The math behind the lines

Linear Regression - Day 2

Let's see the actual math behind the predictive model ⬇️

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If you haven't read the basics yesterday, start here 🔽




1/6

Linear Regression tries to predict the Y variable from X using a linear relationship.

The linear relationship can be visualized as a line.

Mathematically we can write down lines like this 🔽

2/6

In the formula:

- b0 is the point where the line intercepts the y-axis.

- b1 is the slope of the line.

When the slope is 0.5, it means that when we walk along this line, for every unit that we move to the right, we are moving 0.5 units up.

3/6

To find the perfect line the model modifies the b0 and b1 parameters.

It can

- Rotate (increase or decrease slope)

- Translate up and down (modify the y-intercept)

The model does this process until it finds the line that is closest to all the points in the dataset.

4/6

Using the House price example yesterday we

- draw the regression line

- figured out that the price of a house with 4 rooms will be around 300

5/6

The equation for this line is:

y = 61,286x + 52,69

Remember:

Y - the predicted value
x - the attribute = 4
b0 - y-intercept = 52,69
b1 - slope = 61,286

After plugging in:

297.834 = 61.286 (4) + 52.69

The predicted price for a house with 4 rooms is 297.834

6/6

That's it for today.

Tomorrow I will show you how we measure our results and errors in the model.

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Thanks 😉