Univariate-Linear-Regression

Problem statement

Linear Regression is implemented to identify the relationship between profit of a bike sharing company and population of different cities. The main objective is to find the next city in which a new outlet should be opened which results in optimal profitability.

Data visualization

Implementation

• Application of the cost function as shown below:
  
  

• Visualization of the cost function by plotting the cost over a 2-dimensional grid of 𝜃_0 and 𝜃_1 values. The cost function J(𝜃) is bowl-shaped and has a global minimum.
  
  

• Implementation of gradient descent algorithm from scratch in Python without the use of machine learning frameworks such as scikit-learn and statsmodels. Ran the algorithm over 2000 iterations to minimize the cost J(θ). With each step of batch gradient descent, the parameters 𝜃_j come closer to the optimal values that will achieve the lowest cost J(𝜃). The plot of convergence is shown below:
  
  

Results

Univariate Linear Regression Fit:

Libraries used

• matplotlib
• numpy
• pandas
• seaborn
• mpl_toolkits

References

• Coursera
  Course ID: https://www.coursera.org/projects/linear-regression-numpy-python
• https://www.kaggle.com/code/gauravduttakiit/bike-sharing-multiple-linear-regression