Inputs: The training data contain some example measurements of the profit gained by opening an outlet in the cities with the population ranging between 30,000 and 100,000. The y-values are the profit measured in USD, and the x-values are the populations of the city. Each city population and profit tuple constitutes one training example in training dataset.

Problem: Use training dataset to develop a linear regression model and solve it by using gradient descent algorithm. Find the values of 0, 1, and cost function in the first two iterations. Show all calculation steps.

Initialization: 0 = 0, 1 = 0, alpha = 0.01

City Population (10^4)

6.4862

5.5277

8.5186

7.0032

Profit (10^4) y

6.5987

9.1302

13.662

11.854