In this chapter, we will use six libraries. These libraries are as listed in the following code:
# Libraries
library(keras)
library(mlbench)
library(psych)
library(dplyr)
library(magrittr)
library(neuralnet)
The structure of the BostonHousing data is as follows:
# Data structure
data(BostonHousing)
str(BostonHousing)
OUTPUT
'data.frame': 506 obs. of 14 variables: $ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ... $ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ... $ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ... $ chas : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ... $ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ... $ rm : num 6.58 6.42 7.18 7 7.15 ... $ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ... $ dis : num 4.09 4.97 4.97 6.06 6.06 ... $ rad : num 1 2 2 3 3 3 5 5 5 5 ... $ tax : num 296 242 242 222 222 222 311 311 311 311 ... $ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ... $ b : num 397 397 393 395 397 ... $ lstat : num 4.98 9.14 4.03 2.94 5.33 ... $ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...
As you can see from the preceding output, this dataset has 506 observations and 14 variables. Out of the 14 variables, 13 are numeric and 1 variable (chas) is of the factor type. The last variable, medv (the median value of owner-occupied homes in thousand-USD units), is the dependent, or target, variable. The remaining 13 variables are independent. The following is a brief description of all the variables, drawn up in a table for easy reference:
| Variables | Description |
| crim | Per-capita crime rate by town |
| zn | Proportion of residential land zoned for lots over 25,000 sq ft |
| indus | Proportion of nonretail business acres per town |
| chas | Charles River dummy variable (1 if the tract bounds a river; 0 otherwise) |
| nox | Nitric-oxides concentration (parts per 10 million) |
| rm | Average number of rooms per dwelling |
| age | Proportion of owner-occupied units built prior to 1940 |
| dis | Weighted distances to five Boston employment centers |
| rad | Index of accessibility to radial highways |
| tax | Full-value property-tax rate per 10,000 USD |
| ptratio | Pupil–teacher ratio by town |
| lstat | Percentage of lower-income status members of the population |
| medv | Median value of owner-occupied homes in thousand-USD units |
This data is based on the 1970 census. A detailed statistical study using this data was published by Harrison and Rubinfeld in 1978 (reference: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.926.5532&rep=rep1&type=pdf).