Generalized Linear Model

The objective of this project was to construct a Generalized Linear Model (GLM) that establishes a connection between infant mortality and low birth-weight babies.

To initiate the project, we began by reading the file "birthwt.desc.pdf" to gain insights into the data on birth weights. Subsequently, we opened the file "birthwt.data.139.txt," which contained the actual data.

For a comprehensive data analysis, we referred to the file "GLM Birth Weights -pre analysis.edited.pdf," which provided detailed information about the data analysis process.

Throughout the project, the Probit regression link from the following source was utilized: https://en.wikipedia.org/wiki/Probit_model.

In pursuit of our objectives, we employed the following methodologies:

1. Matrix correlation:
   
2. Automatic Variable Selection Algorithms based on the Akaike Information Criterion (AIC)
   

3.Leverage analysis:

$h_{ii}=(H)_{ii}=x_i^{T}(X^TX)^{-1}x_i$ the $i$ diagonal element of the ortho-projection matrix $H=X(X^TX)^{-1}X^T$

4. Cook's distance examination:
   

where $p$ is the rank of the model and $\hat{y}_{j(i)}$ is the fitted response value obtained when excluding $i$,and $s^2=\frac{e^Te}{n-p}$ .

6. Exploration of interactions among explanatory variables:
   By implementing these methodologies, we aimed to establish a robust GLM model that sheds light on the relationship
   between infant mortality and low birth-weight babies.