Case Study #4: Predicting Boston Housing
Prices with Neural Network
For this case, apply the same data set as for case study #1, BostonHousing.csv. It contains information collected
by the U.S. Census Bureau concerning housing in the area of Boston. The goal is to predict the median house
price in new areas based on information such as crime rate, pollution, and number of rooms, etc. The dataset
contains 13 predictors, and the outcome variable is the median house value/price (MVALUE). The table below
describes each of the predictors and the outcome.
Variables Description of Variables
CRIME Per capita crime rate by town.
ZONE Proportion of residential land zoned for lots over 25,000 square feet.
INDUST Percentage of nonretail business acres per town.
CHAR RIV “Y” if house tract bounds Char River, and “N” if otherwise.
NIT OXIDE Nitric oxide concentration (parts per 10 million).
ROOMS Average number of rooms per dwelling.
AGE Proportion of owner-occupied units built prior to 1940.
DISTANCE Weighted distance to five Boston employment centers.
RADIAL Index of accessibility to radial highways.
Full-value property tax rate per $10,000 (does not depend on the median value
TAX of homes).
ST RATIO Student/teacher ratio by town.
LOW STAT Percentage of lower status of the population.
MVALUE Median value (price) of owner-occupied homes in $10000s.
“Yes” for houses with the price equal or greater than $300K, and “No” for
C MVALUE houses with the price of less than $300K.
Questions
1. Upload, explore, clean, and preprocess data for neural network modeling. (This part of the case will
not be graded as all questions below have been already done in case study #1).
a. Create a boston_df data frame by uploading the original data set into Python. Determine and
present in this report the data frame dimensions, i.e., number of rows and columns.
b. Display in Python the column titles and present them in your report. If some of them contain
two (or more) words, convert them into one-word titles, and present the modified titles in
your report.
c. Display column data types in Python and present them in your report. If some of them are
listed as “object’, briefly explain that in your report, convert them into dummy variables with
integer type, and provide in your report the modified list of column titles with dummy
variables.
2. Develop a neural network model for Boston Housing and use it for predictions.
a. Why can a neural network model be used in this case? Briefly explain.
b. Develop in Python the outcome and predictor variables, partition the data set (75% for
training and 25% for validation partitions), display in Python and present in your report the
first five records of the training partition. Then, using the StandardScaler() function, develop
the scaled predictors for training and validation partitions. Display in Python and provide in
your report the first five records of the scaled training partition. Present a brief explanation
of what the scaled values mean and how they are calculated.
c. Train a neural network model using MLPRegressor() with the scaled training data set and the
following parameters: hidden_layer_sizes=15, solver=’lbfgs’, max_iter=10000, and
random_state=1. Identify and display in Python the final intercepts and network weights of
this model. Provide these intercepts and weights in your report and briefly explain what the
values of intercepts in the first and second arrays mean. Also, briefly explain what the values
of weights in the first and second arrays mean.
d. Using the developed neural network model, make in Python predictions for the outcome
variable (MVALUE) using the scaled validation predictors. Based on these predictions, develop
and display in Python a table for the first five validation records that contain actual and
predicted median prices (MVALUE), and their residuals. Present this table in your report.
e. Identify and display in Python the common accuracy measures for training and validation
partitions. Provide and compare these accuracy measures in your report and assess the
possibility of overfitting. Would you recommend applying this neural network model for
predictions? Briefly explain.
3. Develop an improved neural network model with grid search.
a. Use in Python GridSearchCV() function to identify the best number of nodes for the hidden
layer in the Boston Housing neural network model. For that, consider the hidden_layer_sizes
parameter in a range from 2 to 20. For MLPRegressor() function, the solver, max_iter, and
random state values are the same as those in question 2c. Provide in your report the best
score and best parameter value and briefly explain what it means.
b. Train an improved neural network model using MLPRegressor() (solver, max_iter, and random
state values are the same as in question 2c) with the scaled training data set and the best
identified value of the hidden_layer_sizes parameter from the previous question. Present in
your report the final intercepts and network weights of the improved neural network model.
c. Identify and display in Python the common accuracy measures for the training and validation
partitions with the improved neural network model. Provide and compare these accuracy
measures in your report and assess the possibility of overfitting. Would you recommend
applying this neural network model for predictions? Briefly explain.
d. Present and compare the accuracy measures for the validation partition from the Exhaustive
Search model for the multiple linear regression in case study #1 and the validation partition
for the improved neural network model in part 3 of this case. Which model would you
recommend for predictions and why? Briefly explain.
e. How can the best model from the previous question be used in practice and what business
results can you gain from this model being used in practice? Present you explanation.
