Lesson 6
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### Welcome
Notes:

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### Scatterplot Review

```{r Scatterplot Review}

```

***

### Price and Carat Relationship
Response:

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### Frances Gerety
Notes:

#### A diamonds is


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### The Rise of Diamonds
Notes:

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### ggpairs Function
Notes:

```{r ggpairs Function}
# 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)

# 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('.')))
```

What are some things you notice in the ggpairs output?
Response:

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### The Demand of Diamonds
Notes:

```{r The Demand of Diamonds}

```

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### Connecting Demand and Price Distributions
Notes:

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### Scatterplot Transformation

```{r Scatterplot Transformation}

```


### Create a new function to transform the carat variable

```{r cuberoot transformation}
cuberoot_trans = function() trans_new('cuberoot', transform = function(x) x^(1/3),
                                      inverse = function(x) x^3)
```

#### Use the cuberoot_trans function
```{r Use cuberoot_trans}
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')
```

***

### Overplotting Revisited

```{r Sort and Head Tables}

```


```{r Overplotting Revisited}
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')
```

***

### Other Qualitative Factors
Notes:

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### Price vs. Carat and Clarity

Alter the code below.
```{r Price vs. Carat and Clarity}
# install and load the RColorBrewer package
install.packages('RColorBrewer')
library(RColorBrewer)

ggplot(aes(x = carat, y = price), 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')
```

***

### Clarity and Price
Response:

***

### Price vs. Carat and Cut

Alter the code below.
```{r Price vs. Carat and Cut}
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')
```

***

### Cut and Price
Response:

***

### Price vs. Carat and Color

Alter the code below.
```{r Price vs. Carat and Color}
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')
```

***

### Color and Price
Response:

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### Linear Models in R
Notes:

Response:

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### Building the Linear Model
Notes:

```{r Building the Linear Model}
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)
```

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:

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### A Bigger, Better Data Set
Notes:

```{r A Bigger, Better Data Set}
install.package('bitops')
install.packages('RCurl')
library('bitops')
library('RCurl')

diamondsurl = getBinaryURL("https://raw.github.com/solomonm/diamonds-data/master/BigDiamonds.Rda")
load(rawConnection(diamondsurl))
```

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:

```{r Building a Model Using the Big Diamonds Data Set}

```


***

## Predictions

Example Diamond from BlueNile:
Round 1.00 Very Good I VS1 $5,601

```{r}
#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)
```

Evaluate 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:

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Click **KnitHTML** to see all of your hard work and to have an html
page of this lesson, your answers, and your notes!

