diff --git a/README.md b/README.md
index f746e56..4848459 100644
--- a/README.md
+++ b/README.md
@@ -1,29 +1,190 @@
-# Project 2
+# Machine Learning
+## Project 2 
 
-Select one of the following two options:
+# Group Members - Contribution
+* Venkata Naga Lakshmi Sai Snigdha Sri Jata - A20560684 - 33.33%
+* Sharan Rama Prakash Shenoy - A20560684 - 33.33%
+* Adarsh Chidirala - A20561069 - 33.33%
 
-## Boosting Trees
+# ###################################################
+## Usage Instructions
 
-Implement the gradient-boosting tree algorithm (with the usual fit-predict interface) as described in Sections 10.9-10.10 of Elements of Statistical Learning (2nd Edition). Answer the questions below as you did for Project 1.
+### Installation
 
-Put your README below. Answer the following questions.
+To get started with this project, first you need **Python 3.x**. Then follow these installation steps:
 
-* What does the model you have implemented do and when should it be used?
-* How did you test your model to determine if it is working reasonably correctly?
-* What parameters have you exposed to users of your implementation in order to tune performance? (Also perhaps provide some basic usage examples.)
-* Are there specific inputs that your implementation has trouble with? Given more time, could you work around these or is it fundamental?
+#### 1. Clone the Repository to your local machine:
 
-## Model Selection
+```bash
+git clone https://github.com/adarsh-chidirala/Project2_Adarsh_Ch_Group.git 
+```
+#### 2. Steps to Run the Code on Mac
 
-Implement generic k-fold cross-validation and bootstrapping model selection methods.
+Follow these steps to set up and run the project:
 
-In your README, answer the following questions:
+1. **Create a Virtual Environment**:
+   - Navigate to your project directory and create a virtual environment using:
+     ```bash
+     python3 -m venv myenv
+     ```
 
-* Do your cross-validation and bootstrapping model selectors agree with a simpler model selector like AIC in simple cases (like linear regression)?
-* In what cases might the methods you've written fail or give incorrect or undesirable results?
-* What could you implement given more time to mitigate these cases or help users of your methods?
-* What parameters have you exposed to your users in order to use your model selectors.
+2. **Activate the Virtual Environment**:
+   - Activate the created virtual environment by running:
+     ```bash
+     source myenv/bin/activate
+     ```
+
+3. **Install Required Libraries**:
+   - Install the necessary Python libraries with the following command:
+     ```bash
+     pip install numpy pandas matplotlib scikit-learn
+     ```
+
+4. **Run the Script**:
+   - Navigate to the directory containing your script and run it:
+     ```bash
+     python project2.py
+     ```
+
+Make sure that the script `project2.py` and any required dataset files are correctly placed in your project directory.
+
+#### 3. Steps to Run the Code on Windows
+
+Follow these instructions to set up and execute the project on a Windows system:
+
+1. **Create a Virtual Environment**:
+   - Open Command Prompt and navigate to your project directory:
+     ```cmd
+     cd path\to\your\project\directory
+     ```
+   - Create a virtual environment in your project directory by running:
+     ```cmd
+     python -m venv myenv
+     ```
+
+2. **Activate the Virtual Environment**:
+   - Activate the virtual environment with the following command:
+     ```cmd
+     myenv\Scripts\activate
+     ```
+
+3. **Install Required Libraries**:
+   - Install the necessary libraries by executing:
+     ```cmd
+     pip install numpy pandas matplotlib scikit-learn
+     ```
+
+4. **Run the Script**:
+   - Make sure the script `project2.py` and any necessary dataset files are placed in your project directory. Run the script with:
+     ```cmd
+     python project2.py
+     ```
+Ensure that all paths are correct and relevant files are located in the specified directories.
+
+#### 4. Running Datasets:
+   - We are using two datasets: customer_dataset.csv and patient_data.csv. For each of this we need to specify the features and the target column. 
+   - This is done in the main function in the bottom of the code as follows.
+   - For customer_dataset.csv
+``` 
+data = pd.read_csv('customer_dataset.csv')
+
+    feature_columns = ['Age','Annual_Income','Spending_Score']
+    target_column = 'Store_Visits'
+
+```
+   - For patient_data.csv
+``` 
+data = pd.read_csv('patient_data.csv')
+
+    feature_columns = ['RR_Interval','QRS_Duration','QT_Interval']
+    target_column = 'Heart_Rate'
+
+```
+
+## K-fold cross-validation and Bootstrapping model selection models
+## Introduction
+- This project implements the developments of generic k-fold cross-validation and bootstrapping model selection methods, primarily focusing on AIC scores to evaluate the model performance. 
+- These techniques are designed to evaluate and compare the performance of machine learning models on different datasets, providing detailed insights into how effective a model is on the given situations and predict the corresponding outcomes accurately based on the scores calculated. 
+- The implementation can be adapted to various models, and allows customization to suit individual requirements and resources by modifying its features.
+
+## Key Features implemented
+- The model supports 3 different models i.e; Linear, Ridge and Lasso regression models and calculates Mean AIC scores for each model using following validation models.
+- The model successfully implements K-Fold Cross-Validation and Bootstrapping Validation.
+- **K-Fold Cross-Validation:** This validation model provides evaluation by splitting the dataset into k subsets, using k-1 subsets for training the dataset and remaining 1 subset for testing the dataset.
+- **Bootstrapping:** This validation model provides evaluation of the performance by repeatedly resampling the dataset with replacements of the same data.
+- The project also generates the plots of the K-fold cross validation and Bootstrapping AIC scores and Distribution.
+
+
+### 1. Do your cross-validation and bootstrapping model selectors agree with a simpler model selector like AIC in simple cases (like linear regression)?
+In simple cases like linear regression,the relationship between the dependent and independent variables is considered to be linear, it is possible that cross-validation, bootstrapping, and AIC scores may accept on the simpler model selector. 
+However, this may not be constant always because it depends on the dataset provided and the complexity of the models.
+
+Note that cross-validation and bootstrapping provide estimates of model performance, while AIC focuses on model selection. These techniques can be different in model evaluation and selection based on the different purposes.
+
+To determine whether cross-validation and bootstrapping model selectors agree with AIC in a specific case, it is recommended to perform experiments and compare the results.
+
+### 2. In what cases might the methods you've written fail or give incorrect or undesirable results?
+Failures or undesirable results may occur under these conditions:
+**Small Datasets:** k-fold Cross-validation and bootstrapping can give unreliable AIC scores when the dataset is too small.
+**Non-balance Data:** Models training on the non-balance datasets, might make biased predictions which affects the AIC calculations.
+**Connected Predictions:** Strong connections between predictions can lead to wrong estimates, affecting AIC evaluations.
+**Wrong Model Assumptions:** AIC relies on specific model assumptions (e.g., linear regression assumes Gaussian errors). If these assumptions are wrong, AIC might not show the true model fit.
+**Overfitting with Bootstrapping:** Repeated sampling with replacement might  make bootstrapped datasets favor complex models too much, leading to high AIC values.
+
+### 3. What could you implement given more time to mitigate these cases or help users of your methods?
+
+1. Use Ridge and Lasso penalties during cross-validation: Regularization adds a penalty to the model's complexity to reduce overfitting. Ridge regression adds an L2 penalty , while Lasso regression adds an L1 penalty.
+Use RidgeCV and LassoCV from scikit-learn: These classes perform cross-validation to find the better regularization parameter (alpha) for Ridge and Lasso regression.
+
+2. Use categorized sampling for k-fold cross-validation: Categorized k-fold ensures that each fold has the equal proportion of class labels as the original dataset, which shows imbalanced datasets.
+Implement balanced bootstrapping: Bootstrapping involves sampling with a stategy of replacement. Balanced bootstrapping ensures that each class is represented equally in each sample.
+
+3. Add BIC or deviance as options besides AIC: AIC score is a common metric for model selection, but BIC (Bayesian Information Criterion) and deviance can provide additional insights. 
+
+4. Plot performance for different hyperparameters: Validation curves help visualize how the model's performance changes with different values of hyperparameters (e.g., alpha in Ridge/Lasso). This helps in selecting the correct hyperparameter value.
+
+5. Provide summaries for bootstrap and k-fold iterations: Summarizing the results of resampling methods (like bootstrap and k-fold) helps understand the variability and stability of the model's performance.
+
+6. Let users set evaluation metrics and sampling methods: Providing flexibility in setting these parameters allows users to customize the model according to their specific needs and preferences.
+
+### 4. What parameters have you exposed to your users in order to use your model selectors.
+1. **Cross-Validation:**
+k: Number of parts to split the data into for testing.
+model_type: Type of model (e.g., 'linear', 'ridge', 'lasso', 'logistic').
+2. **Bootstrapping:**
+n_bootstraps: Number of times to randomly sample the data.
+model_type: Type of model (e.g., 'linear', 'ridge', 'lasso', 'logistic').
+3. **General Settings:**
+Features (X_columns) and target (y_column): Columns to use from any dataset.
+
+
+### Code Visualization:
+- The following screenshots display the results of each test case implemented in this project:
+
+### 1. customer_dataset.csv:
+- Tests the model on a small dataset, and verifies if the predictions are reasonable.
+- i. K-fold cross validation AIC score:
+    ![Customer Test Image](customer_aic_k_fold.png)
+- ii. Bootstrap AIC score:
+    ![Customer Test Image](customer_aic_bootstrap.png)
+- iii. K-fold cross validation AIC distribution:
+    ![Customer Test Image](customer_aic_distr_k_fold.png)
+- iv. Bootstrap AIC distribution:
+    ![Customer Test Image](customer_aic_dis_bootstrap.png)
+- v. Bootstrap Output:
+    ![Customer Test Image](customer_output.png)
+
+### 2. patient_data.csv:
+- Tests the model on a large dataset, and verifies if the predictions are reasonable.
+- i. K-fold cross validation AIC score:
+    ![Patient Test Image](patient_aic_k_fold.png)
+- ii. Bootstrap AIC score:
+    ![Patient Test Image](patient_aic_bootstrap.png)
+- iii. K-fold cross validation AIC distribution:
+    ![Patient Test Image](patient_aic_dis_k_fold.png)
+- iv. Bootstrap AIC distribution:
+    ![Patient Test Image](patient_aic_dis_bootstrap.png)
+- v. Bootstrap Output:
+    ![Patient Test Image](patient_output.png)
 
-See sections 7.10-7.11 of Elements of Statistical Learning and the lecture notes. Pay particular attention to Section 7.10.2.
 
-As usual, above-and-beyond efforts will be considered for bonus points.
diff --git a/customer_aic_bootstrap.png b/customer_aic_bootstrap.png
new file mode 100644
index 0000000..8a15b7b
Binary files /dev/null and b/customer_aic_bootstrap.png differ
diff --git a/customer_aic_dis_bootstrap.png b/customer_aic_dis_bootstrap.png
new file mode 100644
index 0000000..113e58a
Binary files /dev/null and b/customer_aic_dis_bootstrap.png differ
diff --git a/customer_aic_distr_k_fold.png b/customer_aic_distr_k_fold.png
new file mode 100644
index 0000000..e30fa9e
Binary files /dev/null and b/customer_aic_distr_k_fold.png differ
diff --git a/customer_aic_k_fold.png b/customer_aic_k_fold.png
new file mode 100644
index 0000000..2b10f7e
Binary files /dev/null and b/customer_aic_k_fold.png differ
diff --git a/customer_dataset.csv b/customer_dataset.csv
new file mode 100644
index 0000000..5728d1a
--- /dev/null
+++ b/customer_dataset.csv
@@ -0,0 +1,101 @@
+Customer_ID,Age,Annual_Income,Spending_Score,Store_Visits
+Customer_1,56,21864,42,7
+Customer_2,69,29498,99,10
+Customer_3,46,59544,7,9
+Customer_4,32,36399,16,16
+Customer_5,60,57140,90,7
+Customer_6,25,69554,60,9
+Customer_7,38,53173,2,8
+Customer_8,56,58955,1,14
+Customer_9,36,36554,48,12
+Customer_10,40,48320,12,8
+Customer_11,28,72034,69,7
+Customer_12,28,33141,37,5
+Customer_13,41,64250,32,11
+Customer_14,53,75897,9,4
+Customer_15,57,56868,99,9
+Customer_16,41,24735,19,8
+Customer_17,20,54902,48,14
+Customer_18,39,48783,80,10
+Customer_19,19,57016,3,13
+Customer_20,41,61041,20,18
+Customer_21,61,38304,24,14
+Customer_22,47,37341,54,9
+Customer_23,55,47741,33,6
+Customer_24,19,35516,24,9
+Customer_25,38,52257,75,7
+Customer_26,50,48298,72,4
+Customer_27,29,89502,36,12
+Customer_28,39,34623,38,15
+Customer_29,61,38269,84,7
+Customer_30,42,56359,99,7
+Customer_31,66,63090,89,11
+Customer_32,44,84308,99,11
+Customer_33,59,74343,25,12
+Customer_34,45,62355,93,11
+Customer_35,33,54395,18,6
+Customer_36,32,63449,82,5
+Customer_37,64,40845,66,6
+Customer_38,68,45257,54,8
+Customer_39,61,27763,35,11
+Customer_40,69,46567,80,7
+Customer_41,20,64439,61,16
+Customer_42,54,46854,41,10
+Customer_43,68,38389,33,16
+Customer_44,24,44603,68,11
+Customer_45,38,60861,33,12
+Customer_46,26,46163,14,6
+Customer_47,56,62748,21,13
+Customer_48,35,30330,48,13
+Customer_49,21,36945,20,7
+Customer_50,42,42400,8,7
+Customer_51,31,30350,7,8
+Customer_52,67,94154,67,9
+Customer_53,26,33556,17,8
+Customer_54,43,63723,33,10
+Customer_55,19,40009,48,9
+Customer_56,37,42293,76,11
+Customer_57,45,54519,59,6
+Customer_58,64,28122,86,11
+Customer_59,24,40058,22,12
+Customer_60,61,47802,30,7
+Customer_61,25,37309,38,10
+Customer_62,64,37662,51,9
+Customer_63,52,66300,54,5
+Customer_64,31,65074,8,9
+Customer_65,34,43373,27,12
+Customer_66,53,48737,27,10
+Customer_67,67,68555,98,5
+Customer_68,57,28602,21,10
+Customer_69,21,55070,30,10
+Customer_70,19,79618,97,14
+Customer_71,23,79475,28,7
+Customer_72,59,20901,64,15
+Customer_73,21,38560,97,10
+Customer_74,46,52529,69,14
+Customer_75,35,30171,61,15
+Customer_76,43,39976,48,8
+Customer_77,61,47940,19,10
+Customer_78,51,71019,4,12
+Customer_79,27,49318,35,8
+Customer_80,53,53254,64,7
+Customer_81,31,57686,49,11
+Customer_82,48,58152,17,12
+Customer_83,65,50421,44,7
+Customer_84,32,32043,92,10
+Customer_85,25,61845,30,10
+Customer_86,31,56472,93,10
+Customer_87,40,33548,46,15
+Customer_88,57,39765,6,12
+Customer_89,38,63312,99,6
+Customer_90,33,59082,37,12
+Customer_91,62,39195,24,18
+Customer_92,35,45950,93,9
+Customer_93,64,47848,46,8
+Customer_94,41,59255,53,11
+Customer_95,43,68734,95,7
+Customer_96,42,50984,99,9
+Customer_97,62,67538,60,9
+Customer_98,58,63099,97,8
+Customer_99,46,53084,63,11
+Customer_100,32,28347,85,6
diff --git a/customer_output.png b/customer_output.png
new file mode 100644
index 0000000..1e1aa6d
Binary files /dev/null and b/customer_output.png differ
diff --git a/patient_aic_bootstrap.png b/patient_aic_bootstrap.png
new file mode 100644
index 0000000..31a95e9
Binary files /dev/null and b/patient_aic_bootstrap.png differ
diff --git a/patient_aic_dis_bootstrap.png b/patient_aic_dis_bootstrap.png
new file mode 100644
index 0000000..133437a
Binary files /dev/null and b/patient_aic_dis_bootstrap.png differ
diff --git a/patient_aic_dis_k_fold.png b/patient_aic_dis_k_fold.png
new file mode 100644
index 0000000..9872414
Binary files /dev/null and b/patient_aic_dis_k_fold.png differ
diff --git a/patient_aic_k_fold.png b/patient_aic_k_fold.png
new file mode 100644
index 0000000..9ab0943
Binary files /dev/null and b/patient_aic_k_fold.png differ
diff --git a/patient_data.csv b/patient_data.csv
new file mode 100644
index 0000000..4a781fa
--- /dev/null
+++ b/patient_data.csv
@@ -0,0 +1,101 @@
+Name,RR_Interval,QRS_Duration,QT_Interval,Heart_Rate
+Patient_1,0.8496714153011233,0.07169258515899171,0.3743114944139313,66.470558102682
+Patient_2,0.7861735698828816,0.09158709354469283,0.38243138105472935,73.5181193738789
+Patient_3,0.8647688538100693,0.09314570966946462,0.4033220497270111,73.11917039243617
+Patient_4,0.9523029856408026,0.08395445461556762,0.4021520820813961,66.05700924928192
+Patient_5,0.7765846625276664,0.09677428576667982,0.30489322528171636,77.15686853574789
+Patient_6,0.776586304305082,0.10808101713629077,0.32248699840339506,77.84785008420363
+Patient_7,0.9579212815507392,0.1377237180242106,0.38060141068834635,69.0239513885651
+Patient_8,0.876743472915291,0.10349155625663678,0.38055143803648833,65.47721198252965
+Patient_9,0.7530525614065048,0.1051510078144553,0.3806019074522419,82.41120022914828
+Patient_10,0.8542560043585965,0.09851108168467666,0.5141092596261888,69.22559310251184
+Patient_11,0.7536582307187538,0.061624575694019176,0.3828356204277267,78.5232767790996
+Patient_12,0.7534270246429744,0.09946972249101567,0.405422625607224,85.12999769564942
+Patient_13,0.8241962271566035,0.10120460419882053,0.3981600705397281,76.9252795806596
+Patient_14,0.6086719755342203,0.14926484224970574,0.3860556500522319,102.64281106661645
+Patient_15,0.6275082167486967,0.09615278070437755,0.34738923021438617,102.1436718765265
+Patient_16,0.7437712470759028,0.10603094684667226,0.3903587688197307,80.77498357676075
+Patient_17,0.6987168879665576,0.09930576460589514,0.3290869914184971,89.28145485471593
+Patient_18,0.8314247332595275,0.07662643924760937,0.3505272557303996,70.61394781116486
+Patient_19,0.7091975924478789,0.12285645629030043,0.3405854580868358,86.22348783309093
+Patient_20,0.6587696298664709,0.11503866065373548,0.3632749655754529,90.42816462759119
+Patient_21,0.9465648768921555,0.11582063894086095,0.4525863426669403,63.8720771753293
+Patient_22,0.7774223699513465,0.08181225090410522,0.28530939229633007,80.15390903910003
+Patient_23,0.8067528204687924,0.128055886218722,0.3874504076149805,70.28111875361058
+Patient_24,0.6575251813786543,0.07196297874415439,0.2954913651524139,101.7131944278849
+Patient_25,0.7455617275474817,0.11173714187600542,0.34112272536842264,75.44614702871685
+Patient_26,0.8110922589709867,0.14380911251619957,0.40355802387869466,67.90337901394749
+Patient_27,0.6849006422577697,0.08018927349738623,0.3625712007638185,93.39450200319018
+Patient_28,0.8375698018345672,0.08867404540794457,0.31689020888282776,75.59413399316603
+Patient_29,0.7399361310081195,0.10199302730175283,0.33138785162960127,84.20867883378384
+Patient_30,0.7708306250206723,0.08993048691767602,0.387183909957387,80.97983886732776
+Patient_31,0.7398293387770604,0.06898673137867735,0.3307853347313145,81.03855071470649
+Patient_32,0.9852278184508938,0.10137125949612055,0.368658343583279,56.41334838912456
+Patient_33,0.7986502775262067,0.0787539257254779,0.36182287359615256,75.50577312009649
+Patient_34,0.69422890710441,0.10947184861270363,0.3339359860957673,83.0410160617954
+Patient_35,0.882254491210319,0.08161151531532394,0.445757763573013,72.88318672446336
+Patient_36,0.6779156350028979,0.13099868810035079,0.3853567608927204,87.77130137871981
+Patient_37,0.8208863595004756,0.08433493415327527,0.2789942965336957,68.96423896138931
+Patient_38,0.6040329876120225,0.0935587696758865,0.36745817259077707,97.72539407626846
+Patient_39,0.667181395110157,0.1162703443473934,0.33352854140926447,91.99522254155255
+Patient_40,0.8196861235869124,0.0753827136713209,0.39409733339184894,70.38012767650545
+Patient_41,0.8738466579995411,0.1045491986920826,0.32829917046269197,64.55083023960674
+Patient_42,0.8171368281189971,0.12614285508564857,0.355410542341324,74.64555124221584
+Patient_43,0.788435171761176,0.06785033530877546,0.38019949115921825,77.32493867144008
+Patient_44,0.7698896304410712,0.10369267717064609,0.39463020776680485,75.39853277026003
+Patient_45,0.6521478009632573,0.10519765588496847,0.31198814371776895,89.64849216351446
+Patient_46,0.7280155791605292,0.11563645743554621,0.3466199505663621,83.57606841031834
+Patient_47,0.7539361229040213,0.07526098578243837,0.34100218755356176,72.34191713693855
+Patient_48,0.9057122226218917,0.07359086773831448,0.33386683069705153,59.20888881018827
+Patient_49,0.8343618289568462,0.11043883131233796,0.4306181696112439,68.31902640971597
+Patient_50,0.6236959844637266,0.10593969346466373,0.3761992684384382,95.13347980575513
+Patient_51,0.8324083969394795,0.10500985700691753,0.30956464182659815,73.63454112997775
+Patient_52,0.7614917719583684,0.10692896418993952,0.39671447788219105,86.16949061816116
+Patient_53,0.7323077999694042,0.0863995055684302,0.44488624788050535,86.22105917974149
+Patient_54,0.8611676288840868,0.10464507394322008,0.40129861042204584,68.87315382926947
+Patient_55,0.9030999522495952,0.10586144946597363,0.29922520136183944,66.34274774183217
+Patient_56,0.89312801191162,0.08571297163947265,0.3406306370853499,62.16697267119687
+Patient_57,0.7160782476777362,0.13731549022289513,0.4106764459674649,83.69716008615627
+Patient_58,0.7690787624148786,0.10947665841823576,0.33169322137524876,76.57212334297503
+Patient_59,0.8331263431403564,0.07617393005594703,0.37775277712584915,73.63148119763069
+Patient_60,0.897554512712236,0.1131310721726766,0.39098536213717344,62.71215271115612
+Patient_61,0.752082576215471,0.08050636659545357,0.32292278113687667,82.37520623552601
+Patient_62,0.7814341023336183,0.11574169207484905,0.357618985757528,84.44560083301468
+Patient_63,0.6893665025993972,0.12317191158014809,0.23034930639723708,86.49263020374767
+Patient_64,0.6803793375919329,0.08358635363296579,0.3190244943466284,90.19465816542541
+Patient_65,0.8812525822394198,0.11926752258488645,0.34989727394427356,71.5356268390884
+Patient_66,0.9356240028570824,0.10825561853872998,0.310088672721406,62.12222249839843
+Patient_67,0.7927989878419667,0.1164412031998898,0.4252964521572654,76.8016892018897
+Patient_68,0.9003532897892025,0.13793585965307895,0.3027943448815747,66.70346932526019
+Patient_69,0.8361636025047634,0.0950922376799426,0.34239822053212066,72.24467294588068
+Patient_70,0.7354880245394876,0.08492527671285022,0.36522962309144363,77.71343774278343
+Patient_71,0.8361395605508415,0.08220971140748953,0.4176509315626446,71.88090657027938
+Patient_72,0.9538036566465969,0.08368379430069124,0.3025655139528224,65.39601994740464
+Patient_73,0.7964173960890049,0.09845796581171792,0.40652655008619837,82.59309802922168
+Patient_74,0.9564643655814007,0.10682303949633289,0.36040932244078344,67.52738955538736
+Patient_75,0.5380254895910256,0.10553381598660039,0.32073965395808196,122.28479226777651
+Patient_76,0.8821902504375224,0.11654366498072048,0.3784841389705308,64.17580253073245
+Patient_77,0.8087047068238171,0.10026003783755814,0.3679623878229388,78.55432086376831
+Patient_78,0.7700992649534133,0.12907068154314635,0.3359913249136482,78.82874388010656
+Patient_79,0.8091760776535503,0.09470686333524088,0.36279208339960073,85.09851272587785
+Patient_80,0.6012431085399108,0.15440338333179238,0.3445874561255296,95.75175218429371
+Patient_81,0.7780328112162489,0.11251334695530013,0.3645406938100499,72.91896107023354
+Patient_82,0.8357112571511747,0.08285684887167435,0.38648522698084187,68.79816874758635
+Patient_83,0.9477894044741517,0.07858215003877776,0.4234406726458141,52.685723691077506
+Patient_84,0.7481729781726353,0.10964944830486371,0.310487380046926,77.56658311817392
+Patient_85,0.7191506397106813,0.09553074429348299,0.44532133498625065,79.63609171943745
+Patient_86,0.7498242956415464,0.11428000988184185,0.2819164880190999,80.77071512233246
+Patient_87,0.8915402117702075,0.1094647524914709,0.35392859619857664,69.00804379079206
+Patient_88,0.8328751109659684,0.09854342174686255,0.383532688259383,81.42046639005171
+Patient_89,0.7470239796232961,0.08306412563863191,0.3712396747094013,85.0708260017295
+Patient_90,0.8513267433113356,0.06970305550628271,0.33509201920717624,67.59370934863053
+Patient_91,0.8097077549348041,0.09106970095865959,0.351675109985709,69.60873602087257
+Patient_92,0.896864499053289,0.11712797588646945,0.3402799626136467,69.35933384842717
+Patient_93,0.7297946906122648,0.10428187488260408,0.3364254097222315,75.61373737788642
+Patient_94,0.7672337853402232,0.07508522442576024,0.393984083880841,87.36031505492532
+Patient_95,0.7607891846867842,0.10346361851702364,0.37428061943860186,84.76267504473155
+Patient_96,0.6536485051867882,0.10770634759457674,0.3322836161895738,89.44657521239348
+Patient_97,0.8296120277064577,0.08232285127597734,0.39598399501733,63.757290373627896
+Patient_98,0.826105527217989,0.10307450211891056,0.3722919808350644,79.39930807401652
+Patient_99,0.8005113456642461,0.10116417436892,0.3925144847535584,74.37939273967072
+Patient_100,0.7765412866624853,0.07714059404338755,0.3851851536769445,83.4547737136939
diff --git a/patient_output.png b/patient_output.png
new file mode 100644
index 0000000..d122c2c
Binary files /dev/null and b/patient_output.png differ
diff --git a/project2.py b/project2.py
new file mode 100644
index 0000000..0585afd
--- /dev/null
+++ b/project2.py
@@ -0,0 +1,219 @@
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+
+class Model_Selector:
+    def AIC_calculator(self, X, y, beta):
+    
+        #Calculating the AIC scores for the models
+    
+        length_y = len(y)
+        preds = X @ beta
+        residual = y - preds
+        rss = np.sum(residual**2)
+        square_of_sigma = rss / length_y 
+        log_likelihood = -0.5 * length_y * (np.log(2 * np.pi * square_of_sigma) + 1)
+        
+        length_beta = len(beta)  # Number of coefficients
+        aic_scores = 2 * length_beta - 2 * log_likelihood
+        return aic_scores
+
+    def linear_regression_model(self, X, y):
+
+        #Implement Linear regression model
+
+        XTX = X.T @ X
+        XTy = X.T @ y
+        beta = np.linalg.solve(XTX, XTy)
+        return beta
+
+    def ridge_regression_model(self, X, y, alpha=1.0):
+        #Implement Ridge Regression model.
+        
+        features_n = X.shape[1]
+        XTX = X.T @ X + alpha * np.eye(features_n)
+        XTy = X.T @ y
+        beta = np.linalg.solve(XTX, XTy)
+        return beta
+
+    def lasso_regression_model(self, X, y, alpha=1.0, max_iter=1000, tol=1e-4):
+        #Implement Lasso Regression model
+
+        n, m = X.shape
+        beta = np.zeros(m)
+        for _ in range(max_iter):
+            beta_value = beta.copy()
+            for j in range(m):
+                residual = y - X @ beta + beta[j] * X[:, j]
+                rho = X[:, j].T @ residual
+                if rho < -alpha:
+                    beta[j] = (rho + alpha) / (X[:, j] @ X[:, j])
+                elif rho > alpha:
+                    beta[j] = (rho - alpha) / (X[:, j] @ X[:, j])
+                else:
+                    beta[j] = 0
+            if np.linalg.norm(beta - beta_value, ord=1) < tol:
+                break
+        return beta
+
+    def k_fold_cross_validation(self, X, y, model_fn, alpha=None, k=5):
+        n = len(y)
+        indices = np.arange(n)
+        np.random.shuffle(indices)
+        fold_size = n // k
+        aic_scores = []
+
+        for i in range(k):
+            test_indices = indices[i * fold_size:(i + 1) * fold_size]
+            train_indices = np.setdiff1d(indices, test_indices)
+
+            X_train, X_test = X[train_indices], X[test_indices]
+            y_train, y_test = y[train_indices], y[test_indices]
+
+            if alpha is not None:
+                beta = model_fn(X_train, y_train, alpha)
+            else:
+                beta = model_fn(X_train, y_train)
+
+            aic_score = self.AIC_calculator(X_test, y_test, beta)
+            aic_scores.append(aic_score)
+
+        return aic_scores
+
+    def bootstrap_validation(self, X, y, model_fn, alpha=None, n_bootstraps=100):
+        n = len(y)
+        aic_scores = []
+
+        for _ in range(n_bootstraps):
+            bootstrap_indices = np.random.choice(n, size=n, replace=True)
+            X_bootstrap, y_bootstrap = X[bootstrap_indices], y[bootstrap_indices]
+
+            if alpha is not None:
+                beta = model_fn(X_bootstrap, y_bootstrap, alpha)
+            else:
+                beta = model_fn(X_bootstrap, y_bootstrap)
+
+            aic_score = self.AIC_calculator(X_bootstrap, y_bootstrap, beta)
+            aic_scores.append(aic_score)
+
+        return aic_scores
+
+def summarize_results(aic_scores):
+    n = len(aic_scores)
+    mean_aic = sum(aic_scores) / n
+    variance = sum((x - mean_aic) ** 2 for x in aic_scores) / n
+    std_dev = variance ** 0.5
+    return mean_aic, std_dev
+
+def plot_results(results):
+    """
+    Plot the AIC results for k-Fold and Bootstrapping across models using horizontal bars.
+    """
+    models = list(results.keys())
+    mean_aic_kf = [results[model]["mean_aic_kf"] for model in models]
+    mean_aic_bootstrap = [results[model]["mean_aic_bootstrap"] for model in models]
+    kf_std_dev = [results[model]["kf_std_dev"] for model in models]
+    bootstrap_std_dev = [results[model]["bootstrap_std_dev"] for model in models]
+    
+    # k-Fold Horizontal Bar Plot with Error Bars
+    fig, ax = plt.subplots(figsize=(8, 6))
+    ax.barh(models, mean_aic_kf, color='green', xerr=kf_std_dev, capsize=5)
+    ax.set_title('k-Fold Cross-Validation AIC')
+    ax.set_ylabel('Models')
+    ax.set_xlabel('AIC')
+    plt.show()
+
+    # Bootstrap AIC Horizontal Bar Plot with Error Bars
+    fig, ax = plt.subplots(figsize=(8, 6))
+    ax.barh(models, mean_aic_bootstrap, color='purple', xerr=bootstrap_std_dev, capsize=5)
+    ax.set_title('Bootstrap AIC')
+    ax.set_ylabel('Models')
+    ax.set_xlabel('AIC')
+    plt.show()
+
+    # Boxplots for AIC Distribution
+    fig, ax = plt.subplots(figsize=(8, 6))
+    ax.boxplot([results[model]["kf_scores"] for model in models], vert=True)
+    ax.set_title('k-Fold AIC Distribution')
+    ax.set_xticklabels(models)
+    ax.set_ylabel('AIC')
+    plt.show()
+
+    fig, ax = plt.subplots(figsize=(8, 6))
+    ax.boxplot([results[model]["bootstrap_scores"] for model in models], vert=True)
+    ax.set_title('Bootstrap AIC Distribution')
+    ax.set_xticklabels(models)
+    ax.set_ylabel('AIC')
+    plt.show()
+
+def generic_process(data, X_columns, y_column):
+    """
+    Generic process to evaluate AIC for Linear, Ridge, and Lasso models on any dataset.
+    """
+    # Split features and target
+    X = data[X_columns].values
+    y = data[y_column].values
+
+    # Initialize Model_Selector
+    selector = Model_Selector()
+
+    # Define models
+    models = {
+        'linear': selector.linear_regression_model,
+        'ridge': lambda X, y: selector.ridge_regression_model(X, y, alpha=1.0),
+        'lasso': lambda X, y: selector.lasso_regression_model(X, y, alpha=1.0)
+    }
+
+    results = {}
+
+    for model_name, model_fn in models.items():
+        print(f"Evaluating model: {model_name.capitalize()}")
+
+        # Perform k-Fold Cross-Validation
+        aic_scores_kf = selector.k_fold_cross_validation(X, y, model_fn, k=5)
+
+        # Perform Bootstrapping
+        aic_scores_bootstrap = selector.bootstrap_validation(X, y, model_fn, n_bootstraps=100)
+
+        # Calculate mean and standard deviation
+        mean_aic_kf, std_aic_kf = summarize_results(aic_scores_kf)
+        mean_aic_bootstrap, std_aic_bootstrap = summarize_results(aic_scores_bootstrap)
+
+        # Save the results
+        results[model_name] = {
+            "mean_aic_kf": mean_aic_kf,
+            "mean_aic_bootstrap": mean_aic_bootstrap,
+            "kf_std_dev": std_aic_kf,
+            "bootstrap_std_dev": std_aic_bootstrap,
+            "kf_scores": aic_scores_kf,
+            "bootstrap_scores": aic_scores_bootstrap
+        }
+
+    # Find the best model
+    best_model = None
+    best_mean_aic = float('inf')
+
+    for model_name, scores in results.items():
+        avg_aic = (scores["mean_aic_kf"] + scores["mean_aic_bootstrap"]) / 2
+        print(f"\n{model_name.capitalize()} - Mean AIC: k-Fold: {scores['mean_aic_kf']:.3f}, Bootstrapping: {scores['mean_aic_bootstrap']:.3f}")
+
+        if avg_aic < best_mean_aic:
+            best_mean_aic = avg_aic
+            best_model = model_name
+
+    print(f"\nBest Model: {best_model.capitalize()} with an average AIC of {best_mean_aic:.3f}")
+
+    # Plot results
+    plot_results(results)
+
+
+# Example Usage:
+if __name__ == "__main__":
+
+    data = pd.read_csv('patient_data.csv')
+
+    feature_columns = ['RR_Interval','QRS_Duration','QT_Interval']
+    target_column = 'Heart_Rate'
+
+    # Run the process
+    generic_process(data, feature_columns, target_column)
\ No newline at end of file