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https://github.com/farzeennimran/house-price-prediction-using-simple-linear-regression


https://github.com/farzeennimran/house-price-prediction-using-simple-linear-regression

data-science linear-regression matplotlib numpy pandas python sklearn visualization

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README 

        
# House Price Prediction using simple Linear Regression 🏘️



## Introduction



This project aims to predict house prices using a simple linear regression model. The dataset used for this project contains various features related to house pricing, such as the number of rooms, age, tax rate, and more. The main goal is to understand the relationship between the number of rooms (`rm`) and the median value of owner-occupied homes (`medv`).



## What is Linear Regression?



Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. In simple linear regression, we model the relationship using a straight line. The equation of this line is:



\[ \text{medv} = \text{slope} \times \text{rm} + \text{intercept} \]



Here, `medv` is the dependent variable we want to predict, and `rm` is the independent variable.



## Code Explanation



### Importing Libraries and Loading the Dataset



We start by importing the necessary libraries and loading the dataset:



```python

import pandas as pd

import matplotlib.pyplot as plt

import numpy as np



df = pd.read_csv("House Pricing.csv")

print("First few rows of the dataset:")

print(df.head())

```



### Data Exploration and Preprocessing



We explore the dataset by printing the first few rows and determining the range of the `age` column. We then discretize the `age` column into categories:



```python

max = df['age'].max()

min = df['age'].min()



print(f"Maximum age value: {max}")

print(f"Minimum age value: {min}")



Bins = [min, 30, 70, max]

Labels = ['Young', 'Middle-aged', 'Old']



df['DiscretizeAge'] = pd.cut(df['age'], bins=Bins, labels=Labels, right=False)

print("\n Discretized age is:")

print(df[['age', 'DiscretizeAge']].head())

```



We also create a binary variable `is_charles_river` based on the `chas` column:



```python

df['is_charles_river'] = df['chas'].apply(lambda x: 1 if x == 1 else 0)

print("Dataset with the new binary variable 'is_charles_river'")

print(df[['chas', 'is_charles_river']].head())

```



### Outlier Detection and Removal



To handle outliers, we define a function that uses the Interquartile Range (IQR) method and apply it to the numerical columns:



```python

def outliers(column):

    Q1 = column.quantile(0.25)

    Q3 = column.quantile(0.75)

    IQR = Q3 - Q1



    Lower_bound = Q1 - 1.5 * IQR

    Upper_bound = Q3 + 1.5 * IQR



    CleanedData = column[(column >= Lower_bound) & (column <= Upper_bound)]

    return CleanedData



numerical_columns = df.select_dtypes(include='number').columns

WithOutliers = []

WithoutOutliers = []



for i in numerical_columns:

    WithOutliers.append(df[i].copy())

    df[i] = outliers(df[i])

    WithoutOutliers.append(df[i])



plt.figure(figsize=(18, 6))

plt.subplot(1, 2, 1)

plt.boxplot(WithOutliers, labels=numerical_columns)

plt.title('Original Data')



plt.subplot(1, 2, 2)

plt.boxplot(WithoutOutliers, labels=numerical_columns)

plt.title('Data after Outlier Removal')



plt.show()

```



### Removing Noisy Data



We define a function to remove noisy data based on Z-scores:



```python

def NoisyData(df, threshold=3):

    z_scores = np.abs((df - df.mean()) / df.std())

    noisy_data = z_scores > threshold

    removenoise = df[~noisy_data.any(axis=1)]

    return removenoise



numericalcol = df.select_dtypes(include='number')



removenoise = NoisyData(numericalcol)



print(f"Number of rows before removing noisy data: {len(df)}")

print(f"Number of rows after removing noisy data: {len(removenoise)}")

print(removenoise.head())

```



### Smoothing Data



We smooth the `rm` column using binning:



```python

df.dropna(subset=['rm'], inplace=True)



NoOfBins = 10



Minrm = df['rm'].min()

Maxrm = df['rm'].max()

BinWidth = (Maxrm - Minrm) / NoOfBins

BinEdges = [Minrm + i * BinWidth for i in range(NoOfBins + 1)]



def BinMean(value):

    bin_index = int((value - Minrm) // BinWidth)

    BinMean = (BinEdges[bin_index] + BinEdges[bin_index + 1]) / 2

    return BinMean



df['rm_smoothed'] = df['rm'].apply(BinMean)

print(df[['rm', 'rm_smoothed']].head())

```



### Normalizing Data



We normalize the `tax` and `lstat` columns using Min-Max normalization:



```python

NormalizeColumns = ['tax', 'lstat']



def min_max_normalize(column):

    min_val = column.min()

    max_val = column.max()

    return (column - min_val) / (max_val - min_val)



for col in NormalizeColumns:

    df[col + '_normalized'] = min_max_normalize(df[col])



print("Normalized columns:")

print(df[['tax', 'tax_normalized', 'lstat', 'lstat_normalized']].head())

```



### Simple Linear Regression



Finally, we perform a simple linear regression to predict `medv` based on `rm`:



```python

df.dropna(subset=['medv'], inplace=True)



from sklearn.linear_model import LinearRegression

from sklearn.model_selection import train_test_split

from sklearn.metrics import mean_squared_error, r2_score



X = df[['rm']]

y = df['medv']



X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)



model = LinearRegression()

model.fit(X_train, y_train)



y_pred = model.predict(X_test)



mse = mean_squared_error(y_test, y_pred)

r2 = r2_score(y_test, y_pred)



slope = model.coef_[0]

intercept = model.intercept_

print("Regression Equation:")

print("medv =", slope, "* rm +", intercept)



print("\nMean Squared Error:", mse)

print("R-squared:", r2, "\n")



plt.scatter(X_test, y_test, color='lightblue')

plt.plot(X_test, y_pred, color='gray', linewidth=2)

plt.xlabel('RM')

plt.ylabel('MEDV')

plt.title('Linear Regression: RM vs MEDV')

plt.show()

```



### Interpretation of Results



The linear regression model provides insights into the relationship between `rm` and `medv`. A positive slope indicates that as the number of rooms increases, the median value of homes also tends to increase. The Mean Squared Error (MSE) and R-squared values help evaluate the model's performance. A lower MSE indicates a better fit, while the R-squared value measures the proportion of variance in `medv` explained by `rm`.