Lab Assignment-3

 

Assignment-3- week 3 July

Learning Objective: Optimizing the parameters of the regression model.

1.The following dataset represents the relationship between the number of hours spent practicing a skill and the performance score obtained in an assessment.

Build a Polynomial Regression model and use GridSearchCV to determine the optimal polynomial degree (1–5).

Dataset

Hours of Practice (X) Performance Score (Y)

                    1                 3.2

                    2                 5.1

                    3                 8.8

                    4                 15.6

                    5                 25.4

                    6                 38.2

                    7                 54.1

                    8                 73.5

                    9                 96.8

                    10         123.2

                    11         154.6

                    12         190.8

Tasks

Create the dataset using NumPy.

Split the data into training and testing sets (80:20).

Build a Pipeline consisting of

PolynomialFeatures

LinearRegression

Use GridSearchCV to search for the best polynomial degree from 1 to 5.

Use 5-fold cross-validation.

Display

Best polynomial degree

Best cross-validation score

Predict the test set values.

Compute

Mean Squared Error (MSE)

R² Score

Plot

Original data

Best fitted polynomial curve

2.Implement Polynomial regression on Auto MPG data set using Grid Serach and Cross Validation to select the optimal polinomial for regression.

3.The following dataset represents the relationship between the study hours of students and their examination scores.

Fit Polynomial Regression models of different degrees (1 to 6). Compare their training and testing errors to identify underfitting, overfitting, and the optimal model complexity.

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Dataset

Hours Studied (X)	Exam Score (Y)
1	5
2	8
3	15
4	24
5	36
6	50
7	67
8	85
9	108
10	130
11	158
12	190
13	225
14	265
15	310

The data approximately follows a quadratic relationship with a small amount of noise.

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Tasks

1. Create the dataset using NumPy.
2. Split the data into training and testing sets (70:30).
3. Train Polynomial Regression models with degrees 1, 2, 3, 4, 5, and 6.
4. For each model:
   • Calculate the training MSE.
   • Calculate the testing MSE.
5. Display the results in a table.
6. Plot:
   • Training Error vs Degree
   • Testing Error vs Degree
7. Identify:
   • Underfitting model
   • Best model
   • Overfitting model

4.Use California Housing dataset from sklearn and do the following ( understand bias variance trade off)

• Load dataset
• Select one feature (e.g., RM: average rooms)
• Split into train and validation sets
• Apply polynomial regression for different degrees
• Compute training and validation MSE
• Plot error curves
• Analyze results

5.The following dataset contains the advertising expenditure on TV, Radio, and Newspaper and the corresponding product sales.

Develop Linear Regression, Ridge Regression, and Lasso Regression models to predict sales. Compare the models based on regression coefficients, Mean Squared Error (MSE), and R² Score.

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Dataset

TV	Radio	Newspaper	Sales
50	30	10	11
60	25	12	13
70	35	15	16
80	40	18	18
90	45	20	20
100	50	22	23
110	55	24	25
120	60	26	28
130	65	28	30
140	70	30	33
150	75	32	35
160	80	35	38

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Tasks

1. Create the dataset using Pandas.
2. Split the dataset into training and testing sets (80:20).
3. Train a Linear Regression model.
4. Train a Ridge Regression model with alpha = 1.0.
5. Train a Lasso Regression model with alpha = 1.0.
6. Predict the test data.
7. Compare the models using:
   • Regression coefficients
   • Mean Squared Error
   • R² Score

6.Implement Ridge and Lasso regression on the Diabetes dataset. Compare the performance of these regularized models with standard linear regression.

Tasks:

● Load and preprocess the dataset.

● Implement Ridge and Lasso regression.

● Tune hyperparameters using cross-validation.

● Compare performance metrics (MSE, R-squared) with standard linear regression.