# scikit-learn: Predicting Sales Revenue with Simple Linear Regression

This project will cover how to implement simple linear regression using Python. We will alternatively use the `statsmodels`

and `sklearn`

modules for calculating the linear regression, while using `pandas`

for data management, and `seaborn`

for plotting. We will be working with the very popular advertising dataset to predict sales revenue based on advertising spending on different mediums.

The following topics will be covered in this project: Exploratory Analysis and Data Visualization, Data Preparation, Building a Simple Linear Regression Model, Understanding Ordinary Least Squares (OLS) to Estimate Model Parameters, Interpreting Model Coefficients, Making Predictions Using the Model, Model Evaluation Using RMSE and R-Square Statistics.

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## Task List

We will cover the following tasks in 1 hour and 4 minutes:

### Introduction and Overview

We will understand the Rhyme interface and our learning environment. You will be provided with a cloud desktop with Jupyter Notebooks and all the software you will need to complete the project. Jupyter Notebooks are very popular with Data Science and Machine Learning Engineers as one can write code in cells and use other cells for documentation.

We will also introduce the model we will be building as well the dataset for this Project.

### Loading the Data

In this task, we will load the very popular advertising dataset about various costs incurred on advertising by different mediums such as through TV, radio, newspaper, and the sales for a particular product. Next, we will briefly explore the data to get some basic information about what we are going to be working with.

### Exploratory Analysis

It’s good practice to first visualize the data before doing any analysis and model building. If the data is high dimensional, at least examine few slices using simple techniques like box plots. In this task, we will look at the distributions of our response variable , `Sales`

, and also looked at the distributions of our predictors, `TV`

, `Radio`

, and `Newspaper`

.

### Exploring Relationships between Predictors and Response

Here we visualize pairwise correlations between our predictors and response. We also create a heatmap of the corresponding correlation matrix. This is done so as to ascertain whether there exists any relationship between the sales revenue and the expenditure on the various advertisement channels.

### Creating the Simple Linear Regression Model

Linear regression is an approach for modeling the relationship between a scalar dependent response variable y and one or more predictors (or independent variables) denoted X. The case where we have just one predictor is known as simple linear regression.

In this task, we are going to use the `statsmodels.api`

to create our ordinary least squares (OLS) linear regression model. We will use `sklearn`

to split our data into training and test sets.

### Making Predictions with our Model

Now that we have trained our OLS regression model on the training data, we will use it to make predictions on the test data. Note that the predictions are made on data the model has never seen during train time. Next, will will use the `rmse`

helper function from `statsmodels.tools.eval_measures`

to calculate the root mean squared error (RMSE), which is the difference between the actual value and predicted value of the response variable.

### Plotting the Residuals

One of a few core assumptions of OLS is the normality of errors. If error terms are not normal, then the standard errors of OLS estimates won’t be reliable, meaning that linearity assumption made during model selection does not hold. In this task, we will get the residuals and plot them to check whether they are normally distributed. We will use the `jointplot`

method from `seaborn`

to do this. Upon looking at this result, we can come to a conclusion about the efficacy of our simple linear regression model and whether it could be improved by other methods

## About the Host (Snehan Kekre)

Snehan hosts Machine Learning courses at Rhyme. He is in his senior year of university at the Minerva Schools at KGI, pursuing a double major in the Natural Sciences and Computational Sciences, with a focus on physics and machine learning. When not applying computational and quantitative methods to identify the structures shaping the world around him, he can sometimes be seen trekking in the mountains of Nepal.