7.494 6.77e-14 ***
## cut^4 -0.002253 0.002079 -1.084 0.278
## clarity.L 1.322709 0.005161 256.274 < 2e-16 ***
## clarity.Q -0.350630 0.004804 -72.982 < 2e-16 ***
## clarity.C 0.191013 0.004118 46.387 < 2e-16 ***
## clarity^4 -0.095368 0.003294 -28.955 < 2e-16 ***
## clarity^5 0.039556 0.002689 14.711 < 2e-16 ***
## clarity^6 -0.002624 0.002342 -1.120 0.263
## clarity^7 0.048375 0.002066 23.412 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.193 on 53921 degrees of freedom
## Multiple R-squared: 0.9826, Adjusted R-squared: 0.9826
## F-statistic: 1.693e+05 on 18 and 53921 DF, p-value: < 2.2e-16# R squared value is 0.9826, Model may have been overfit, so do not depend on the model