*This is part of my notes taken while studying machine learning. I’m learning as I go along, and may update these with corrections and additional info.*

In my Linear Regression for ML notes, we discussed need way to move the line to best fit our data. Two methods for doing so are:

- Absolute Trick
- Square Trick

### Square Trick

Similar to the absolute trick, but takes into account the distance the line is from the point. If the line is a small distance away from the point, we want to move it a small amount. If it is a large distance away, move it a larger amount.

*y = (w _{1} – p(q-q’)⍺)x + (w_{2} + (q-q’)⍺)*

*q’* = (called q prime) is y position of where the point is located on the line. So *q – q’* is the vertical distance between the point and the line.

### Square Trick Example

Using our same example from the absolute trick, let’s do it again using square trick. Our line is currently at *y = 2x + 3* and we want to move it closer to the point at (5, 15).

With a learning rate of 0.1, we are going to use the square trick expression:

*y = 2x + 3* starting expression

*y = (w _{1} + p(q-q’)⍺)x + (w_{2} + (q-q’)⍺)* move it to this

*y = (2 + (5 x (15-13) x 0.1))x + (3 + ((15-13)x0.1))* add our learning rate and p’

*y = 3x + 3.3 *and now we have this.

When we plot our new expression, the line is getting closer to our point: