#linearregression

Mastering Linear Regression in Machine Learning | Imarticus Learning

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Linear Regression is one of the most essential and widely used algorithms in Machine Learning and Data Science. It forms the foundation of predictive analytics — helping us understand relationships between variables and make accurate, data-driven predictions.

In this video, we’ll break down everything you need to know about Simple and Multiple Linear Regression, with clear explanations and real-world applications.

📘 What You’ll Learn

💡 What is Linear Regression? Understand how linear models work and how they form the backbone of predictive analytics.

📊 Types of Linear Regression Explore the difference between Simple and Multiple Linear Regression with examples that bring the concept to life.

📈 Evaluating a Regression Model Learn about essential model evaluation metrics — R² Score, MAE, MSE, and RMSE — and what they reveal about your model’s performance.

🧠 Key Assumptions of Linear Regression Get familiar with the conditions that ensure accurate modeling — Linearity, Independence, Multicollinearity, and Homoscedasticity.

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Predicting Home Prices using Multivariate Linear Regression in Python

Introduction:

In this machine learning tutorial, we will explore how to predict home prices using multivariate linear regression in Python. Linear regression is a powerful technique that allows us to model the relationship between a dependent variable (in this case, home prices) and multiple independent variables (area, bedrooms, and age). We will use the popular scikit-learn library to implement the regression model. Additionally, we will preprocess the data using pandas to handle missing values effectively.

Understanding the Problem:

Imagine you are in charge of predicting home prices in Monroe Township, New Jersey, USA. You have a dataset that contains information about previous home sales, including the area (in square feet), number of bedrooms, age of the home (in years), and their respective prices. Based on this data, you have to predict the prices of new homes based on their area, bedrooms, and age.

Data Preprocessing:

Before building the regression model, it's essential to preprocess the data and handle missing values. In our dataset, some homes have missing values for the number of bedrooms. We will fill these missing values with the median value of the bedroom column. This step ensures that our model does not encounter any issues due to missing data.

Building the Multivariate Linear Regression Model:

Now that we have preprocessed the data, we can proceed to build our multivariate linear regression model using the scikit-learn library. The linear regression model will learn the coefficients for each independent variable (area, bedrooms, and age) to predict the dependent variable (price).

# Importing necessary libraries

import pandas as pd

import numpy as np

from sklearn import linear_model

# Reading the dataset

df = pd.read_csv('homeprices.csv')

# Handling missing values in the 'bedrooms' column

df.bedrooms = df.bedrooms.fillna(df.bedrooms.median())

# Building the linear regression model

reg = linear_model.LinearRegression()

reg.fit(df.drop('price', axis='columns'), df.price)

Interpreting the Model:

After training the model, we can access the coefficients and intercept to understand the relationship between the independent variables and the dependent variable.

# Coefficients and intercept of the model

print(reg.coef_)   

print(reg.intercept_)

Making Predictions:

Now that our model is trained, we can use it to predict the prices of new homes based on their area, bedrooms, and age.

Let's find the price of a home with 3000 square feet area, 3 bedrooms, and 40 years old.

# Predicting the price for a home with 3000 sqr ft area, 3 bedrooms, and 40 years old

new_home_1 = [[3000, 3, 40]]

predicted_price_1 = reg.predict(new_home_1)

print(predicted_price_1)

Similarly, let's find the price of a home with 2500 square feet area, 4 bedrooms, and 5 years old.

# Predicting the price for a home with 2500 sqr ft area, 4 bedrooms, and 5 years old

new_home_2 = [[2500, 4, 5]]

predicted_price_2 = reg.predict(new_home_2)

print(predicted_price_2)

Conclusion:

In this tutorial, we learned how to use multivariate linear regression to predict home prices based on area, bedrooms, and age. We also explored data preprocessing techniques to handle missing values and implemented the regression model using the scikit-learn library. With this knowledge, you can now apply linear regression to other real-world problems and make accurate predictions based on multiple variables.

Predicting Home Prices Using Linear Regression: A Step-by-Step Guide

Introduction:

Welcome to our tutorial on predicting home prices using Linear Regression! In this blog post, we will walk you through the process of building a machine learning model that can accurately predict home prices based on the square footage area of homes in Monroe Township, New Jersey. We will be using Python, the popular library sklearn, and matplotlib for visualization.

Understanding Linear Regression:

Linear Regression is a powerful machine learning algorithm used for predicting numerical values based on input data. In our case, the input data will be the square footage area of homes, and the output will be the corresponding home prices. The fundamental idea behind Linear Regression is to find the best-fitting straight line through the data points, minimizing the sum of errors (residuals) between the actual and predicted values.

Getting Started:

We begin by importing the necessary libraries and loading the dataset into a pandas DataFrame. The dataset contains two columns: 'area' representing the square footage area and 'price' representing the corresponding home prices.

import pandas as pd

import numpy as np

from sklearn import linear_model

import matplotlib.pyplot as plt

df = pd.read_csv('homeprices.csv')

Visualizing the Data:

Before we dive into building the model, let's visualize the data to gain insights and understand the relationship between the square footage area and home prices.

plt.xlabel('area')

plt.ylabel('price')

plt.scatter(df.area, df.price, color='red', marker='+')

plt.show()

Building the Linear Regression Model:

Next, we create a linear regression object and fit it to our data. This process will determine the best-fitting line that represents the relationship between home prices and square footage area.

# Separate the input features (area) and target variable (price)

new_df = df.drop('price', axis='columns')

price = df.price

# Create linear regression object

reg = linear_model.LinearRegression()

reg.fit(new_df, price)

Making Predictions:

Now that our model is trained, we can use it to predict the home price for a given square footage area. Let's predict the price for an area of 3300 square feet and 5000 square feet.

# Predict price for a home with area = 3300 sq. ft.

predicted_price_3300 = reg.predict([[3300]])[0]

print(f"Predicted price for a home with area 3300 sq. ft.: ${predicted_price_3300:.2f}")

# Predict price for a home with area = 5000 sq. ft.

predicted_price_5000 = reg.predict([[5000]])[0]

print(f"Predicted price for a home with area 5000 sq. ft.: ${predicted_price_5000:.2f}")

Generating Predictions for New Data:

Now, let's use our trained model to predict the prices for a list of home areas provided in a separate CSV file named "areas.csv".

area_df = pd.read_csv("areas.csv")

predictions = reg.predict(area_df)

area_df['predicted_prices'] = predictions

area_df.to_csv("prediction.csv", index=False)

Conclusion:

In this tutorial, we successfully built a Linear Regression model to predict home prices based on the square footage area of homes. We learned how to visualize the data, create a Linear Regression object, train the model, and make predictions on new data. Linear Regression is a simple yet powerful algorithm, and it can be used for various prediction tasks beyond home prices.

We hope this tutorial helps you understand the basics of Linear Regression and how it can be applied to real-world problems. Happy predicting!

Note: For a more in-depth understanding, it is essential to explore various evaluation metrics and methods to handle larger datasets. We encourage you to continue your exploration of machine learning to expand your knowledge and skills in this exciting field!

Regression Modeling In Practice 2

In the second week of our assignments at Regression Modeling in Practice, we were expected to perform a basic linear regression model between any two variables from a large dataset.

I chose the ‘gapminder’ dataset which provides data about the population, life expectancy and GDP in different countries of the world from 1952 to 2007. Within this large dataset, I would like to examine a possible relationship between the Per Capita Income in a country versus it’s life expectancy.

Experiment

It is logically expected that a higher income provides access to better healthcare, increases affordability of prescription drugs, and possibly access to better insurance policies, thus improving life expectancy. Let’s examine if the data says the same too. For this study, we consider the follow hypothesis

Null Hypothesis: There is no significant effect of Income per Person on the Life-Expectancy in a country.

Alternate Hypothesis: There is a significant effect of Income per Person on the Life-Expectancy in a country.

Details

Here, the ‘Income Per Person’ is the explanatory variable while the ‘Life Expectancy’ becomes the response variable. The following code snippet is executed from Python to analyze the above problem.

We start by importing the data into Python together with the essential libraries

import numpy as np import pandas as pd import statsmodels.api import statsmodels.formula.api as smf import seaborn import matplotlib.pyplot as plt

#Reading the DataSet df = pd.read_excel (r'C:\Users\deepa\Downloads\gapminder.xlsx')

There are several data points missing across countries for either life-expectancy or per-capita-income. We will remove these entries in order to make a fair estimate.

#Isolating the variables under study and eliminating blank entries

subset1 = df[['lifeexpectancy', 'incomeperperson']] subset1 = subset1.apply(pd.to_numeric, errors='coerce') mainset = subset1[['lifeexpectancy', 'incomeperperson']].dropna()

The explanatory variable is now centered by subtracting each value from its mean

#Centering the Explanatory Variable mainset[["incomeperperson_c"]]=mainset[["incomeperperson"]]-mainset[["incomeperperson"]].mean() ppincome = mainset.incomeperperson ppincome_c = mainset.incomeperperson_c lifeyears = mainset.lifeexpectancy

Printing out the mean of the original and centered explanatory variable print ("Mean for Income Per Person") meanppi = ppincome.mean() print(meanppi) print ("Mean for Centered Income Per Person") meanppi_c = ppincome_c.mean() print(meanppi_c)

We now plot the variables against each other, both with the centered and uncentered explanatory variables and calculate the regression coefficients using the OLD Model.

#Plotting the explanatory variable and response variable scat1 = seaborn.regplot(x="incomeperperson", y="lifeexpectancy", scatter=True, data=mainset) plt.xlabel('Per Capita Income') plt.ylabel('Life Expectancy') plt.title ('Scatterplot for the Association Between Per Capita Income and Life Expectancy') print(scat1)

#Basic Linear Regression with explanatory variable print('OLS Regression Model for Association between Per Capita Income and Life Expectancy') reg1 = smf.ols('lifeexpectancy ~ incomeperperson',data=mainset).fit() print(reg1.summary())

#Plotting the centered explanatory variable and response variable scat1 = seaborn.regplot(x="incomeperperson_c", y="lifeexpectancy", scatter=True, data=mainset) plt.xlabel('Centered Per Capita Income') plt.ylabel('Life Expectancy') plt.title ('Scatterplot for the Association Between Centered Per Capita Income and Life Expectancy') print(scat1)

#Basic Linear Regression with centered explanatory variable print('OLS Regression Model for Association between Centered Per Capita Income and Life Expectancy') reg2 = smf.ols('lifeexpectancy ~ incomeperperson_c',data=mainset).fit() print(reg2.summary())

We end by visualizing the Bi-Variate Bar Graph

seaborn.factorplot(x="incomeperperson_c", y="lifeexpectancy", data=mainset, kind="bar", ci=None) plt.xlabel('Per Capita Income') plt.ylabel('Life Expectancy')

Results

Python gives the following results for the above code

Mean for Income Per Person 7327.444413651806 Mean for Centered Income Per Person -1.0180139559617436e-12

#Do note the near-zero mean value for the Centered Explanatory Variable

Scatter Plot for the association (Non-Centered):

OLS regression model for the association (Non-Centered):

Scatter for the association (Centered):

OLS regression model for the association (Centered):

Interpretation

From the R-Squared values reported in the OLS Model, we can understand that about 36.2% of the variance seen in the Life Expectancy can be attributed to the Per Capita Income.

The p-value is very small <0.0001, this indicating that the null hypothesis can be rejected. There is indeed a significant effect of Per Capita Income on the Life Expectancy.

The Life Expectancy can be calculated using either of the following  formulae. These are the regression coefficients

Life Expectancy = 0.0006*(Income Per Person)+65.5966

Life Expectancy = 0.0006*(Centered Income Per Person)+69.6547 

In this video, we discuss how a machine can build a linear regression model. This is one of many ways the machine builds a regression model. However, the mechanics of creating a regression model by the machine is essentially the same as discussed in this video.