Missing data is a common issue in datasets, and can affect the accuracy of any analysis. It is important to handle missing data appropriately in order to avoid biased results. One way to handle missing data is through imputation, which involves filling in missing values with estimated values based on the available data. In this blog, we will focus on regression imputation, which is a method for imputing missing data using regression models.

## What is Regression imputation?- Handle Missing Data

Regression imputation is a technique for imputing missing values by predicting them with regression models. This technique involves using the observed values of the variable with missing data as the dependent variable and the other variables as the independent variables to fit a regression model. The resulting regression model is then used to predict the missing values.

## Missing Data Imputation using Regression- Step-by-Step

The process of regression imputation involves the following steps:

Step 1: Identify the variables with missing data The first step in regression imputation is to identify the variables with missing data. Once these variables have been identified, they can be used as the dependent variables in the regression model.

Step 2: Identify the variables that can be used to predict missing values The next step is to identify the variables that can be used as independent variables in the regression model. These variables should be strongly correlated with the dependent variable and should not have missing values themselves.

Step 3: Fit a regression model Once the variables have been identified, a regression model can be fit using the available data. The regression model can be any appropriate regression model, such as linear regression or logistic regression.

Step 4: Use the regression model to impute missing values Finally, the regression model can be used to predict the missing values. The predicted values can be substituted for the missing values in the dataset.

## What are the advantages of regression imputation?

Regression imputation takes into account the relationships between variables and preserves the original distribution, which can reduce bias and improve accuracy in imputing missing values.

- Takes into account the relationships between variables: Regression imputation takes into account the relationships between variables in the dataset, which can improve the accuracy of the imputed values. By using a regression model to predict the missing values, regression imputation can capture the underlying patterns in the data.
- Retains the original distribution: Regression imputation retains the original distribution of the variable being imputed. This is important because it preserves the variability and patterns in the data.
- Reduces bias: Regression imputation can reduce bias in the imputed values. By using a regression model that includes multiple predictors, regression imputation can adjust for confounding factors that may affect the missing values.
- Easy to implement: Regression imputation is easy to implement in software packages such as Scikit-learn, which provides a variety of regression models and imputation algorithms.

## How to do regression imputation in Python?

Let’s look at this well-commented and simple example of Regression Imputation in Python using sklearn (Scikit-learn).

```
import numpy as np
import pandas as pd
from sklearn.experimental import enable_iterative_imputer
from sklearn.impute import IterativeImputer
from sklearn.linear_model import BayesianRidge
# create dummy dataset with missing values
data = pd.DataFrame({'var1': [1, 2, np.nan, 4, 5],
'var2': [2, np.nan, 4, 5, 6],
'var3': [np.nan, 3, 4, 5, np.nan],
'var4': [3, 4, 5, 6, 7],
'var5': [4, 5, 6, np.nan, 8],
'var6': [5, 6, 7, 8, 9]})
# identify variables with missing data
missing_vars = ['var1', 'var2', 'var3']
# identify variables to use as predictors
predictor_vars = ['var4', 'var5', 'var6']
# fit regression model using Bayesian Ridge
imputer = IterativeImputer(estimator=BayesianRidge())
# impute missing values
imputed_data = imputer.fit_transform(data[predictor_vars + missing_vars])
# substitute imputed values for missing values
data[missing_vars] = imputed_data[:, -len(missing_vars):]
print(data)
```

Here is a step-by-step explanation of the Python code for Regression Imputation:

- First, we import the necessary libraries, including NumPy and pandas for data manipulation, and Scikit-learn for the regression imputation algorithm.
- We create a dummy dataset with missing values. This dataset has 6 variables (var1 through var6), with missing values in variables var1, var2, and var3.
- We create two lists: one with the variables that have missing data (missing_vars), and another with the variables to use as predictors in the regression model (predictor_vars). In this example, we use var4, var5, and var6 as predictors.
- We create an instance of the Bayesian Ridge estimator from Scikit-learn, which will be used to fit the regression model.
- We create an instance of the IterativeImputer class from Scikit-learn, which uses the Bayesian Ridge estimator to impute missing values in the dataset.
- We fit the imputer using the predictor variables and the variables with missing data.
- We use the imputer to impute missing values in the dataset. This creates a new array of imputed data, which includes both the predictor variables and the imputed values for the missing variables.
- Finally, we substitute the imputed values for the missing values in the original dataset.
- We print the resulting dataset, which now has imputed values for the missing variables.

## Conclusion

Regression imputation is a powerful technique for dealing with missing data, as it takes into account the relationships between variables in the dataset. The code above provides an example of how to use Scikit-learn in Python to implement this technique.

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