MATH 494: Mathematical Foundations of Machine Learning

Assignment #5

(Due Monday, March 11, 2024)

In this assignment you will be performing linear regression of a linearized dataset that originally can be assumed to follow the exponential model y = a e^(bx).

· Use the last digit of your USD ID # for ‘a’ (with 9 instead of 0). Ask the user to enter the value of ‘b’.

· Generate a dataset of 100 observations, where x is between 0 and 5 (you may use random values or use numpy.arange), and y is computed from the exponential formula.

· Add substantial Gaussian noise to each computed value of y (meaning the exponential trend should be maintained but the pattern should be visibly noisy).

· Display the noisy dataset (cloud of points).

· Linearize the dataset.

· Perform the complete linear regression, using all the sums that we derived on Friday, March 1

· Obtain the estimated values of a and b and compare them with the original values.