ANLY 505 - DiamondsDataModel
Week 3
yizhu zhang
2020-02-24
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?
# Answers:The bright vertical strips mean that diamonds are cut to different qualities. The brighter, the higher count they have.The bright verticals tripes represent areas of high concentration.Question #2
If log(price) = a_0 + a_1 * log(carat), what does that say about the relationship between price and carat?
# Anwers:If log(price) = a_0 + a_1 * log(carat), it means that price and carat have a linear relationship. 1% increase in carat is related to a 1% increase in 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?
diamonds3 <- diamonds2 %>%
filter(lresid > quantile(lresid)[[4]] | lresid < quantile(lresid)[[2]] )
diamonds3 %>%
ggplot(aes(color,price))+ geom_boxplot()+ facet_grid(~clarity)
###From the anaylysis we have here, relationship between price and clarity level is not consistent and there are few errors here. Diamonds with better clarity are priced lowerQuestion #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?
lmdiamond2 <- lm(lprice ~ lcarat + color + cut + clarity, diamonds2)
summary(lmdiamond2)##
## Call:
## lm(formula = lprice ~ lcarat + color + cut + clarity, data = diamonds2)
##
## 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-16diamondsv <- diamonds2 %>%
add_predictions(lmdiamond2)
ggplot(diamondsv, aes(lprice, pred)) + geom_point() +
geom_abline(slope=1, color="red")
residualsm <- summarise(diamonds2,
rmse = sqrt(mean(lresid2^2)),
mae = mean(abs(lresid2)))
residualsm## # A tibble: 1 x 2
## rmse mae
## <dbl> <dbl>
## 1 0.192 0.149###From the result of residualsm we could tell, rmse is only 0.19 which indcates that 98.1% of the errors can be presented by the model. The result shows that the model works well to present the condition of the diamonds.We could trust it if we want to assess the diamond when we are going to buy one.