Lesson 6
setwd("D:/R/Udacity/EDA_Course_Materials/lesson6")
library(ggplot2)Welcome
Notes:
Scatterplot Review
ggplot(data = diamonds, aes(x = carat, y = price)) +
scale_x_continuous(lim = c(0, quantile(diamonds$carat, 0.99))) +
scale_y_continuous(lim = c(0, quantile(diamonds$price, 0.99))) +
geom_point(fill= I('#F79420'), color = I('black'), shape = 21) +
stat_smooth(method = 'lm')## Warning: Removed 926 rows containing missing values (stat_smooth).## Warning: Removed 926 rows containing missing values (geom_point).## Warning: Removed 4 rows containing missing values (geom_path).
Price and Carat Relationship
Response: Price is growing with carat size and most of diamonds are concentrated in 1.0, 1.5, 2.0 carat sizes. Relationship between varialbes is not linear. ***
Frances Gerety
Notes:
A diamonds is
The Rise of Diamonds
Notes:
ggpairs Function
Notes:
# install these if necessary
#install.packages('GGally')
#install.packages('scales')
#install.packages('memisc')
#install.packages('lattice')
#install.packages('MASS')
#install.packages('car')
#install.packages('reshape')
#install.packages('plyr')
# load the ggplot graphics package and the others
library(ggplot2)
library(GGally)
library(scales)
library(memisc)## Loading required package: lattice
## Loading required package: MASS
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## Attaching package: 'memisc'
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## The following object is masked from 'package:scales':
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## percent
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## The following objects are masked from 'package:stats':
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## The following object is masked from 'package:base':
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## as.array# sample 10,000 diamonds from the data set
set.seed(20022012)
diamond_samp <- diamonds[sample(1:length(diamonds$price), 10000), ]
ggpairs(diamond_samp, params = c(shape = I('.'), outlier.shape = I('.')))## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
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What are some things you notice in the ggpairs output? Response: The value which is driving the price is carat of diamonds. ***
The Demand of Diamonds
Notes:
library(gridExtra)## Loading required package: gridplot1 <- qplot(data = diamonds, x = price, binwidth = 100, fill = I('#099DD9')) +
ggtitle('Price')
plot2 <- qplot(data = diamonds, x = price, binwidth = 0.01, fill = I('#F79420')) +
scale_x_log10() +
ggtitle('Price (log10)')
grid.arrange(plot1, plot2, ncol = 2)## Warning: position_stack requires constant width: output may be incorrect
Connecting Demand and Price Distributions
Notes: Picks on Price(log10) histogram are the most frequent price poor buyers and rich buyers get diamonds for. ***
Scatterplot Transformation
Create a new function to transform the carat variable
cuberoot_trans = function() trans_new('cuberoot', transform = function(x) x^(1/3),
inverse = function(x) x^3)Use the cuberoot_trans function
Overplotting Revisited
head(sort(table(diamonds$carat), decreasing = T))##
## 0.3 0.31 1.01 0.7 0.32 1
## 2604 2249 2242 1981 1840 1558head(sort(table(diamonds$price), decreasing = T))##
## 605 802 625 828 776 698
## 132 127 126 125 124 121ggplot(aes(carat, price), data = diamonds) +
geom_point(alpha = 1/2, size = 3/4, position = 'jitter') +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat')## Warning: Removed 1691 rows containing missing values (geom_point).
Other Qualitative Factors
Notes:
Price vs. Carat and Clarity
Alter the code below.
# install and load the RColorBrewer package
#install.packages('RColorBrewer')
library(RColorBrewer)
ggplot(aes(x = carat, y = price, color = clarity), data = diamonds) +
geom_point(alpha = 0.5, size = 1, position = 'jitter') +
scale_color_brewer(type = 'div',
guide = guide_legend(title = 'Clarity', reverse = T,
override.aes = list(alpha = 1, size = 2))) +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat and Clarity')## Warning: Removed 1693 rows containing missing values (geom_point).
Clarity and Price
Response: Diamonds of one size with higher clarity have higher price. ***
Price vs. Carat and Cut
Alter the code below.
ggplot(aes(x = carat, y = price, color = cut), data = diamonds) +
geom_point(alpha = 0.5, size = 1, position = 'jitter') +
scale_color_brewer(type = 'div',
guide = guide_legend(title = 'Cut', reverse = T,
override.aes = list(alpha = 1, size = 2))) +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat and Cut')## Warning: Removed 1696 rows containing missing values (geom_point).
Cut and Price
Response: We cannot say if cut accounts for variance in price. In this dataset we mostly have diamonds of ideal cut. ***
Price vs. Carat and Color
Alter the code below.
ggplot(aes(x = carat, y = price, color = color), data = diamonds) +
geom_point(alpha = 0.5, size = 1, position = 'jitter') +
scale_color_brewer(type = 'div',
guide = guide_legend(title = 'Color',
override.aes = list(alpha = 1, size = 2))) +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat and Color')## Warning: Removed 1688 rows containing missing values (geom_point).
Color and Price
Response: Color influences price as we see diamonds of D color usually have higher price. ***
Linear Models in R
Notes:
Response:
Building the Linear Model
Notes:
m1 <- lm(I(log(price)) ~ I(carat^(1/3)), data = diamonds)
m2 <- update(m1, ~ . + carat)
m3 <- update(m2, ~ . + cut)
m4 <- update(m3, ~ . + color)
m5 <- update(m4, ~ . + clarity)
mtable(m1, m2, m3, m4, m5)##
## Calls:
## m1: lm(formula = I(log(price)) ~ I(carat^(1/3)), data = diamonds)
## m2: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat, data = diamonds)
## m3: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut, data = diamonds)
## m4: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut + color,
## data = diamonds)
## m5: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut + color +
## clarity, data = diamonds)
##
## ======================================================================
## m1 m2 m3 m4 m5
## ----------------------------------------------------------------------
## (Intercept) 2.821*** 1.039*** 0.874*** 0.932*** 0.415***
## (0.006) (0.019) (0.019) (0.017) (0.010)
## I(carat^(1/3)) 5.558*** 8.568*** 8.703*** 8.438*** 9.144***
## (0.007) (0.032) (0.031) (0.028) (0.016)
## carat -1.137*** -1.163*** -0.992*** -1.093***
## (0.012) (0.011) (0.010) (0.006)
## cut: .L 0.224*** 0.224*** 0.120***
## (0.004) (0.004) (0.002)
## cut: .Q -0.062*** -0.062*** -0.031***
## (0.004) (0.003) (0.002)
## cut: .C 0.051*** 0.052*** 0.014***
## (0.003) (0.003) (0.002)
## cut: ^4 0.018*** 0.018*** -0.002
## (0.003) (0.002) (0.001)
## color: .L -0.373*** -0.441***
## (0.003) (0.002)
## color: .Q -0.129*** -0.093***
## (0.003) (0.002)
## color: .C 0.001 -0.013***
## (0.003) (0.002)
## color: ^4 0.029*** 0.012***
## (0.003) (0.002)
## color: ^5 -0.016*** -0.003*
## (0.003) (0.001)
## color: ^6 -0.023*** 0.001
## (0.002) (0.001)
## clarity: .L 0.907***
## (0.003)
## clarity: .Q -0.240***
## (0.003)
## clarity: .C 0.131***
## (0.003)
## clarity: ^4 -0.063***
## (0.002)
## clarity: ^5 0.026***
## (0.002)
## clarity: ^6 -0.002
## (0.002)
## clarity: ^7 0.032***
## (0.001)
## ----------------------------------------------------------------------
## R-squared 0.924 0.935 0.939 0.951 0.984
## adj. R-squared 0.924 0.935 0.939 0.951 0.984
## sigma 0.280 0.259 0.250 0.224 0.129
## F 652012.063 387489.366 138654.523 87959.467 173791.084
## p 0.000 0.000 0.000 0.000 0.000
## Log-likelihood -7962.499 -3631.319 -1837.416 4235.240 34091.272
## Deviance 4242.831 3613.360 3380.837 2699.212 892.214
## AIC 15930.999 7270.637 3690.832 -8442.481 -68140.544
## BIC 15957.685 7306.220 3761.997 -8317.942 -67953.736
## N 53940 53940 53940 53940 53940
## ======================================================================Notice how adding cut to our model does not help explain much of the variance in the price of diamonds. This fits with out exploration earlier.
Model Problems
Video Notes: We didn’t count inflation or any financial market changes.
Research: (Take some time to come up with 2-4 problems for the model) (You should 10-20 min on this)
Response:
A Bigger, Better Data Set
Notes:
#install.packages('bitops')
#install.packages('RCurl')
library('bitops')
library('RCurl')
#diamondsurl <- getBinaryURL("https://raw.github.com/solomonm/diamonds-data/master/BigDiamonds.Rda")
#load(rawConnection(diamondsurl))
load("BigDiamonds.rda")
diamondsBig <- read.csv('diamondsBig.csv')The code used to obtain the data is available here: https://github.com/solomonm/diamonds-data
Building a Model Using the Big Diamonds Data Set
Notes:
m1 <- lm(I(log(price)) ~ I(carat^(1/3)), data = diamondsBig)
m2 <- update(m1, ~ . + carat)
m3 <- update(m2, ~ . + cut)
m4 <- update(m3, ~ . + color)
m5 <- update(m4, ~ . + clarity)
mtable(m1, m2, m3, m4, m5)##
## Calls:
## m1: lm(formula = I(log(price)) ~ I(carat^(1/3)), data = diamondsBig)
## m2: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat, data = diamondsBig)
## m3: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut, data = diamondsBig)
## m4: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut + color,
## data = diamondsBig)
## m5: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut + color +
## clarity, data = diamondsBig)
##
## ===========================================================================
## m1 m2 m3 m4 m5
## ---------------------------------------------------------------------------
## (Intercept) 3.096*** 1.406*** 1.218*** 1.299*** 0.578***
## (0.002) (0.005) (0.005) (0.005) (0.004)
## I(carat^(1/3)) 5.317*** 7.911*** 7.920*** 8.170*** 8.368***
## (0.002) (0.008) (0.008) (0.007) (0.005)
## carat -0.767*** -0.779*** -0.782*** -0.815***
## (0.002) (0.002) (0.002) (0.001)
## cut: Ideal 0.256*** 0.222*** 0.130***
## (0.002) (0.001) (0.001)
## cut: V.Good 0.119*** 0.092*** 0.059***
## (0.002) (0.002) (0.001)
## color: E/D -0.104*** -0.081***
## (0.002) (0.001)
## color: F/D -0.171*** -0.135***
## (0.002) (0.001)
## color: G/D -0.267*** -0.225***
## (0.002) (0.001)
## color: H/D -0.377*** -0.327***
## (0.002) (0.001)
## color: I/D -0.472*** -0.429***
## (0.002) (0.001)
## color: J/D -0.592*** -0.561***
## (0.002) (0.001)
## color: K/D -0.760*** -0.758***
## (0.002) (0.002)
## color: L/D -0.894*** -0.886***
## (0.003) (0.003)
## clarity: I2 -0.355***
## (0.005)
## clarity: IF 0.992***
## (0.002)
## clarity: SI1 0.479***
## (0.002)
## clarity: SI2 0.329***
## (0.002)
## clarity: VS1 0.713***
## (0.002)
## clarity: VS2 0.625***
## (0.002)
## clarity: VVS1 0.869***
## (0.002)
## clarity: VVS2 0.790***
## (0.002)
## ---------------------------------------------------------------------------
## R-squared 0.893 0.911 0.915 0.940 0.968
## adj. R-squared 0.893 0.911 0.915 0.940 0.968
## sigma 0.425 0.389 0.379 0.318 0.233
## F 5000339.553 3039162.591 1608418.407 785005.644 903078.293
## p 0.000 0.000 0.000 0.000 0.000
## Log-likelihood -336293.722 -283694.777 -268204.909 -162478.620 23289.316
## Deviance 107833.287 90420.162 85850.030 60255.534 32348.910
## AIC 672593.443 567397.553 536421.818 324985.239 -46534.632
## BIC 672627.344 567442.754 536489.619 325143.442 -46286.028
## N 597311 597311 597311 597311 597311
## ===========================================================================Predictions
Example Diamond from BlueNile: Round 1.00 Very Good I VS1 $5,601
#Be sure you’ve loaded the library memisc and have m5 saved as an object in your workspace.
thisDiamond = data.frame(carat = 1.00, cut = "V.Good",
color = "I", clarity="VS1")
modelEstimate = predict(m5, newdata = thisDiamond,
interval="prediction", level = .95)
exp(modelEstimate)## fit lwr upr
## 1 4786.053 3033.06 7552.207Evaluate how well the model predicts the BlueNile diamond’s price. Think about the fitted point estimate as well as the 95% CI.
Final Thoughts
Notes: This model to realize if you’re overpaying for a diamond. But it doesn’t predict the exact price of the diamond. ***
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