Machine Learning Case Study - Housing Price Prediction

In this tutorial we will be using supervised machine learning technique 'Linear Regression' to predict the housing price.
We will be using a very power and scalable machine learning framework 'GraphLab' to do this case study.

Note:
Graphlab is free for academic and  personal use. For details about GraphLab Create,please visit.

Coding Time

Let's start your python editor,i'm using ipython notebook.

# Fire up graphlab create
import graphlab

Load some house sales data

Data set is from house sales in King County, the region where the city of Seattle, WA is located.This data set is taken from a machine learning course that i have done recently.

sales = graphlab.SFrame.read_csv('home_data.csv')

# Check some sample data
sales.head(3)

Exploring the data for housing sales

The house price is correlated with the number of square feet of living space.
Uncomment ,if you want to view the plot in same ipython notebook

#graphlab.canvas.set_target('ipynb')
sales.show(view="Scatter Plot", x="sqft_living", y="price")

Creating a simple regression model of sqft_living to price.

Let's create a simple linear regression model with one feature(sqft_living). This is also called univariate model as it is using only feature/independent variable.

Split data into training and testing

We use seed=0 so that everyone following this tutorial gets the same results. In practice, you may set a random seed (or let GraphLab Create pick a random seed for you).

train_data,test_data = sales.random_split(.8,seed=0)

Building the regression model using only sqft_living as a feature 

sqft_model = graphlab.linear_regression.create(train_data, target='price', features=['sqft_living'],validation_set=None)

Evaluating the simple model
Now its time to evaluate our simple model

print test_data['price'].mean()
print sqft_model.evaluate(test_data)

RMSE of about $255,170! Not good, can we create a better model??

Plotting with Matplotlib

Let's us check what our predictions look like,Matplotlib is a Python plotting library that is also useful for plotting.

import matplotlib.pyplot as plt
%matplotlib inline

plt.plot(test_data['sqft_living'],test_data['price'],'.',
        test_data['sqft_living'],sqft_model.predict(test_data),'-')

Above: blue dots are original data, green line is the prediction from the simple regression.
We can also view the learned regression coefficients using following command:
sqft_model.get('coefficients')

Explore other features in the data

To build a more elaborate model, we will explore using more features.

my_features = ['bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', 'zipcode']

We can have some visualization for better understanding as well:

sales[my_features].show()
sales.show(view='BoxWhisker Plot', x='zipcode', y='price')

** Pull the bar at the bottom to view more of the data.
98039 is the most expensive zip code.


Build a regression model with more features

my_features_model = graphlab.linear_regression.create(train_data,target='price',features=my_features,validation_set=None)
print my_features


Comparing the results of the simple model with adding more features

print sqft_model.evaluate(test_data)
print my_features_model.evaluate(test_data)

The RMSE goes down from $255,170 to $179,508 with more features.

Applying the learned models to predict prices of a house

The first house we will use is considered an "average" house in Seattle.

house1 = sales[sales['id']==5309101200]

#Check the price of house
print house1['price']

Output:
620000


Now check how the sqft model and my_feature model predict

print sqft_model.predict(graphlab.SFrame(house1))
Output:
629584.819

print my_features_model.predict(house1)
Output:
730345.745

In this case, the model with more features provides a worse prediction than the simpler model with only 1 feature. However, on average, the model with more features might be  better.

All codes available at github.

Machine Learning case study - Predicting Income Level with R

In this real world data analytics case study tutorial, we will use the US census data to build a model to predict if the income of any individual in the US is greater than or less than USD 50000 based on the information available about that individual in the census data.

The dataset used for the analysis is an extraction from the 1994 census data by Barry Becker and donated to the public site http://archive.ics.uci.edu/ml/datasets/Census+Income. This dataset is popularly called the “Adult” data set.

In this tutorial you will learn the following:

• Description about the data
• Acquiring and Reading the data
• Exploring the independent variables
• Building the prediction model
• Validating the prediction model

Note: I will be using caret package to do model building and cross validation in this tutorial, you can use any other library of your choice. caret is very powerful and handy library while doing Machine Learning or Analytics task using R. For more info :

https://cran.r-project.org/web/packages/caret/vignettes/caret.pdf

Description about the data:

As mentioned earlier, the data set is from http://archive.ics.uci.edu/ml/datasets/Census+Income.

Specifically the predictor variables (also called independent variables features) from the Census data and the dependent variable which is the level of income (either “greater than USD 50000” or “less than USD 50000”).

Dependent Variable

The dependent variable is “incomelevel”, representing the level of income. A value of “<=50K” indicates “less than or equal to USD 50000” and “>50K” indicates “greater than USD 50000”.

Independent Variable

Below are the independent variables (features or predictors) from the Census Data.

Variable Name	Description	Type	Possible Values
Age	Age of the individual	Continuous	Numeric
Workclass	Class of Work	Categorical	Private, Self-emp-not-inc, Self-emp-inc, Federal-gov, Local-gov, State-gov, Without-pay, Never-worked
fnlwgt	Final Weight Determined by Census Org	Continuous	Numeric
Education	Education of the individual	Ordered Factor	Bachelors, Some-college, 11th, HS-grad, Prof-school, Assoc-acdm, Assoc-voc, 9th, 7th-8th, 12th, Masters, 1st-4th, 10th, Doctorate, 5th-6th, Preschool
Education-num	Number of years of education	Continuous	Numeric
Marital-status	Marital status of the individual	Categorical	Married-civ-spouse, Divorced, Never-married, Separated, Widowed, Married-spouse-absent, Married-AF-spouse
Occupation	Occupation of the individual	Categorical	Tech-support, Craft-repair, Other-service, Sales, Exec-managerial, Prof-specialty, Handlers-cleaners, Machine-op-inspct, Adm-clerical, Farming-fishing, Transport-moving, Priv-house-serv, Protective-serv, Armed-Forces.
Relationship	Present relationship	Categorical	Wife, Own-child, Husband, Not-in-family, Other-relative, Unmarried
Race	Race of the individual	Categorical	White, Asian-Pac-Islander, Amer-Indian-Eskimo, Other, Black
Sex	Sex of the individual	Categorical	Female, Male
Capital-gain	Capital gain made by the individual	Continuous	Numeric
Capital-loss	Capital loss made by the individual	Continuous	Numeric
Hours-per-week	Average number of hours spent by the individual on work	Continuous	Numeric
Native-country	Native country of orgin	Categorical	United-States, Cambodia, England, Puerto-Rico, Canada, Germany, Outlying-US(Guam-USVI-etc), India, Japan, Greece, South, China, Cuba, Iran, Honduras, Philippines, Italy, Poland, Jamaica, Vietnam, Mexico, Portugal, Ireland, France, Dominican-Republic, Laos, Ecuador, Taiwan, Haiti, Columbia, Hungary, Guatemala, Nicaragua, Scotland, Thailand, Yugoslavia, El-Salvador, Trinadad&Tobago, Peru, Hong, Holand-Netherlands.

Load and Read the Data

Training data and test data are both separately available at the UCI source .

As the training data file does not contain the variable names, the variable names are explicitly specified while reading the data set. While reading the data, extra spaces are stripped.

colNames = c ("age", "workclass", "fnlwgt", "education", 
              "educationnum", "maritalstatus", "occupation",
              "relationship", "race", "sex", "capitalgain",
              "capitalloss", "hoursperweek", "nativecountry",
              "incomelevel")

train = read.table ("adult.data", header = FALSE, sep = ",",
                       strip.white = TRUE, col.names = colNames,
                        na.strings = "?", stringsAsFactors = TRUE)

Dataset is read and stored as train data frame of 32561 rows and 15 columns. A high level summary of the data is below. All the variables have been read in their expected classes.

str (train)

## 'data.frame':    32561 obs. of  15 variables:
##  $ age          : int  39 50 38 53 28 37 49 52 31 42 ...
##  $ workclass    : Factor w/ 8 levels "Federal-gov",..: 7 6 4 4 4 4 4 6 4 4 ...
##  $ fnlwgt       : int  77516 83311 215646 234721 338409 284582 160187 209642 45781 159449 ...
##  $ education    : Factor w/ 16 levels "10th","11th",..: 10 10 12 2 10 13 7 12 13 10 ...
##  $ educationnum : int  13 13 9 7 13 14 5 9 14 13 ...
##  $ maritalstatus: Factor w/ 7 levels "Divorced","Married-AF-spouse",..: 5 3 1 3 3 3 4 3 5 3 ...
##  $ occupation   : Factor w/ 14 levels "Adm-clerical",..: 1 4 6 6 10 4 8 4 10 4 ...
##  $ relationship : Factor w/ 6 levels "Husband","Not-in-family",..: 2 1 2 1 6 6 2 1 2 1 ...
##  $ race         : Factor w/ 5 levels "Amer-Indian-Eskimo",..: 5 5 5 3 3 5 3 5 5 5 ...
##  $ sex          : Factor w/ 2 levels "Female","Male": 2 2 2 2 1 1 1 2 1 2 ...
##  $ capitalgain  : int  2174 0 0 0 0 0 0 0 14084 5178 ...
##  $ capitalloss  : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ hoursperweek : int  40 13 40 40 40 40 16 45 50 40 ...
##  $ nativecountry: Factor w/ 41 levels "Cambodia","Canada",..: 39 39 39 39 5 39 23 39 39 39 ...
##  $ incomelevel  : Factor w/ 2 levels "<=50K",">50K": 1 1 1 1 1 1 1 2 2 2 ...

Cleaning the Data

The training data set is cleaned for missing or invalid data.

About 8% (2399/30162) of the dataset has NAs in them. It is observed that in most of the missing dataset, the ‘workclass’ variable and ‘occupation’ variable are missing data together. And the remaining have ‘nativecountry’ variable missing. We could, handle the missing values by imputing the data. However, since ‘workclass’, ‘occupation’ and ‘nativecountry’ could potentially be very good predictors of income, imputing may simply skew the model.

Also, since most of the missing data 2066/2399 (~86%) rows pertain to the “<=50K” incomelevel and the dataset is predominently of “<=50K” incomelevel, there will not be much information loss for predictive model building if we removed the NAs data set.

table (complete.cases (train))

## 
## FALSE  TRUE 
##  2399 30162

# Summarize all data sets with NAs only
summary  (train [!complete.cases(train),])

Data distribution

# Distribution of the income level factor in the entire training data set.
table (train$incomelevel)

## 
## <=50K  >50K 
## 24720  7841

Data sets with NAs are removed below:

cleanTrain = train [!is.na (train$workclass) & !is.na (train$occupation), ]
cleanTrain = cleanTrain [!is.na (cleanTrain$nativecountry), ]

The ‘fnlwgt’ final weight estimate refers to population totals derived from CPS by creating “weighted tallies” of any specified socio-economic characteristics of the population. This variable is removed from the training data set due to it’s diminished impact on income level.

cleanTrain$fnlwgt = NULL

The cleaned data set is now cleanTrain.

Exploring the Data

Each of the variable is explored for quirks, distribution, variance and predictability.

Explore the Continuous Variables

Since the model of choice here is Boosting, which is non-parametric (does not follow any statistical distribution), we will not be transforming variables to address skewness. We will however try to understand the data to determine each variable’s predictability.

Explore the Age variable

The Age variable has a wide range and variability. The distribution and mean are quite different for income level <=50K and >50K, implying that ‘age’ will be a good predictor of ‘incomelevel’.

summary (cleanTrain$age)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   17.00   28.00   37.00   38.44   47.00   90.00

boxplot (age ~ incomelevel, data = cleanTrain, 
         main = "Age distribution for different income levels",
         xlab = "Income Levels", ylab = "Age", col = "salmon")

incomeBelow50K = (cleanTrain$incomelevel == "<=50K")
xlimit = c (min (cleanTrain$age), max (cleanTrain$age))
ylimit = c (0, 1600)

hist1 = qplot (age, data = cleanTrain[incomeBelow50K,], margins = TRUE, 
           binwidth = 2, xlim = xlimit, ylim = ylimit, colour = incomelevel)

hist2 = qplot (age, data = cleanTrain[!incomeBelow50K,], margins = TRUE, 
           binwidth = 2, xlim = xlimit, ylim = ylimit, colour = incomelevel)

grid.arrange (hist1, hist2, nrow = 2)

Exploring the Years of Education Variable

The Years of Education variable has good variability. The statistics are quite different for income level <=50K and >50K, implying that ‘educationnum’ will be a good predictor of ‘incomelevel’.

summary (cleanTrain$educationnum)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1.00    9.00   10.00   10.12   13.00   16.00

boxplot (educationnum ~ incomelevel, data = cleanTrain, 
         main = "Years of Education distribution for different income levels",
         xlab = "Income Levels", ylab = "Years of Education", col = "blue")

Explore the correlation between continuous variables

The below shows that there is no correlation between the continuous variables and that they are independent of each other.

corMat = cor (cleanTrain[, c("age", "educationnum", "capitalgain", "capitalloss", "hoursperweek")])

diag (corMat) = 0 #Remove self correlations
corMat

##                     age educationnum capitalgain capitalloss hoursperweek
## age          0.00000000   0.04352609  0.08015423  0.06016548   0.10159876
## educationnum 0.04352609   0.00000000  0.12441600  0.07964641   0.15252207
## capitalgain  0.08015423   0.12441600  0.00000000 -0.03222933   0.08043180
## capitalloss  0.06016548   0.07964641 -0.03222933  0.00000000   0.05241705
## hoursperweek 0.10159876   0.15252207  0.08043180  0.05241705   0.00000000

Explore Categorical Variables

Exploring the Sex variable

Mostly the sex variable is not a good predictor, and so is the case for the incomelevel prediction too. This variable will not be used for the model.

table (cleanTrain[,c("sex", "incomelevel")])

##         incomelevel
## sex      <=50K  >50K
##   Female  8670  1112
##   Male   13984  6396

Exploring the workclass & occupation variables

The variables workclass & occupation  show good predictability of the incomelevel variable.

qplot (incomelevel, data = cleanTrain, fill = workclass) + facet_grid (. ~ workclass)

qplot (incomelevel, data = cleanTrain, fill = occupation) + facet_grid (. ~ occupation)

Exploring the education variables

The education variable however needs to be reordered and marked an ordinal variable (ordered factor variable). The new ordinal variable also shows good predictability of incomelevel.

# Modify the levels to be ordinal
cleanTrain$education = ordered (cleanTrain$education,
    levels (cleanTrain$education) [c(14, 4:7, 1:3, 12, 15, 8:9, 16, 10, 13, 11)])

print (levels (cleanTrain$education))

##  [1] "Preschool"    "1st-4th"      "5th-6th"      "7th-8th"     
##  [5] "9th"          "10th"         "11th"         "12th"        
##  [9] "HS-grad"      "Prof-school"  "Assoc-acdm"   "Assoc-voc"   
## [13] "Some-college" "Bachelors"    "Masters"      "Doctorate"

qplot (incomelevel, data = cleanTrain, fill = education) + facet_grid (. ~ education)

Building the Prediction Model

Finally, down to building the prediction model, we will be using all the independent variables except the Sex variable to build a model that predicts the income level of an individual to be greater than USD 50000 or less than USD 50000 using Census data.

Since, Census data is typically of weak predictors, Boosting algorithm is used for this classification modelling.

I have  used Cross Validation (CV) where the training data is partitioned a specific number of times and separate boosted models are built on each. The resulting models are ensembled to arrive at final model. This helps avoid overfitting the model to the training data.

library(caret)

set.seed (32323)
trCtrl = trainControl (method = "cv", number = 10)

boostFit = train (incomelevel ~ age + workclass + education + educationnum +
                      maritalstatus + occupation + relationship +
                      race + capitalgain + capitalloss + hoursperweek +
                      nativecountry, trControl = trCtrl, 
                  method = "gbm", data = cleanTrain, verbose = FALSE)

The confusion matrix below shows an in-sample overall accuracy of ~86%, sensitivity of ~88% and specificity of ~79%.

This implies that 86% of times, the model has classified the income level correctly, 88% of the times, the income level being less than or equal to USD 50000 in classified correctly and 79% of the times, the income level being greater than USD 50000 is classified correctly.

confusionMatrix (cleanTrain$incomelevel, predict (boostFit, cCleanTrain))

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction <=50K  >50K
##      <=50K 21415  1239
##      >50K   2900  4608
##                                           
##                Accuracy : 0.8628          
##                  95% CI : (0.8588, 0.8666)
##     No Information Rate : 0.8061          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.6037          
##  Mcnemar's Test P-Value : < 2.2e-16       
##                                           
##             Sensitivity : 0.8807          
##             Specificity : 0.7881          
##          Pos Pred Value : 0.9453          
##          Neg Pred Value : 0.6137          
##              Prevalence : 0.8061          
##          Detection Rate : 0.7100          
##    Detection Prevalence : 0.7511          
##       Balanced Accuracy : 0.8344          
##                                           
##        'Positive' Class : <=50K           
## 

Validating the Prediction Model

The created prediction model is applied on the test data to validate the true performance. The test data is cleaned similar to the training data before applying the model.

## 
## FALSE 
## 15060

The cleaning is not shown to keep the tutorial concise. The cleaned test dataset has 15060 rows and 14 columns with no missing data.

The prediction model is applied on the test data. From the confusion matrix below the performance measures are out-of-sample overall accuracy of ~86%, sensitivity of ~88% and specificity of ~78%, which is quite similar to the in-sample performance.

cleanTest$predicted = predict (boostFit, cleanTest)
confusionMatrix (cleanTest$incomelevel, cleanTest$predicted)

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction <=50K  >50K
##      <=50K 10731   629
##      >50K   1446  2254
##                                           
##                Accuracy : 0.8622          
##                  95% CI : (0.8566, 0.8677)
##     No Information Rate : 0.8086          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.5984          
##  Mcnemar's Test P-Value : < 2.2e-16       
##                                           
##             Sensitivity : 0.8813          
##             Specificity : 0.7818          
##          Pos Pred Value : 0.9446          
##          Neg Pred Value : 0.6092          
##              Prevalence : 0.8086          
##          Detection Rate : 0.7125          
##    Detection Prevalence : 0.7543          
##       Balanced Accuracy : 0.8315          
##                                           
##        'Positive' Class : <=50K           
## 

Note:

During a data analytics work, it is very important to understand how the built model has performed with respect to a baseline model. This helps the analyst understand if there is really any value that the new model adds.

The baseline accuracy (here, accuracy of selection by random chance as there is no prior model) is 75% for income less than USD 50000 (sensitivity) and 25% for income more than USD 50000 (specificity) with an overall accuracy of 68% (Refer the skewed number of data sets for both the incomelevels in the cleaned test data).

The prediction model built using the boosting algorithm can predict a less than USD 50000 income level with 88% accuracy (sensitivity) and a more than USD 50000 income level with 78% accuracy (specificity) and a overall accuracy of 86%.

So the prediction model does perform better than the baseline model.

All code available at github.