California Housing Prices
Housing prices include housing rent prices indices, real and nominal house prices indices, and ratios of price to rent and price to income. In most cases, the nominal house price index covers the sales of newly-built and existing dwellings, following the recommendations from the RPPI (Residential Property Prices Indices) manual.
The goal of this challenge is to build a machine learning model that predicts the price of the houses in california with the help of various features.Further accurate prediction of house price will help the customer to analyze the price of various houses and select the most appropriate for them according to their budget.
Dataset: -
The data pertains to the houses found in a given California district and some summary stats about them based on the 1990 census data.
Attribute Information:
- longitude
- latitude
- housing_median_age
- total_rooms
- total_bedrooms
- population
- households
- median_income
- median_house_value
- ocean_proximity
Step 1: Import all the required libraries
- Pandas : In computer programming, pandas is a software library written for the Python programming language for data manipulation and analysis and storing in a proper way. In particular, it offers data structures and operations for manipulating numerical tables and time series
- Sklearn : Scikit-learn (formerly scikits.learn) is a free software machine learning library for the Python programming language. It features various classification, regression and clustering algorithms including support vector machines, random forests, gradient boosting, k-means and DBSCAN, and is designed to interoperate with the Python numerical and scientific libraries NumPy and SciPy. The library is built upon the SciPy (Scientific Python) that must be installed before you can use scikit-learn.
- Pickle : Python pickle module is used for serializing and de-serializing a Python object structure. Pickling is a way to convert a python object (list, dict, etc.) into a character stream. The idea is that this character stream contains all the information necessary to reconstruct the object in another python script.
- Seaborn : Seaborn is a Python data visualization library based on matplotlib. It provides a high-level interface for drawing attractive and informative statistical graphics.
- Matplotlib : Matplotlib is a plotting library for the Python programming language and its numerical mathematics extension NumPy. It provides an object-oriented API for embedding plots into applications using general-purpose GUI toolkits like Tkinter, wxPython, Qt, or GTK.
#Loading libraries
import pandas as pd
import seaborn as sns
import pickle
import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression, Ridge, RidgeCV, Lasso, LassoCV
from sklearn.model_selection import KFold, cross_val_score, train_test_split
import warnings
warnings.filterwarnings('ignore')Step 2 : Read dataset and basic details of dataset
Goal:- In this step we are going to read the dataset, view the dataset and analysis the basic details like total number of rows and columns, what are the column data types and see to need to create new column or not.
In this stage we are going to read our problem dataset and have a look on it.
#loading the dataset
try:
df = pd.read_csv('C:/Users/YAJENDRA/Documents/final notebooks/California Housing Prices/data/housing.csv') #Path for the file
print('Data read done successfully...')
except (FileNotFoundError, IOError):
print("Wrong file or file path")Data read done successfully...# To view the content inside the dataset we can use the head() method that returns a specified number of rows, string from the top.
# The head() method returns the first 5 rows if a number is not specified.
df.head()
Step3: Data Preprocessing
Why need of Data Preprocessing?
Preprocessing data is an important step for data analysis. The following are some benefits of preprocessing data:
- It improves accuracy and reliability. Preprocessing data removes missing or inconsistent data values resulting from human or computer error, which can improve the accuracy and quality of a dataset, making it more reliable.
- It makes data consistent. When collecting data, it’s possible to have data duplicates, and discarding them during preprocessing can ensure the data values for analysis are consistent, which helps produce accurate results.
- It increases the data’s algorithm readability. Preprocessing enhances the data’s quality and makes it easier for machine learning algorithms to read, use, and interpret it.
Why we drop column?
There is no column required to drop.
Axis are defined for arrays with more than one dimension. A 2-dimensional array has two corresponding axes: the first running vertically downwards across rows (axis 0) and the second running horizontally across columns (axis 1).
(axis=1) defines that the column named (‘Unnamed: 32’) should be dropped from the dataset.
After we read the data, we can look at the data using:
df = df.drop(['housing_median_age'],axis = 1)# count the total number of rows and columns.
print ('The train data has {0} rows and {1} columns'.format(df.shape[0],df.shape[1]))The train data has 20640 rows and 9 columns
The df.value_counts() method counts the number of types of values a particular column contains.
df.shape(20640, 9)
The df.shape method shows the shape of the dataset.
df.info()<class 'pandas.core.frame.DataFrame'>
RangeIndex: 20640 entries, 0 to 20639
Data columns (total 9 columns):
# Column Non-Null Count Dtype
--- ------ -------------- -----
0 longitude 20640 non-null float64
1 latitude 20640 non-null float64
2 total_rooms 20640 non-null int64
3 total_bedrooms 20433 non-null float64
4 population 20640 non-null int64
5 households 20640 non-null int64
6 median_income 20640 non-null float64
7 median_house_value 20640 non-null int64
8 ocean_proximity 20640 non-null object
dtypes: float64(4), int64(4), object(1)
memory usage: 1.4+ MB
The df.info() method prints information about a DataFrame including the index dtype and columns, non-null values and memory usage.
df.iloc[1]longitude -122.22
latitude 37.86
total_rooms 7099
total_bedrooms 1106.0
population 2401
households 1138
median_income 8.3014
median_house_value 358500
ocean_proximity NEAR BAY
Name: 1, dtype: object
df.iloc[ ] is primarily integer position based (from 0 to length-1 of the axis), but may also be used with a boolean array. The iloc property gets, or sets, the value(s) of the specified indexes.
Data Type Check for every column
Why data type check is required?
Data type check helps us with understanding what type of variables our dataset contains. It helps us with identifying whether to keep that variable or not. If the dataset contains contiguous data, then only float and integer type variables will be beneficial and if we have to classify any value then categorical variables will be beneficial.
objects_cols = ['object']
objects_lst = list(df.select_dtypes(include=objects_cols).columns)print("Total number of categorical columns are ", len(objects_lst))
print("There names are as follows: ", objects_lst)Total number of categorical columns are 1
There names are as follows: ['ocean_proximity']int64_cols = ['int64']
int64_lst = list(df.select_dtypes(include=int64_cols).columns)print("Total number of numerical columns are ", len(int64_lst))
print("There names are as follows: ", int64_lst)Total number of numerical columns are 4
There names are as follows: ['total_rooms', 'population', 'households', 'median_house_value']float64_cols = ['float64']
float64_lst = list(df.select_dtypes(include=float64_cols).columns)print("Total number of float64 columns are ", len(float64_lst))
print("There name are as follow: ", float64_lst)Total number of float64 columns are 4
There name are as follow: ['longitude', 'latitude', 'total_bedrooms', 'median_income']
Step 2 Insights: -
- We have total 9 features where 1 is categoria type and 4 are integer type while 4 are float type.
After this step we have to calculate various evaluation parameters which will help us in cleaning and analysing the data more accurately.
Step 3: Descriptive Analysis
Goal/Purpose: Finding the data distribution of the features. Visualization helps to understand data and also to explain the data to another person.
df.describe()
The df.describe() method returns description of the data in the DataFrame. If the DataFrame contains numerical data, the description contains these information for each column: count — The number of not-empty values. mean — The average (mean) value.
Measure the variability of data of the dataset
Variability describes how far apart data points lie from each other and from the center of a distribution.
Standard Deviation
The standard deviation is the average amount of variability in your dataset.
It tells you, on average, how far each data point lies from the mean. The larger the standard deviation, the more variable the data set is and if zero variance then there is no variability in the dataset that means there no use of that dataset.
So, it helps in understanding the measurements when the data is distributed. The more the data is distributed, the greater will be the standard deviation of that data.Here, you as an individual can determine which company is beneficial in long term. But, if you didn’t know the SD you would have choosen a wrong compnay for you.
df.std()longitude 2.003532
latitude 2.135952
total_rooms 2181.615252
total_bedrooms 421.385070
population 1132.462122
households 382.329753
median_income 1.899822
median_house_value 115395.615874
dtype: float64
We can also understand the standard deviation using the below function.
def std_cal(df,float64_lst):
cols = ['normal_value', 'zero_value']
zero_value = 0
normal_value = 0
for value in float64_lst:
rs = round(df[value].std(),6)
if rs > 0:
normal_value = normal_value + 1
elif rs == 0:
zero_value = zero_value + 1
std_total_df = pd.DataFrame([[normal_value, zero_value]], columns=cols)
return std_total_dfstd_cal(df, float64_lst)
int64_cols = ['int64']
int64_lst = list(df.select_dtypes(include=int64_cols).columns)
std_cal(df,int64_lst)zero_value -> is the zero variance and when then there is no variability in the dataset that means there no use of that dataset.
Variance
The variance is the average of squared deviations from the mean. A deviation from the mean is how far a score lies from the mean.
Variance is the square of the standard deviation. This means that the units of variance are much larger than those of a typical value of a data set.
Why do we used Variance ?
By Squairng the number we get non-negative computation i.e. Disperson cannot be negative. The presence of variance is very important in your dataset because this will allow the model to learn about the different patterns hidden in the data
df.var()longitude 4.014139e+00
latitude 4.562293e+00
total_rooms 4.759445e+06
total_bedrooms 1.775654e+05
population 1.282470e+06
households 1.461760e+05
median_income 3.609323e+00
median_house_value 1.331615e+10
dtype: float64
We can also understand the Variance using the below function.
zero_cols = []
def var_cal(df,float64_lst):
cols = ['normal_value', 'zero_value']
zero_value = 0
normal_value = 0
for value in float64_lst:
rs = round(df[value].var(),6)
if rs > 0:
normal_value = normal_value + 1
elif rs == 0:
zero_value = zero_value + 1
zero_cols.append(value)
var_total_df = pd.DataFrame([[normal_value, zero_value]], columns=cols)
return var_total_dfvar_cal(df, float64_lst)
var_cal(df, int64_lst)zero_value -> Zero variance means that there is no difference in the data values, which means that they are all the same.
Measure central tendency
A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data. As such, measures of central tendency are sometimes called measures of central location. They are also classed as summary statistics.
Mean — The average value. Median — The mid point value. Mode — The most common value.
Mean
The mean is the arithmetic average, and it is probably the measure of central tendency that you are most familiar.
Why do we calculate mean?
The mean is used to summarize a data set. It is a measure of the center of a data set.
df.mean()longitude -119.569704
latitude 35.631861
total_rooms 2635.763081
total_bedrooms 537.870553
population 1425.476744
households 499.539680
median_income 3.870671
median_house_value 206855.816909
dtype: float64
We can also understand the mean using the below function.
def mean_cal(df,int64_lst):
cols = ['normal_value', 'zero_value']
zero_value = 0
normal_value = 0
for value in int64_lst:
rs = round(df[value].mean(),6)
if rs > 0:
normal_value = normal_value + 1
elif rs == 0:
zero_value = zero_value + 1
mean_total_df = pd.DataFrame([[normal_value, zero_value]], columns=cols)
return mean_total_dfmean_cal(df, int64_lst)
mean_cal(df,float64_lst)
zero_value -> that the mean of a paticular column is zero, which isn’t usefull in anyway and need to be drop.
Null and Nan values
- Null Values
A null value in a relational database is used when the value in a column is unknown or missing. A null is neither an empty string (for character or datetime data types) nor a zero value (for numeric data types).
df.isnull().sum()longitude 0
latitude 0
total_rooms 0
total_bedrooms 207
population 0
households 0
median_income 0
median_house_value 0
ocean_proximity 0
dtype: int64
As we notice that there are no null values in our dataset.
- Nan Values
NaN, standing for Not a Number, is a member of a numeric data type that can be interpreted as a value that is undefined or unrepresentable, especially in floating-point arithmetic.
df.isna().sum()longitude 0
latitude 0
total_rooms 0
total_bedrooms 207
population 0
households 0
median_income 0
median_house_value 0
ocean_proximity 0
dtype: int64df = df.dropna()df.isna().sum()longitude 0
latitude 0
total_rooms 0
total_bedrooms 0
population 0
households 0
median_income 0
median_house_value 0
ocean_proximity 0
dtype: int64
As we notice that there are is nan values in our dataset.
Another way to remove null and nan values is to use the method “df.dropna(inplace=True)”.
Count of unique occurences of every value in all categorical value
for value in objects_lst:
print(f"{value:{10}} {df[value].value_counts()}")ocean_proximity <1H OCEAN 9034
INLAND 6496
NEAR OCEAN 2628
NEAR BAY 2270
ISLAND 5
Name: ocean_proximity, dtype: int64
- Categorical data are variables that contain label values rather than numeric values.The number of possible values is often limited to a fixed set.
- Use Label Encoder to label the categorical data. Label Encoder is the part of SciKit Learn library in Python and used to convert categorical data, or text data, into numbers, which our predictive models can better understand.
Label Encoding refers to converting the labels into a numeric form so as to convert them into the machine-readable form. Machine learning algorithms can then decide in a better way how those labels must be operated. It is an important pre-processing step for the structured dataset in supervised learning.
#Before Encoding
a = ['ocean_proximity']
for i in a:
print(df[i])0 NEAR BAY
1 NEAR BAY
2 NEAR BAY
3 NEAR BAY
4 NEAR BAY
...
20635 INLAND
20636 INLAND
20637 INLAND
20638 INLAND
20639 INLAND
Name: ocean_proximity, Length: 20433, dtype: object#Encoding categorical data values
from sklearn.preprocessing import LabelEncoder
le = LabelEncoder()
df.ocean_proximity = le.fit_transform(df.ocean_proximity)#After encoding or converting categorical col values into numbers
for i in a:
print(df[i])0 3
1 3
2 3
3 3
4 3
..
20635 1
20636 1
20637 1
20638 1
20639 1
Name: ocean_proximity, Length: 20433, dtype: int32
Skewness
Skewness is a measure of the asymmetry of a distribution. A distribution is asymmetrical when its left and right side are not mirror images. A distribution can have right (or positive), left (or negative), or zero skewness
Why do we calculate Skewness ?
Skewness gives the direction of the outliers if it is right-skewed, most of the outliers are present on the right side of the distribution while if it is left-skewed, most of the outliers will present on the left side of the distribution
Below is the function to calculate skewness.
def right_nor_left(df, int64_lst):
temp_skewness = ['column', 'skewness_value', 'skewness (+ve or -ve)']
temp_skewness_values = []
temp_total = ["positive (+ve) skewed", "normal distrbution" , "negative (-ve) skewed"]
positive = 0
negative = 0
normal = 0
for value in float64_lst:
rs = round(df[value].skew(),4)
if rs > 0:
temp_skewness_values.append([value,rs , "positive (+ve) skewed"])
positive = positive + 1
elif rs == 0:
temp_skewness_values.append([value,rs,"normal distrbution"])
normal = normal + 1
elif rs < 0:
temp_skewness_values.append([value,rs, "negative (-ve) skewed"])
negative = negative + 1
skewness_df = pd.DataFrame(temp_skewness_values, columns=temp_skewness)
skewness_total_df = pd.DataFrame([[positive, normal, negative]], columns=temp_total)
return skewness_df, skewness_total_dffloat64_cols = ['float64']
float64_lst_col = list(df.select_dtypes(include=float64_cols).columns)
skew_df,skew_total_df = right_nor_left(df, float64_lst_col)skew_df
skew_total_df
columns = df.columns.tolist()
for i in columns:
if df[i].skew()>0:
print(f"{i} : Positive skewed")
else:
print(f"{i} : Negative skewed")longitude : Negative skewed
latitude : Positive skewed
total_rooms : Positive skewed
total_bedrooms : Positive skewed
population : Positive skewed
households : Positive skewed
median_income : Positive skewed
median_house_value : Positive skewed
ocean_proximity : Positive skewed
Step 3 Insights: -
With the statistical analysis we have found that the data have a lot of skewness in them all the columns are positively skewed with mostly zero variance.
Statistical analysis is little difficult to understand at one glance so to make it more understandable we will perform visulatization on the data which will help us to understand the process easily.
Why we are calculating all these metrics?
Mean / Median /Mode/ Variance /Standard Deviation are all very basic but very important concept of statistics used in data science. Almost all the machine learning algorithm uses these concepts in data preprocessing steps. These concepts are part of descriptive statistics where we basically used to describe and understand the data for features in Machine learning
Step 4: Data Exploration
Graphs we are going to develop in this step
1. Histogram
A histogram is a bar graph-like representation of data that buckets a range of classes into columns along the horizontal x-axis.The vertical y-axis represents the number count or percentage of occurrences in the data for each column
# Distribution in attributes
%matplotlib inline
import matplotlib.pyplot as plt
df.hist(bins=50, figsize=(20,20))
plt.show()
Histogram Insight: -
Histogram helps in identifying the following:
- View the shape of your data set’s distribution to look for outliers or other significant data points.
- Determine whether something significant has boccurred from one time period to another.
Why Histogram?
It is used to illustrate the major features of the distribution of the data in a convenient form. It is also useful when dealing with large data sets (greater than 100 observations). It can help detect any unusual observations (outliers) or any gaps in the data.
From the above graphical representation we can identify that the highest bar represents the outliers which is above the maximum range.
We can also identify that the values are moving on the right side, which determines positive and the centered values determines normal skewness.
plt.bar(df['total_rooms'],df['total_bedrooms'])
plt.xlabel('Rooms')
plt.ylabel('Bedrooms')
plt.title('BAR GRAPH')
plt.show()
The graph defines the relation between total rooms available to total number of bedrooms.
x=df['median_income']
y=df['ocean_proximity']
plt.scatter(x,y)
plt.xlabel('x')
plt.ylabel('y')
plt.title('scatter plot')
plt.show()
The graph defines proximity between ocean proximity and the income of the house.
2. Distplot
A Distplot or distribution plot, depicts the variation in the data distribution. Seaborn Distplot represents the overall distribution of continuous data variables. The Seaborn module along with the Matplotlib module is used to depict the distplot with different variations in it
num = [f for f in df.columns if df.dtypes[f] != 'object']
nd = pd.melt(df, value_vars = num)
n1 = sns.FacetGrid (nd, col='variable', col_wrap=4, sharex=False, sharey = False)
n1 = n1.map(sns.distplot, 'value')
n1<seaborn.axisgrid.FacetGrid at 0x2a9c301bb50>
Distplot Insights: -
Above is the distrution bar graphs to confirm about the statistics of the data about the skewness.
Why Distplot?
Skewness is demonstrated on a bell curve when data points are not distributed symmetrically to the left and right sides of the median on a bell curve. If the bell curve is shifted to the left or the right, it is said to be skewed.
We can observe that the bell curve is shifted to left we indicates positive skewness.As all the column are positively skewed we don’t need to do scaling.
Let’s proceed and check the distribution of the target variable.
The target variable is positively skewed.A normally distributed (or close to normal) target variable helps in better modeling the relationship between target and independent variables.
3. Heatmap
A heatmap (or heat map) is a graphical representation of data where values are depicted by color.Heatmaps make it easy to visualize complex data and understand it at a glance
Correlation — A positive correlation is a relationship between two variables in which both variables move in the same direction. Therefore, when one variable increases as the other variable increases, or one variable decreases while the other decreases.
Correlation can have a value:
- 1 is a perfect positive correlation
- 0 is no correlation (the values don’t seem linked at all)
- -1 is a perfect negative correlation
#correlation plot
sns.set(rc = {'figure.figsize':(25,20)})
corr = df.corr().abs()
sns.heatmap(corr,annot=True)
plt.show()
Notice the last column from right side of this map. We can see the correlation of all variables.
corr
Heatmap insights: -
As we know, it is recommended to avoid correlated features in your dataset. Indeed, a group of highly correlated features will not bring additional information (or just very few), but will increase the complexity of the algorithm, hence increasing the risk of errors.
Why Heatmap?
Heatmaps are used to show relationships between two variables, one plotted on each axis. By observing how cell colors change across each axis, you can observe if there are any patterns in value for one or both variables.
4. Boxplot
A boxplot is a standardized way of displaying the distribution of data based on a five number summary (“minimum”, first quartile [Q1], median, third quartile [Q3] and “maximum”).
Basically, to find the outlier in a dataset/column.
features = df.columns.tolist()sns.boxplot(data=df)<Axes: >
The dark points are known as Outliers. Outliers are those data points that are significantly different from the rest of the dataset. They are often abnormal observations that skew the data distribution, and arise due to inconsistent data entry, or erroneous observations.
Boxplot Insights: -
- Sometimes outliers may be an error in the data and should be removed. In this case these points are correct readings yet they are different from the other points that they appear to be incorrect.
- The best way to decide wether to remove them or not is to train models with and without these data points and compare their validation accuracy.
- So we will keep it unchanged as it won’t affect our model.
Here, we can see that most of the variables possess outlier values. It would take us days if we start treating these outlier values one by one. Hence, for now we’ll leave them as is and let our algorithm deal with them. As we know, tree-based algorithms are usually robust to outliers.
Why Boxplot?
Box plots are used to show distributions of numeric data values, especially when you want to compare them between multiple groups. They are built to provide high-level information at a glance, offering general information about a group of data’s symmetry, skew, variance, and outliers.
In the next step we will divide our cleaned data into training data and testing data.
Step 2: Data Preparation
Goal:-
Tasks we are going to in this step:
- Now we will spearate the target variable and feature columns in two different dataframe and will check the shape of the dataset for validation purpose.
- Split dataset into train and test dataset.
- Scaling on train dataset.
1. Now we spearate the target variable and feature columns in two different dataframe and will check the shape of the dataset for validation purpose.
# Separate target and feature column in X and y variable
target = 'median_house_value'
# X will be the features
X = df.drop(target,axis=1)
#y will be the target variable
y = df[target]X.info()<class 'pandas.core.frame.DataFrame'>
Int64Index: 20433 entries, 0 to 20639
Data columns (total 8 columns):
# Column Non-Null Count Dtype
--- ------ -------------- -----
0 longitude 20433 non-null float64
1 latitude 20433 non-null float64
2 total_rooms 20433 non-null int64
3 total_bedrooms 20433 non-null float64
4 population 20433 non-null int64
5 households 20433 non-null int64
6 median_income 20433 non-null float64
7 ocean_proximity 20433 non-null int32
dtypes: float64(4), int32(1), int64(3)
memory usage: 1.3 MBy0 452600
1 358500
2 352100
3 341300
4 342200
...
20635 78100
20636 77100
20637 92300
20638 84700
20639 89400
Name: median_house_value, Length: 20433, dtype: int64# Check the shape of X and y variable
X.shape, y.shape((20433, 8), (20433,))# Reshape the y variable
y = y.values.reshape(-1,1)# Again check the shape of X and y variable
X.shape, y.shape((20433, 8), (20433, 1))
2. Spliting the dataset in training and testing data.
Here we are spliting our dataset into 80/20 percentage where 80% dataset goes into the training part and 20% goes into testing part.
# Split the X and y into X_train, X_test, y_train, y_test variables with 80-20% split.
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)# Check shape of the splitted variables
X_train.shape, X_test.shape, y_train.shape, y_test.shape((16346, 8), (4087, 8), (16346, 1), (4087, 1))
Insights: -
Train test split technique is used to estimate the performance of machine learning algorithms which are used to make predictions on data not used to train the model.It is a fast and easy procedure to perform, the results of which allow you to compare the performance of machine learning algorithms for your predictive modeling problem. Although simple to use and interpret, there are times when the procedure should not be used, such as when you have a small dataset and situations where additional configuration is required, such as when it is used for classification and the dataset is not balanced.
In the next step we will train our model on the basis of our training and testing data.
Step 3: Model Training
Goal:
In this step we are going to train our dataset on different regression algorithms. As we know that our target variable is in continuous format so we have to apply regression algorithm. Target variable is a continous value.In our dataset we have the outcome variable or Dependent variable i.e Price. So we will use Regression algorithm**
Algorithms we are going to use in this step
- Linear Regression
- Lasso Regression
- Rigde Regression
K-fold cross validation is a procedure used to estimate the skill of the model on new data. There are common tactics that you can use to select the value of k for your dataset. There are commonly used variations on cross-validation, such as stratified and repeated, that are available in scikit-learn
# Define kfold with 10 split
cv = KFold(n_splits=10, shuffle=True, random_state=42)The goal of cross-validation is to test the model’s ability to predict new data that was not used in estimating it, in order to flag problems like overfitting or selection bias and to give an insight on how the model will generalize to an independent dataset (i.e., an unknown dataset, for instance from a real problem).
1. Linear Regression
Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable’s value is called the independent variable.
This form of analysis estimates the coefficients of the linear equation, involving one or more independent variables that best predict the value of the dependent variable. Linear regression fits a straight line or surface that minimizes the discrepancies between predicted and actual output values. There are simple linear regression calculators that use a “least squares” method to discover the best-fit line for a set of paired data. You then estimate the value of X (dependent variable) from Y (independent variable).
Train set cross-validation
#Using linear regression on our training data
from sklearn.linear_model import LinearRegressionreg = LinearRegression()
reg.fit(X_train,y_train)LinearRegression()
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
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LinearRegression
LinearRegression()#Accuracy check of trainig data
#Get R2 score
reg.score(X_train, y_train)0.6233437847737873#Accuracy of test data
reg.score(X_test, y_test)0.6273957380409203# Getting kfold values
lg_scores = -1 * cross_val_score(reg,
X_train,
y_train,
cv=cv,
scoring='neg_root_mean_squared_error')
lg_scoresarray([67122.23905126, 69908.40807063, 72213.86867656, 69697.79133167,
71308.53828975, 70637.54315897, 70672.86289553, 73327.66916008,
70081.03617478, 73225.95603902])# Mean of the train kfold scores
lg_score_train = np.mean(lg_scores)
lg_score_train70819.59128482438
Prediction
Now we will perform prediction on the dataset using Logistic Regression.
# Predict the values on X_test_scaled dataset
y_predicted = reg.predict(X_test)Various parameters are calculated for analysing the predictions.
- Confusion Matrix 2)Classification Report 3)Accuracy Score 4)Precision Score 5)Recall Score 6)F1 Score
Confusion Matrix
A confusion matrix presents a table layout of the different outcomes of the prediction and results of a classification problem and helps visualize its outcomes. It plots a table of all the predicted and actual values of a classifier.
This diagram helps in understanding the concept of confusion matrix.
Evaluating all kinds of evaluating parameters.
Classification Report :
A classification report is a performance evaluation metric in machine learning. It is used to show the precision, recall, F1 Score, and support of your trained classification model.
F1_score :
The F1 score is a machine learning metric that can be used in classification models.
Precision_score :
The precision is the ratio tp / (tp + fp) where tp is the number of true positives and fp the number of false positives. The precision is intuitively the ability of the classifier not to label as positive a sample that is negative. The best value is 1 and the worst value is 0.
Recall_score :
Recall score is used to measure the model performance in terms of measuring the count of true positives in a correct manner out of all the actual positive values. Precision-Recall score is a useful measure of success of prediction when the classes are very imbalanced.
# Evaluating the classifier
# printing every score of the classifier
# scoring in anything
from sklearn.metrics import classification_report
from sklearn.metrics import f1_score, accuracy_score, precision_score,recall_score,r2_score
from sklearn.metrics import confusion_matrix
from sklearn.metrics import mean_squared_error
print("The model used is Linear Regression")
l_acc = r2_score(y_test, y_predicted)
print("\nThe accuracy is: {}".format(l_acc))The model used is Linear Regression
The accuracy is: 0.6273957380409203
As the data is continuous we cannot create confusion matrix and other evaluating parameters.
2. Lasso Regression
Lasso regression is a regularization technique. It is used over regression methods for a more accurate prediction. This model uses shrinkage. Shrinkage is where data values are shrunk towards a central point as the mean. The lasso procedure encourages simple, sparse models (i.e. models with fewer parameters). This particular type of regression is well-suited for models showing high levels of multicollinearity or when you want to automate certain parts of model selection, like variable selection/parameter elimination.
#Using Lasso Regression
from sklearn import linear_model
lreg = linear_model.Lasso(alpha=0.1)
lreg.fit(X_train, y_train)Lasso(alpha=0.1)
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Lasso
Lasso(alpha=0.1)#Accuracy check of trainig data
#Get R2 score
lreg.score(X_train, y_train)0.6233437847672894#Accuracy of test data
lreg.score(X_test, y_test)0.6273957556457749#Get kfold values
Nn_scores = -1 * cross_val_score(lreg,
X_train,
y_train,
cv=cv,
scoring='neg_root_mean_squared_error')
Nn_scoresarray([67122.24863879, 69908.41337353, 72213.86676208, 69697.79687047,
71308.5429111 , 70637.53162666, 70672.86464265, 73327.66930041,
70081.01994543, 73225.94190625])# Mean of the train kfold scores
Nn_score_train = np.mean(Nn_scores)
Nn_score_train70819.58959773756
Prediction
# Predict the values on X_test_scaled dataset
y_predicted = lreg.predict(X_test)Evaluating all kinds of evaluating parameters.
from sklearn.metrics import f1_score, accuracy_score, precision_score,recall_score
print("The model used is Lasso Regression")
k_acc = r2_score(y_test, y_predicted)
print("\nThe accuracy is: {}".format(k_acc))The model used is Lasso Regression
The accuracy is: 0.6273957556457749
3. Ridge Regression
Ridge regression is a model tuning method that is used to analyse any data that suffers from multicollinearity. This method performs L2 regularization. When the issue of multicollinearity occurs, least-squares are unbiased, and variances are large, this results in predicted values being far away from the actual values.
Ridge regression is a method of estimating the coefficients of multiple-regression models in scenarios where the independent variables are highly correlated. It has been used in many fields including econometrics, chemistry, and engineering.
#Using Ridge Regression
from sklearn.linear_model import Ridge
rig = Ridge(alpha=1.0)
rig.fit(X_train, y_train)Ridge()
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Ridge
Ridge()#Accuracy check of trainig data
#Get R2 score
rig.score(X_train, y_train)0.6233437802459998#Accuracy of test data
rig.score(X_test, y_test)0.627395534108943# Get kfold values
Dta_scores = -1 * cross_val_score(rig,
X_train,
y_train,
cv=cv,
scoring='neg_root_mean_squared_error')
Dta_scoresarray([67122.5885148 , 69908.54038561, 72213.83926757, 69697.94753927,
71308.75097258, 70637.29982288, 70672.91488443, 73327.66370516,
70080.62943212, 73225.59474354])# Mean of the train kfold scores
Dta_score_train = np.mean(Dta_scores)
Dta_score_train70819.57692679751
Prediction
# predict the values on X_test_scaled dataset
y_predicted = rig.predict(X_test)Evaluating all kinds of evaluating parameters.
from sklearn.metrics import f1_score, accuracy_score, precision_score,recall_score
print("The model used is Ridge Regression")
r_acc = r2_score(y_test, y_predicted)
print("\nThe accuracy is {}".format(r_acc))The model used is Ridge Regression
The accuracy is 0.627395534108943
Insight: -
cal_metric=pd.DataFrame([l_acc,k_acc,r_acc],columns=["Score in percentage"])
cal_metric.index=['Linear Regression',
'Lasso Regression',
'Ridge Regression']
cal_metric
- As you can see that all the models have the same accuracy. We will prefer Linear Regression to save our model.
Step 4: Save Model
Goal:- In this step we are going to save our model in pickel format file.
import pickle
pickle.dump(reg , open('california_housing_prices_LinearRegression.pkl', 'wb'))
pickle.dump(lreg , open('california_housing_prices_LassoRegression.pkl', 'wb'))
pickle.dump(rig , open('california_housing_prices_RidgeRegression.pkl', 'wb'))import pickle
def model_prediction(features):
pickled_model = pickle.load(open('california_housing_prices_LinearRegression.pkl', 'rb'))
median_house_value = str(list(pickled_model.predict(features)))
return str(f'The Price is {median_house_value}')
We can test our model by giving our own parameters or features to predict.
longitude = -122.24
latitude = 37.86
total_rooms = 1462
total_bedrooms = 190.0
population = 322
households = 177
median_income = 7.2574
ocean_proximity = 3print(model_prediction([[longitude,latitude,total_rooms,total_bedrooms,population,households,median_income,ocean_proximity]]))The Price is [array([362053.99132426])]
Conclusion
After observing the problem statement we have build an efficient model to overcome it. The above model helps in predicting the price of the houses in california. It helps the customer to analyze the price of various houses and select the most appropriate for them according to their budget and choice.
Checkout whole project code here (github repo).
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