# Introduction

Multivariable Linear regression is a common machine learning algorithm. When getting started with machine learning, multivariable linear regression is a great place to dive into next. If you haven’t read the previous article about Simple Linear Regression, I would recommend it, because that is the best place to start.

# What is Multivariable Linear Regression?

Multivariable Linear regression in simple terms is a statistical way of measuring the relationship between multiple variables. Such as, as time increases, so does cost.

Why does linear regression matter? In real life, generally there isn’t 1 variable that predicts a value, often times multiple variable predicts a value. Simply put, you can predict the future!

# Variable vs Feature

In machine learning, you may hear the term “feature” used often. Feature and variable are often times used interchangeably. Let’s use an example of a feature. Let’s take an apple, what are the basic features of this apple?

The apple is:

• Red
• Round
• Has a stem

# Feature Selection

Feature selection in reality is nearly a field on it’s own. Feature selection is the process of selecting the best features to use to best predict the y value. Here are a few tips when trying to select features:

1. The less correlated the features are, the better – Using the correlation coefficient
2. Features must describe the predictive value
3. Features must be related to the predictive value

# The Math

If you recall back to the linear regression formula, y = mx + b, you may notice that the formula is similar. The basic formula is:

y = m1x1 + m2x2 + b

or another way to write this is:

y = w1x1 + w2x2 + b

• y – the predicted value
• w1x1 – the first feature
• w2x– the second feature
• – the bias

# Implement the Math

Let’s say that we are given the following dataset:

 House Value (y) Square Footage (x1) Number of Bedrooms (x2) \$141,000 1,300 2 \$151,000 1,300 3 \$163,000 1,500 2 \$174,000 1,500 3

Let’s also say that we have a house with:

• 3 bedrooms
• 2,005 square feet

What is the house value?

First, we figure out the slope between feature one, which is the square foot and the house value, y.

The slope is \$112.50 per square foot.

Next, we figure out the slope between feature two, which is the number of bedrooms and the house value, y.

The slope is \$10,500 per bedroom added to the house.

## Plugin the Values

Using the same formula as found above, y = w1x1 + w2x2 + b, we now plugin the values into the formula.

1. Plugin feature one – the square footage slope and the 2,005 square footage value
1. y = \$112.5 * 2,005 + w2x2 + b
2. Plugin feature two – the number of bedrooms and the 3 bedroom house value
1. y = \$112.5 * 2,005 + \$10,500 * 3 + b
3. Finally, plugin the bias – which in our case is \$0
1. y = \$112.5 * 2,005 + \$10,500 * 3 + 0
4. Complete the math
1. y = \$257,062.50

# Conclusion

From this article and video, you were able to understand what multivariable linear regression is, what the math looks like, and how to implement multivariable linear regression in a simple problem. Please provide any comments to help improve this post or video for future learners.