Hi, I have an exercise, see screenshot attached.

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Hi, I have an exercise, see screenshot attached.

 

 

Q2. Linear Regression 

Consider the following regression problem, where the task is to estimate the target variable y using a set of regressors (or 

features) x Ex 1, x 2). Suppose to have n traning samples and to fit the data using a linear model family f(x, theta) 

theta a + theta 1 x 1 + theta 2 * x 2. 

Now; add another regressor x 3 (to obtain f(x, theta) 

theta a + theta 1 x 1 + theta 2 x 2 + theta 3 x 3) and 

fit a linear model on the same data agam Comment and compare how the training error, test error and coefficients change 

in the following cases: 

2 x 3 is a random variable independent from y. 

x 1 2 is the square of x 1 (in Python is the "power" operator, so 3 2 

How would your answers change if you we were using Lasso? 

Motivate your answers. 

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