A linear regression refresher (Model KP!!!)

[anjineyulutv]

Please try to use linear regression,to get the best fit curve!!!

Here are few ideas to work on
Here are 13 ideas that are intuitively and logically challenging but avoid overly complex concepts, focusing more on applying linear regression in creative and thought-provoking ways:

1. Implement a linear regression model to predict the future values of the "KP" shape, given a set of new independent variable values.
2. Explore the impact of different data transformations (e.g., logarithmic, square root, etc.) on the independent and dependent variables, and compare the performance of the linear regression models.
3. Develop a method to automatically identify and separate the "K" and "P" segments of the data, and fit separate linear regression models to each segment.
4. Implement a technique to detect and handle multicollinearity (if additional independent variables are introduced) without relying on specific statistical tests or methods.
5. Devise a strategy to evaluate the performance of the linear regression model under different imputation methods.
6. Explore the effect of different types of noise (e.g., uniform, exponential, etc.) on the linear regression model and develop a method to identify and mitigate the impact of different noise distributions.
7. Implement a cross-validation technique that involves splitting the data into training and validation sets in a non-random manner (e.g., based on specific patterns or characteristics of the data).
8. Develop a method to identify and interpret influential data points that significantly impact the linear regression model's coefficients.
9. Implement a technique to automatically detect and handle non-linearity in the data, and decide when to apply linear regression or switch to a non-linear model.
10. Explore the impact of different scaling techniques (e.g., normalization, standardization, etc.) on the independent variables, and develop a method to choose the most appropriate scaling method for the given data.
11. Devise a strategy to visualize and interpret the residuals of the linear regression model in a way that provides insights into the model's assumptions and potential violations.
12. Implement a method to automatically identify and handle multimodal distributions in the residuals, and explore the implications of such distributions on the linear regression model.
13. Develop a technique to assess the stability and robustness of the linear regression model's coefficients under different perturbations or subsamples of the data.

[anjineyulutv]

Here is the code to generate the dataset

import numpy as np
import matplotlib.pyplot as plt

Generating points for "K"

k_x = []
k_y = []

Vertical line of "K"

k_x.extend([-6] * 60)
k_y.extend(np.linspace(0, 6, 60))

Diagonal lines of "K"

k_x.extend(np.linspace(-6, -2, 60))
k_y.extend(np.linspace(3, 5, 60))
k_x.extend(np.linspace(-6, -2, 60))
k_y.extend(np.linspace(3, 0, 60))

Generating points for "P"

p_x = []
p_y = []

Vertical line of "P"

p_x.extend([-1] * 60)
p_y.extend(np.linspace(0, 6, 60))

Semicircular top part of "P" (left-right inverted)

theta = np.linspace(np.pi/2, 3*np.pi/2, 60)
p_x.extend(-1 - 2 * np.cos(theta))
p_y.extend(4 + 2 * np.sin(theta))

Plotting the points

plt.figure(figsize=(8, 6))
plt.scatter(k_x, k_y, c='blue', label='K')
plt.scatter(p_x, p_y, c='red', label='P')
plt.title('Synthetic Data Resembling "KP"')
plt.xlabel('X-axis')
plt.ylabel('Y-axis')
plt.axhline(0, color='black', linewidth=0.5)
plt.axvline(0, color='black', linewidth=0.5)
plt.grid(which='both')
plt.legend()
plt.show()

[madheshlogan]

few more ideas :
1.Implement techniques to calculate and visualize confidence intervals for the linear regression model's predictions. This can provide valuable information about the uncertainty associated with the predictions and aid in decision-making or interpreting the results.
2.Implement robust regression techniques, such as Huber Regression or Theil-Sen Estimator, to mitigate the impact of potential outliers or noise in the data. This can be particularly useful if the "KP" shape data contains anomalies or deviations from the expected pattern.
3. Implement techniques for analyzing the residuals (the difference between the actual and predicted values) of the linear regression model. This can provide insights into the model's assumptions, potential violations, and areas where the model may not be performing well
4. Implement techniques to identify influential observations, such as calculating leverage values, Cook's distance, or DFFITS (Difference in Fits). Influential observations can significantly impact the regression coefficients and should be examined carefully.
5.Conduct sensitivity analyses to assess the impact of different assumptions, data transformations, or modeling choices on the performance of the linear regression model. This can help identify critical factors and inform the selection of the most appropriate modeling approach for the "KP" shape problem

[anjineyulutv]

let's try these also