Build Regression Models in Python for House Price Prediction

Project Overview

For this project, we will use Linear Regression to predict house prices. First, we load and explore our dataset, then deal with missing values and outliers. Our main aim is that the model can predict prices based on features like area, bedrooms, bathrooms, and so on.

We split the data into training and test sets first. In addition, to normalize the features we also apply the Min-Max Scaling, so that each feature can be uniform. We used Recursive Feature Elimination (RFE) to select features. This helps us select the most important features of the model.

We use the statsmodels library to build the model using Linear Regression. Adding a constant (intercept) to the feature set is the key step here. This is to ensure that the model features the baseline price, despite any other feature being zero.

We finally evaluate the model’s outperformance using R Square and Mean Squared Error to see if it effectively predicts the house price. This is a fun first project endeavor to work with data preprocessing, feature selection, and building regression models.

Prerequisites

Learners must develop some skills before undertaking this project. Here’s what you should ideally know:

• Understanding of basic knowledge of Python for data analysis and manipulation
• Knowledge of libraries such as Pandas, Numpy, and Matplotlib for data manipulation and data visualization respectively.
• Understanding of data preprocessing steps such as how to deal with missing values, normalization, and scaling.
• Familiarity with exploratory data analysis (EDA) to find out patterns and growing trends in sets.
• Elementary concepts about regression models to learn how predictive modeling works
• Machine learning frameworks such as Scikit-Learn for building, training, and assessing models

Approach

We followed several key steps that are involved in building an accurate house price prediction model. So we load the dataset to understand its structure, clean missing or invalid data, etc. We then deal with outliers in box plots and ensure the dataset is fit for training the model. Once the data is split into two sets, the training, and the testing, we shall use the latter later to evaluate the model's performance. To normalize the features and to give all variables the same status in front of the model, we apply Min-Max Scaling. To address the accuracy of the model, we apply Recursive Feature elimination (RFE) that allows us to choose which variables will be the key to the model. Then we use Linear regression to fit the regression model with a constant term so that we have the intercept. We then apply the model until performance metrics such as R2 and Mean Squared error are attained with the best prediction.

Workflow and Methodology

Workflow

1. Data Collection: Collect the dataset from the public dataset repository, and load it into a DataFrame in Pandas for further analysis.
2. Data Cleaning: You need to deal with missing values, remove outliers, and check that the right data type is used and that all the data is ready for modeling.
3. Feature Scaling: Apply Min-Max Scaling to normalize the features.
4. Feature Selection: Use Recursive Feature Elimination to select the most relevant features for the regression model.
5. Train-Test Split: Split the dataset into training and testing sets to evaluate model performance.
6. Model Building: Train a Linear regression model using the prepared data.
7. Model Evaluation: Evaluate the models using metrics MSE, R2.

Methodology

The methodology takes a systematic approach to estimating house prices with the help of predictive modeling techniques in regression. The very first step involves preparing and processing the data by performing actions such as cleaning the data, settling outliers if any, and handling missing values. After the data was prepared, features were scaled using the Min-Max Scaling so as not to let any attribute dominate the model by its scale. Feature Selection is then carried out using RFE to come up with the most pertinent features while ensuring that the model does not become ineffective. After the relevant features have been chosen, a Linear Regression model is constructed with the addition of a constant to account for intercept. Finally, the result of the computed model is checked for R-squared values to analyze the fit of the data, and Mean Squared Error (MSE) is used to check the accuracy of the predictions.

Data Collection and Preparation

Data Collection:
In this project, we collected the dataset from a public repository. If you are looking to work on a real-world problem, you can get these kinds of datasets from publicly available repositories such as Kaggle, UCI Machine Learning Repository, or company-specific data. We will provide the dataset in this project so that you can work on the same dataset.

Data Preparation Workflow:

• Load the Data: The first step will be to load the dataset into a Pandas DataFrame which can be utilized for analysis.
• Exploratory Data Analysis (EDA): The initial analysis focuses on the data’s structure and its distribution.
• Handle Missing Values: Handle the null values by either filling in or erasing the missing values to achieve an intact dataset.
• Remove Outliers: Recognize and exclude any outliers as they may affect the outcome of the results.
• Encode Categorical Variables: Implement encoding techniques to change categorical values into numerical form.
• Feature Scaling: Perform Min-Max Scaling to standardize features and avoid scaling conflicts.
• Feature Selection: Employ RFE to determine the key features to be utilized in the model.

Code Explanation

STEP 1:

Mounting Google Drive

First, mount Google Drive to access the dataset that is stored in the cloud.

Importing Library

This code imports necessary libraries for data analysis, visualization, feature selection, and building a regression model, including Pandas, Numpy, Seaborn, and Scikit-learn tools.

STEP 2:

Loading Data and Checking Dimensions:

This code loads the CSV file. After loading the dataset it prints the dataset’s shape to check the number of rows and columns. The %time magic command in the notebook records the time taken to perform the task.

Previewing Data

This block of code displays the first few rows of the dataset to give a quick overview of its structure.

The purpose of the given code is to provide a summary of the DataFrame Aionlinecourse_housing by displaying the number of records, names of the columns, types of columns, count of non-null values, and the size in memory.

Descriptive Statistics

This code displays a summary of the numerical variables contained in the Data Frame, including mean, standard deviation, minimum, maximum, and quartiles, etc.

Checking Null Values

The code measures the proportion of missing (null) values in the columns of the DataFrame, and since the output reveals 0%, it shows that the dataset does not have any null values.

STEP 3:

Creating Pie Chart

The following code snippet first computes the frequency of occurrences in the ‘mainroad’ column and then it proceeds to draw and display a pie chart indicating which proportion of the houses have main road access and which are not, along with the percentage numbers.

Outlier Analysis

This code plots six box plots to represent outliers of some important features that include ‘price’, ‘area’, ‘bedrooms’, ‘bathrooms’, ‘stories’, and ‘parking’ in the features dataset.

Outlier Handling for Price

The following code draws a box plot for the ‘price’ feature, determines the Interquartile Range (IQR), and eliminates outliers by truncating values at 1.5 and above and below the IQR from the lower and upper quartiles.

Outlier Handling for Area

The following code draws a box plot for the area feature, determines the Interquartile Range (IQR), and eliminates outliers by truncating values at 1.5 and above and below the IQR from the lower and upper quartiles.

Outlier Analysis

This code creates a 2x3 grid of box plots to visualize and check if all the outliers are handled or not.

Pairplot Visualization

This code plots a pair plot for the given Aionlinecourse_housing dataset to show the correlation or distribution of features in the form of a scatter plot and histogram respectively for all features in the dataset.

Features vs Price Boxplot Analysis

The code generates the box plots analyzing the relationship between price and different categorical features such as mainroad, guestroom, basement, hotwaterheating, airconditioning, and furnishingstatus in a 2×3 grid.

Use of Boxplot with Hues

This piece of code generates a boxplot to determine the dependency of ‘price’ on ‘furnishingstatus’ making use of the ‘airconditioning’ feature to allow a further breakdown as one compares different groups of air conditioning.

STEP 4:

Converting Of Categorical Variables Into Binary

This piece of code defines how to convert categorical values to binary values (categorical ‘yes’ to ‘1’ and ‘no’ to ‘0 ‘) and uses the function prepared to change the indicated columns in the dataset Aionlinecourse_housing.

Previewing Data

This block of code displays the first few rows of the dataset to have a quick overview of changes.

Making Dummy Variables

This piece of coding does the creation of dummy variables for the categorical feature ‘furnishingstatus’ and puts them into a newly created variable ‘status’ that creates a separate binary column for each of the categories.

This code previews the first few rows of the dataset to have a quick overview.

Eliminating the First Dummy Variable

This piece of code creates dummy variables for the categorical variable named 'furnishingstatus' while discarding the first column with multicollinearity concerns. This makes a better and more efficient representation of the feature in the dataset.

Adding Dummy Variables to the DataFrame

This code appends the dummy variables created out of ‘furnishingstatus’ to the actual Aionlinecourse_housing data frame by concatenating them in terms of column.

Previewing Data

This block of code displays the first few rows of the dataset to have a quick overview to see the changes.

Eliminating the Primary Categorical Column

This piece of code removes the initial ‘furnishingstatus’ column from the Aionlinecourse_housing DataFrame as its dummy variables have been created and included already.

Dividing the Data into Train and Test Sets

This snippet splits the Aionlinecourse_housing DataFrame, such that 70 percent of the data and 30 of the data are used for training and testing, respectively. Ensuring the same random split each time by fixing the seed.

Initialize the Scaler

The following lines of code set up a MinMaxScaler object that will be employed to change the values of the numeric features in the dataset to fit within a desired range, between 0 and 1.

Utilizing MinMax Scaler for Numeric Features

This segment of code fits the MinMaxScaler to the numerical attributes (‘area’, ‘bedrooms’, ‘bathrooms’, ‘stories’, ‘parking’, ‘price’) present in the training data, aims to rescale them between 0 to 1 range, and then shows some records from the revised training dataset.

Descriptive Statistics

This code displays a summary of the numerical variables contained in the Data Frame, including mean, standard deviation, minimum, maximum, and quartiles, etc

Correlation Heatmap

This code produces a heatmap to highlight the relationships between different numerical variables in the df_train DataFrame. This facilitates the identification of the variables that are very much interdependent among themselves.

STEP 5:

Separating Between Features and The Target Variable

This piece of code separates the target variable (‘price’) from the training dataset and saves it as y_train and later on, saves all of the other variables in X_train.

Model Building and Fitting

Building and Compiling a Linear Regression Model. As this code creates a Linear Regression model, it trains the model with the training data (X_train) and appropriate dependent variable (y_train) to fit them.

Executing RFE - Recursive Feature Elimination

This section of the code implements Recursive Feature Elimination (RFE) to choose the 6 most relevant features out of X_train using the trained Linear Regression algorithm. It then prints out all of the names of the features, whether they were selected or not (True or False), and the corresponding ranks.

This block of code retrieves the features' names that were selected in the Recursive Feature Elimination process (RFE) according to the rfe.support_ mask that shows the selected features.

This block of code displays the features' names that were rejected in the Recursive Feature Elimination process (RFE) according to the rfe.support_ mask.

Generation of RFE Filtered Training Data

This code generates an X_train_rfe DataFrame that includes only the Recursive Feature Elimination (RFE) selected features under their names as captured in the col variable, which consists of those feature names.

Inclusion of Constant in Training Data

This code makes use of the add_constant() function provided by Statsmodels library to append an additional column in X_train_rfe DataFrame which is called constant. Such that when running the regression model aside from the features chosen there will be an intercept included.

Fitting the Linear Regression Model

This code implements Ordinary Least Squares (OLS) regression with Statsmodels on the training dataset (X_train_rfe) and the target matrix (y_train), regarding the fitting of the linear model to the features taken in.

Presenting Summary of Linear Models

The following code displays the summary of the fitted Ordinary Least Squares (OLS) linear regression model.

Computing Variance Inflation Factors (VIF)

This code makes use of the function variance_inflation_factor defined within the Statsmodels Library to compute the VIF for each of the attributes included in the model, thereby helping identify problems of multicollinearity among the predictor variables.

Computation and Visualization of VIFs

This section of codes computes the Variance Inflation Factor (VIF) for every variable present in X_train_rfe DataFrame, VIF values are rounded off to the second decimal places and displayed in descending order in a standard VIF table to assist in identifying multicollinearity among the features.

STEP 6:

Making Predictions with the Model

In this section, the provided code applies the trained Linear Regression model (lm) on the X_train_rfe data to predict the target variable (y_train_price), which is considered as the house price estimated by the variables chosen.

Determining the Residuals

The residuals are computed in this code by taking the y_train values which represent the actual values and deducting them from the y_train_price values (representing the predicted prices). In this case, the difference pertains to the observed house prices versus the estimated ones.

Visualization of Error Terms

The provided code generates a histogram with a kernel density estimate (KDE) for the distribution of the residuals (errors) resulting from the difference between actual (y_train) and predicted (y_train_price) values of the model to evaluate the accuracy of predictions made by the model.

Scatter Plot of Residuals vs Actual Values

This code implements a scatter plot depicting the relation between actual prices of houses (y_train) and the corresponding residuals (errors) of the predictions made by the model to ascertain any trends, patterns, or heteroscedasticity in the errors made by the model.

STEP 7:

Model Evaluation

This function specifies a set of numerical variables (num_vars) consisting of attributes such as 'area', 'stories', 'bathrooms', 'airconditioning', 'prefarea', 'parking' and the dependent variable ‘price’ that would be needed for scaling or modeling purposes.

Test Data Scaling

This piece of code is used to perform fit_transform on MinMaxScaler of the df_test DataFrame’s numerical variables, such that they obtained a confined range similar to training data(1-0) for the proper prediction of the model.

Splitting features from the Target Variable in the Test Set

Using this code the target variable (i.e. ‘price’) is extracted from the df_test DataFrame and assigned as y_test, and the remaining features are assigned as X_test to predict the target variable ‘price’.

Inclusion of Constant in Test Data

This code makes use of the add_constant() function provided by the Statsmodels library to append an additional column in X_test DataFrame which is called constant. Such that when running the regression model aside from the features chosen there will be an intercept included.

Generating Test Data with Applied Filters

The X_test_rfe new DataFrame is created by taking only those columns from X_test that were present in the X_train_rfe DataFrame. This allows us to maintain the features used for predicting the test data.

Making Predictions on Test Data

In this segment, predictions (y_pred) are made on the X_test_rfe using the fitted Linear Regression model (lm) and the predicted house prices for the test set are achieved depending on the selected features.

Calculating R-squared Score

The given code finds the R squared (R²) score, which is the percentage of the target variable (y_test) predicted values (y_pred) and informs the accuracy of the model.

Graphing Actual vs Predicted Amount

This code generates a scatter plot to check how well the testing data fits into our predictions and therefore how good our model is in the real world.

Conclusion

For this project, we have developed a house price prediction model using Linear Regression integrating features such as area, number of bedrooms, and garage usage. To begin with, we sought to understand the database and addressed the problems of missing data and outliers. We built the model by eliminating any insignificant features using Recursive Feature Elimination (RFE) so that the model remained on the most pertinent of the data.

After the features had been selected, MinMaxScaler was used to scale the features, where all variables were maintained at the same interval allowing for increased accuracy of the model. Upon training the model with the training dataset then tested its performance with the test dataset recalling the R-squared score that displayed how efficient our model was to the gathered data. The scatter plots and residual analysis also served to explicate the efficiency of the model in predicting outputs as well as pointing out the possible areas of improvement.

After this project, we proved how common problems such as predicting the price of a house can be solved with regression analysis noting that the process of data preparation, feature selection, and model evaluation is essential in generating reliable predictive models. This project illustrates the efficiency of machine learning algorithms and techniques like Linear Regression, feature selection, and data preprocessing in realizing accurate predictions.

Challenges New Coders Might Face

• Challenge: Handling Missing Data
  Solution: Implement imputation methods such as replacing the missing values by mean or median values or more advanced methods such as KNN imputation and K-nearest neighbor imputation should be used.

• Challenge: Outliers in Numerical Data
  Solution: Outliers should be identified by statistical means (for example; IQR ) and such outliers then transformed or deleted. Boxplots assist in the recognition of outliers at an early stage during the cleaning of the data.

• Challenge: Dealing with Categorical Variables
  Solution: Incorporate label encoding or one-hot encoding techniques into the categorical variables. Label encoding is handy when dealing with ordinal data, while one-hot encoding is most suitable for categorical features that are not ordinal.

• Challenge: Choosing the Right Model
  Solution: For example, when building a model one can start with a linear regression baseline model and then intermediate models. Also, compare the models with the MSE or R² score metrics on the validation set and choose the model that will give the best results after the training phase.

• Challenge: Hyperparameter Tuning for Optimization:
  Solution: Use Grid Search or Random Search for hyperparameter tuning to systematically find the optimal settings. These techniques carry out the tuning process automatically, which tends to enhance the performance of the model with very minimal effort.

Frequently Asked Questions (FAQs)

Question 1: In what way does the use of linear regression assist in making predictions on house prices?

Answer: Machine learning is applied using linear regression as it helps people in estimating intermediate variables like house prices. It relates the input features to the output target; for instance, area, number of bedrooms, number of parking, etc to price. Having a trained model on historical data will then be able to house prices given new inputs.

Question 2: What do you understand by Coefficient of Determination R or R Squared and its significance in the prediction of house prices?

Answer: R squared is simply the coefficient of determination which is used to find out the proportion of variation of the target variable that is the house price explained by the model. If the R squared value is closer to 1, it means that there is a good fit and the model does predict the price accurately. However, if the R squared value is about 0, it means that the model has failed to explain this variation. This is very important since it is used to assess the overall quality of a model.

Question 3: What approach can be adopted in house price prediction in case there is missing data in the dataset?

Answer: To avoid a situation where the house price prediction model is likely to fail due to missing data, one can either impute the mean/median of a column in place of its missing values or discard any row containing excessive missing values. A thorough clean-up of such data would mean that the model would not make use of some incomplete data thus increasing predictability.

Question 4: Explain why the selection of features is necessary when estimating the price of a house.

Answer: The selection of features assists in determining the most significant of the factors that are responsible for the cost of the house thus enhancing the performance of the model. Creating models with the Recursive Feature Elimination (RFE) technique, allows us to exclude the RFE-excluded features which are unnecessary and may cause overfitting, lowering the accuracy of the model.

Question 5: What role does data scaling play in the prediction model?

Answer: Data scaling addresses the problem of having all features on a similar scale and often helps improve the performance of regression models owing to their sensitivity to feature scale.

Question 6: What are the primary metrics used to assess regression models?

Answer: For this project, we assessed the performance of models for laptop price prediction using Mean Absolute Error (MAE), Mean Squared Error (MSE), R-Square (R2), and Root Mean Squared Error (RMSE).