• Accurate pricing estimation is crucial when investing in, selling, or buying real estate properties.

• Determining the "right price" involves considering various factors beyond basic features like square footage and neighborhood.

• Features such as basement finish quality, porch type, and roof material impact the perceived value of a property.

• This project focuses on predicting property sale prices in Ames, Iowa using machine learning models.

• Ames is a city located in Story County, Iowa, approximately 30 miles north of Des Moines.

• The housing dataset used contains over 80 different property features and corresponding sale prices.

• Two datasets, train.csv and test.csv, are provided for the project.

• Both datasets have the same number of feature columns.

• The train.csv dataset is used for training and fitting the model.

• It contains listing information for 2051 properties.

• The test.csv dataset does not include sale price information.

• It consists of listing information for 878 properties.

• Predictions are generated on the test.csv dataset to evaluate the model's performance.

• The model's prediction on the test dataset is uploaded to Kaggle for scoring.

Data Dictionary:

• Dean De Cock's data dictionary provides a comprehensive description of the features in the train.csv dataset. These features are categorized into Nominal, Ordinal, Discrete, and Continuous variables. Understanding these categories is crucial for feature engineering.

Data Cleaning:

• The train.csv dataset contains approximately 10,000 missing values out of 160,000 values. Null values are present in every row.

• The top 5 features with the highest count of missing values are Pool QC (2042), Misc Feature (1986), Alley (1911), Fence (1651), and Fireplace Qu (1000).

• A crucial step in the model workflow involved addressing these missing values. Various techniques, including data visualization and analysis of related features, were employed to impute the missing values.

• For instance, the absence of a garage was inferred from the 114 properties with missing garage-related features but with a Garage Area value of zero. This association was used to impute the missing garage feature values.

• By the end of this step, both the train.csv and test.csv datasets were cleaned, ensuring no missing values remained.

Data Visualization:

In this step of the model building workflow, a comprehensive suite of data visualizations is employed to explore the relationship between the predictors (features) and the response variable (sale price). These visualizations serve multiple purposes, providing valuable insights and aiding in the decision-making process. Here are the key aspects and descriptions of the data visualizations used:

• Scatter Plots: Scatter plots are used to examine the relationship between continuous predictors and the sale price. Each data point represents a property, with the x-axis representing the predictor variable and the y-axis representing the sale price. Scatter plots help identify patterns, trends, and potential outliers in the data.

• Bar Plots: Bar plots are utilized to visualize categorical predictors and their impact on the sale price. Each bar represents a category, and the height of the bar represents the average sale price for properties within that category. Bar plots enable comparisons between different categories and help identify significant differences in sale prices.

• Box Plots: Box plots provide a graphical representation of the distribution and variation of the sale price across different categories or groups. They display the median, quartiles, and any potential outliers. Box plots help assess the spread of sale prices within each category and identify potential anomalies.

• Heatmaps: Heatmaps visualize the correlation between different predictors and the sale price. They utilize color gradients to represent the strength and direction of the correlation. Heatmaps help identify highly correlated predictors and determine which features have the most significant impact on the sale price.

• Histograms: Histograms illustrate the distribution of a continuous predictor variable. They display the frequency or count of values within specific intervals, providing insights into the shape, central tendency, and spread of the predictor's distribution.

• Point plots: Point plots were utilized to explore the relationship between categorical variables and the sale price. They provide a visual representation of the median sale prices for different categories within a variable, allowing for quick comparison and identification of trends and potential outliers.

By employing these various data visualizations, the relationships, patterns, and trends within the dataset can be effectively explored, providing valuable insights for further analysis and modeling decisions.

Assessing Data Integrity and Completeness: A Comparison of Feature Distributions Before and After Cleaning:

One important step in the data preprocessing phase is cleaning the dataset by handling missing values. To assess the impact of this cleaning process, a distribution plot of various features was created, comparing the original dataset with the cleaned dataset.

This comparison is crucial as it allows us to understand the extent of missing values and their effect on the distribution of features. By visualizing the distributions before and after cleaning, we can identify any significant changes or patterns that may have emerged.

The comparison can provide insights into the following aspects:

1. Data Completeness: It helps assess the proportion of missing values in each feature and determine whether the cleaning process effectively addressed the missing data issue.

2. Data Integrity: It allows us to identify any outliers or irregularities in the original dataset that might have affected the distribution of features.

3. Data Consistency: By comparing the distributions between the original and cleaned datasets, we can ensure that the cleaning process did not introduce any unintended biases or distortions.

4. Data Quality: A comparison of the distributions can reveal any discrepancies or inconsistencies in the cleaned dataset that may require further investigation or refinement.

Overall, this comparison of distribution plots provides a visual representation of the impact of data cleaning on the dataset, allowing us to make informed decisions about the data's quality and suitability for subsequent modeling and analysis.

Original Dataset

Cleaned Dataset

Comparing Distribution of Numeric Columns: Train Dataset vs. Test Dataset:

This plot visually compares the distributions of numeric columns between the train dataset and the test dataset. The test dataset is overlapped with the train dataset, allowing for a direct visual comparison. The purpose of this comparison is to assess the consistency of variable distributions between the two datasets. By examining the overlap or deviation of the distributions, insights can be gained regarding the suitability of the training dataset for modeling the test dataset. This analysis aids in identifying any outliers or discrepancies that may impact the model building process and helps ensure robust and accurate predictions.

Exploring Correlation, Distribution, and Relationships among Continuous Variables:

This analysis focuses on investigating the correlation matrix, distribution, and relationship nature among the continuous variables in the dataset. The purpose of these visualizations is threefold:

1. Checking Linearity: By examining the relationship between predictor variables and the response variable, it helps assess whether there is a linear association. This information is crucial for building a regression model that assumes a linear relationship.

2. Exploring Variable Distribution: The distribution of continuous variables provides insights into their spread and skewness. Understanding the distribution helps identify any outliers or unusual patterns that may affect the model's performance.

3. Detecting Multicollinearity: Multicollinearity refers to high correlations between predictor variables. These visualizations help detect multicollinearity by examining the correlation matrix among continuous variables. Identifying multicollinearity is important as it can affect the model's interpretability and stability.

By conducting this analysis, we gain a deeper understanding of the relationships and dependencies among the continuous variables in the dataset. This knowledge assists in making informed decisions during feature selection, model building, and interpretation of the results.

Analyzing the Relationship Between Nominal Variables and Sale Price:

This analysis aims to investigate the trends and correlations between the nominal variables and the sale price of properties. Nominal variables represent categorical features with multiple categories associated with them. The visualizations employed in this analysis include box plots and point plots.

1. Box Plots: Box plots are utilized to examine the spread and distribution of the sale prices across different categories within each nominal variable. They help identify any outliers and provide insights into the variability of sale prices within each category. By comparing the box plots of different nominal categories, we can assess the variations in sale prices and potential differences among the categories.

2. Point Plots: Point plots are used to analyze the median home prices for each nominal category. They enable the identification of trends and patterns in the relationship between the nominal variables and the sale price. By comparing the median home prices across different categories, we can establish whether certain categories tend to have higher or lower sale prices.

Through these visualizations, we gain insights into the strength of correlation between different nominal categories and the sale price. This information helps us understand the impact of each nominal variable on the property's selling price. It can assist in identifying influential nominal categories and selecting relevant features for the model building process. Additionally, detecting any outliers or anomalies within the categories aids in refining the dataset and improving the accuracy of the predictive models.

Along the same lines as nominal variables, a similar analysis was carried out for ordinal variables

Exploring the Relationship Between Time Series Variables and Sale Price:

In this analysis, we delve into the trends and correlations between the time series variables and the sale price of properties. Time series variables represent discrete categories that capture time-related information or events associated with the properties. To investigate this relationship, we employ point plots for visual representation.

1. Point Plots: Point plots are used to illustrate the relationship between different discrete time series categories and the corresponding sale prices. By plotting the median or average sale prices for each time series category, we can observe any patterns or trends in how the sale prices vary over time. This analysis helps to assess the correlation between time-related factors and the sale price of properties.

By examining these point plots, we can identify any notable associations between the discrete time series variables and the sale price. This information provides insights into how specific time-related factors may influence the pricing of properties. Understanding the impact of time on the sale price can assist in making informed decisions, such as identifying the optimal timing for property sales or recognizing market trends and fluctuations. Additionally, it aids in selecting relevant time series variables for inclusion in predictive models and enhancing the overall accuracy of the price prediction process.

Overall, this analysis allows us to uncover the relationships between time series variables and the sale price, providing valuable insights for understanding and predicting property prices in relation to specific time-related factors.

Exploring the Relationship Between Discrete Variables and Sale Price:

In this analysis, we examine the trends and correlations between discrete variables and the sale price of properties. Discrete variables represent distinct categories or counts, such as the number of rooms, fireplaces, or cars in the garage. To investigate this relationship, we utilize violin plots as they provide insights into both the distribution and spread of these variables in relation to the sale price.

1. Violin Plots: Violin plots are effective visualization tools for exploring the relationship between discrete variables and the corresponding sale prices. They display the distribution of the discrete variable on the y-axis, while the width of the plot represents the density or frequency of values. By dividing the violin plot based on the different discrete categories and observing the shape and spread of each category, we can gain insights into how these variables impact the sale price.

These plots allow us to identify any notable patterns or trends in how the sale price varies across different discrete categories. They provide a comprehensive view of the distribution, spread, and central tendency of the sale prices for each category. By analyzing these plots, we can determine whether certain discrete variables strongly influence the sale price or if there are any significant outliers within specific categories.

Feature Selection and Engineering: Enhancing Model Performance

During the feature selection and engineering stage, several steps were undertaken to optimize the model's performance and improve its predictive power. This stage involved a careful examination of the relationship between variables, feature engineering techniques, standardization for specific models, outlier identification, and an iterative process to achieve a favorable variance-bias tradeoff.

1. Feature Selection: The data visualizations generated earlier played a crucial role in identifying relevant features for the model. By analyzing the relationships between variables, we gained insights into which features had a significant impact on the sale price. This information guided the selection of key features that were highly correlated with the target variable, allowing us to focus on the most influential predictors.

2. Feature Engineering: To enhance the predictive capabilities of the model, feature engineering techniques were applied. This involved transforming or creating new features based on existing information. For example, a new feature representing the age of the property at the time of sale was derived from the data on the construction year and sale year. Additionally, dummy variables were created for selected categorical variables to capture their effects in the model. These feature engineering strategies aimed to capture valuable information and improve the model's ability to capture the complexities of the housing market.

3. Standardization for Ridge and Lasso: Ridge and Lasso regression models require standardized features to ensure fair and comparable regularization. Therefore, feature standardization was performed on the relevant predictors to scale them appropriately and remove any biases introduced by differences in measurement units or scales. This step facilitated effective regularization and improved the model's performance when using these specific algorithms.

4. Outlier Identification: Outliers can significantly impact the model's performance and predictions. During this stage, outliers that had a notable influence on the model's performance were identified. These outliers were carefully examined and appropriate actions were taken, such as removing or adjusting them to mitigate their impact on the final model.

5. Iterative Process: The feature selection and engineering process involved an iterative approach to refine the model and achieve the desired prediction accuracy. The selection of features, engineering transformations, standardization, and outlier handling were repeatedly revisited and refined to optimize the model's performance and achieve a balanced variance-bias tradeoff.

It's important to note that the final list of features used in the model consisted of approximately 140 carefully chosen variables. Additionally, certain data points in the training dataset were identified as outliers and handled accordingly. For instance, categories of a particular feature that were not observed in the test dataset were excluded during model training. Similarly, extreme values in the lot area column for residential properties were identified and removed to avoid skewing the model's predictions.

The feature selection and engineering stage aims to maximize the predictive power of the model by incorporating relevant variables, transforming and creating new features, addressing outliers, and refining the model iteratively. By carefully selecting and engineering features, we can capture the underlying patterns and relationships in the data, leading to improved accuracy in predicting the sale price of properties.

Assessing Performance and Predictive Accuracy

In the model evaluation stage, four linear regression models were developed and evaluated for their ability to predict the sale price of properties. These models included the regularized models of Ridge, Lasso, and ElasticNet, along with a standard linear regression model. The evaluation process involved cross-validation, splitting the train dataset into a train-test split to assess the models' performance.

The main metric used to evaluate the models' performance was the root mean squared error (RMSE), which measures the average deviation between the predicted sale prices and the actual sale prices. Additionally, the models' performance was also evaluated using the R2 score, which indicates the proportion of variance in the target variable (sale price) explained by the predictors.

The results of the model evaluation, including the cross-validated mean R2 scores for both the train and test datasets, as well as the RMSE scores, are summarized in the table below:

From the results, it can be observed that all the models achieved relatively high R2 scores on the train dataset, indicating a good fit to the data. However, when applied to the test dataset, slight decreases in the R2 scores were observed, suggesting a slightly reduced predictive performance. The RMSE scores provide a measure of the average prediction error, with lower values indicating better accuracy. Overall, the models achieved similar RMSE scores, with the linear regression model performing slightly better in terms of lower RMSE.

LINEM Assumptions Validity Check

Based on the residuals plots for the Linear, Ridge, Lasso, and ElasticNet models, it can be inferred that these models satisfy the LINE assumptions.

1. Linearity: The residuals in the plots show a random pattern around zero, indicating that the models capture the linear relationship between the predictors and the response variable. This suggests that the models adequately represent the underlying data patterns.

2. Independence: There are no clear clustering or patterns in the residuals plots, indicating that the observations in the dataset are independent of each other. This suggests that the independence assumption is met and there is no evidence of dependence among the residuals.

3. Normality: The distribution of residuals in the plots approximately follows a normal distribution. This suggests that the residuals exhibit a symmetric distribution around zero, supporting the normality assumption. It indicates that the statistical tests and confidence intervals based on the models are reliable.

4. Equal Variance (Homoscedasticity): The spread of the residuals in the plots appears to be relatively consistent across the range of predicted values. This indicates that the variability of the residuals is relatively constant, supporting the equal variance assumption. It implies that the models do not exhibit a systematic change in the spread of residuals as the predicted values vary.

5. In addition to the residuals plots, the cross-plot of predicted sale price vs actual sale price provides further insight into the model performance. If the predicted values are tightly clustered around the 45-degree line, it indicates that the models generate predictions that are close to the actual sale prices. This suggests that the models are effective in predicting the sale price of properties.

   Overall, based on the residuals plots and the cross-plot of predicted vs actual sale price, it can be inferred that the Linear, Ridge, Lasso, and ElasticNet models exhibit satisfactory performance and adhere to the LINE assumptions. These models can be considered reliable for predicting the sale price of properties, providing valuable insights for decision-making and analysis in the real estate domain.

Based on the analysis of the Ames housing dataset and the trained linear regression model, several conclusions can be drawn:

1. Sale Price Estimation: The linear regression model developed using the dataset can be utilized to estimate the sale price of houses. The model takes into account various features and their relationships with the sale price to provide an accurate prediction.

2. Model Performance: The model's performance is assessed using the Root Mean Squared Error (RMSE) metric, which measures the average prediction error. With an RMSE score of 18,000, the model demonstrates reasonable accuracy in predicting the sale price. However, it's important to note that the model's performance can vary depending on the specific dataset and features used.

3. Linear Model Assumptions: The assumptions of linearity, independence, normality, and equal variance (homoscedasticity) have been validated for the linear regression model. This indicates that the model's predictions are based on a reasonable representation of the underlying relationships between the predictors and the response variable.

4. Feature Importance: Among the various features considered in the model, the overall quality of a property has the most significant positive impact on its sale price. This suggests that houses with higher overall quality tend to have higher sale prices. Conversely, the absence of a garage is identified as the biggest negative contributor to the sale price, implying that properties without a garage may have lower sale prices.

These conclusions provide insights into the factors that influence the sale price of houses in the Ames housing market. The developed linear regression model can be a valuable tool for estimating the sale price and understanding the relative importance of different features in determining property values.