Lesson 6
Welcome
Notes:
Scatterplot Review
# Let's start by examining two variables in the data set.
# The scatterplot is a powerful tool to help you understand
# the relationship between two continuous variables.
# We can quickly see if the relationship is linear or not.
# In this case, we can use a variety of diamond
# characteristics to help us figure out whether
# the price advertised for any given diamond is
# reasonable or a rip-off.
# Let's consider the price of a diamond and it's carat weight.
# Create a scatterplot of price (y) vs carat weight (x).
# Limit the x-axis and y-axis to omit the top 1% of values.
# ENTER YOUR CODE BELOW THIS LINE
# ================================================================
library(ggplot2)
library(dplyr)
data(diamonds)
subset(diamonds, price < quantile(price, 0.99) && carat < quantile(carat, 0.99)) %>%
ggplot(aes(x=carat, y=price)) +
geom_point()
Price and Carat Relationship
Response:
Frances Gerety
Notes:
A diamonds is forever
The Rise of Diamonds
Notes:
ggpairs Function
Notes:
# load the ggplot graphics package and the others
library(ggplot2)
library(GGally)
library(scales)
library(memisc)
# sample 10,000 diamonds from the data set
set.seed(20022012)
diamond_samp <- diamonds[sample(1:length(diamonds$price), 10000), ]
ggpairs(diamond_samp,
lower = list(continuous = wrap("points", shape = I('.'))),
upper = list(combo = wrap("box", outlier.shape = I('.'))))
What are some things you notice in the ggpairs output? Response:
The Demand of Diamonds
Notes:
# Create two histograms of the price variable
# and place them side by side on one output image.
# We've put some code below to get you started.
# The first plot should be a histogram of price
# and the second plot should transform
# the price variable using log10.
# Set appropriate bin widths for each plot.
# ggtitle() will add a title to each histogram.
# You can self-assess your work with the plots
# in the solution video.
# ALTER THE CODE BELOW THIS LINE
# ==============================================
library(gridExtra)
plot1 <- qplot(data=diamonds, x=price) +
ggtitle('Price')
plot2 <- qplot(data=diamonds, x=price) +
ggtitle('Price (log10)') +
scale_x_log10()
grid.arrange(plot1, plot2, ncol=2)
Connecting Demand and Price Distributions
Notes:
Scatterplot Transformation
qplot(carat, price, data=diamonds) +
scale_y_continuous( trans=log10_trans() ) +
ggtitle('Price (log10) by Carat')
Create a new function to transform the carat variable
cuberoot_trans = function() trans_new('cuberoot', transform = function(x) x^(1/3),
inverse = function(x) x^3)Use the cuberoot_trans function
ggplot(aes(carat, price), data = diamonds) +
geom_point() +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat')## Warning: Removed 1683 rows containing missing values (geom_point).
Overplotting Revisited
head(sort(table(diamonds$carat), decreasing=TRUE))##
## 0.3 0.31 1.01 0.7 0.32 1
## 2604 2249 2242 1981 1840 1558head(sort(table(diamonds$price), decreasing=TRUE))##
## 605 802 625 828 776 698
## 132 127 126 125 124 121ggplot(aes(carat, price), data = diamonds) +
geom_point() +
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 1683 rows containing missing values (geom_point).
# Add a layer to adjust the features of the
# scatterplot. Set the transparency to one half,
# the size to three-fourths, and jitter the points.
# If you need hints, see the Instructor Notes.
# There are three hints so scroll down slowly if
# you don't want all the hints at once.
# ALTER THE CODE BELOW THIS LINE
# =======================================================================
ggplot(aes(carat, price), data = diamonds) +
geom_point(alpha=0.5, size=0.75, position=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
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:
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:
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:
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 0.9 0.9 0.9 1.0 1.0
## adj. R-squared 0.9 0.9 0.9 1.0 1.0
## sigma 0.3 0.3 0.3 0.2 0.1
## F 652012.1 387489.4 138654.5 87959.5 173791.1
## p 0.0 0.0 0.0 0.0 0.0
## Log-likelihood -7962.5 -3631.3 -1837.4 4235.2 34091.3
## Deviance 4242.8 3613.4 3380.8 2699.2 892.2
## AIC 15931.0 7270.6 3690.8 -8442.5 -68140.5
## BIC 15957.7 7306.2 3762.0 -8317.9 -67953.7
## 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:
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:
library('bitops')
library('RCurl')
diamondsurl = getBinaryURL("https://raw.github.com/solomonm/diamonds-data/master/BigDiamonds.Rda")
#load(rawConnection(diamondsurl))
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:
# Your task is to build five linear models like Solomon
# did for the diamonds data set only this
# time you'll use a sample of diamonds from the
# diamondsbig data set.
# Be sure to make use of the same variables
# (logprice, carat, etc.) and model
# names (m1, m2, m3, m4, m5).
# To get the diamondsbig data into RStudio
# on your machine, copy, paste, and run the
# code in the Instructor Notes. There's
# 598,024 diamonds in this data set!
# Since the data set is so large,
# you are going to use a sample of the
# data set to compute the models. You can use
# the entire data set on your machine which
# will produce slightly different coefficients
# and statistics for the models.
# This exercise WILL BE automatically graded.
# You can leave off the code to load in the data.
# We've sampled the data for you.
# You also don't need code to create the table output of the models.
# We'll do that for you and check your model summaries (R^2 values, AIC, etc.)
# Your task is to write the code to create the models.
# DO NOT ALTER THE CODE BELOW THIS LINE (Reads in a sample of the diamondsbig data set)
#===========================================================================================
#diamondsBigSample <- read.csv('diamondsBigSample.csv')
# ENTER YOUR CODE BELOW THIS LINE. (Create the five models)
#===========================================================================================
diamondsBigSample <- subset(diamondsbig, cert='GIA' & price < 10000)
m1 <- lm(I(log(price)) ~ I(carat^(1/3)), data = diamondsBigSample)
m2 <- update(m1, ~ . + carat)
m3 <- update(m2, ~ . + cut)
m4 <- update(m3, ~ . + color)
m5 <- update(m4, ~ . + clarity)
# DO NOT ALTER THE CODE BELOW THIS LINE (Tables your models and pulls out the statistics)
#===========================================================================================
suppressMessages(library(lattice))
suppressMessages(library(MASS))
suppressMessages(library(memisc))
models <- mtable(m1, m2, m3, m4, m5)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:
Click KnitHTML to see all of your hard work and to have an html page of this lesson, your answers, and your notes!