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Implementing Linear Regression model | Sample Assignment

Updated: May 10, 2022



Description


In the Assignment you will implement a linear model for a set of 20 x/y data points. We assume that the data can be described by a straight line with the slope a through the origin and an intercept b.


y = a * x + b


Task 1

Read the x/y data points from the file datapoints.csv into Python

Task 2

Create a scatterplot of the data.

Task 3

Set the slope a to 10 and the intercept b to 0. Calculate y for every value of x.

Task 4

Calculate the Mean Squared Error (MSE) of y and ytrue using the formula:

MSE = 1/N∑(y−ytrue)2


Task 5

Find a value for a that gives the lowest possible MSE. Implement the following procedure:

  • initially set a to 10

  • repeat the following procedure 100 times:

    • decrease a by 0.1

    • re-calculate y using the modified a

    • re-calculate the MSE

    • check if the new MSE is smaller than the previous one

    • if it is smaller, keep the new values for the MSE and a, otherwise discard it

  • print the final value for a and the corresponding MSE

Task 6

Also modify b in the above procedure.

Task 7

How could the algorithm be improved? Write down one or two ideas.

  • Hints

    • the implementation must be done in Python

    • do not use any existing linear regression functions

    • you may use pandas or numpy

    • use any Python plotting library you like. Do not use Excel for plotting.

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