# Linear regression with white Gaussian noise

I am new to machine learning , so this question may sound fundamental. My task is to estimate the parameter vector of the equation with the least squares method:

$$y = \theta_0 + \theta_1x + \theta_2x^2 + η$$

Where η corresponds to white Gaussian noise with mean 0 and variance 0.1

Also , I have been given the prior values of the parameter vector , say [-1,0.3,0.6] . I have to generate the N points of the training set .

Should regresor be like this :

[1 0.1 (o.1)^2] (for x = 0.1)


And should I calculate a priori results by adding noise

## 1 Answer

η is an error term with distribution (0, sigma). The error or residual is how the true x differ from the estimated function.

Do you mean the theta when you say „parameter vector“.

In this case, the estimated function is: y_hat = -1 + 0.3x + 0.6x^2.

So if you want to infer the training set, you need to generate x points, evenly scattered around the quadratic function (mean of error = 0) with a variance of 0.1.

• Thanks! Now I get it! – HeroMonk Jun 2 '19 at 9:17