Simple Linear Regression¶
Problem Statement¶
In this notebook, we will predict sales revenue for a given advertising budget using a simple linear regression model. For this purpose, we will use the kaggle dataset Advertising.csv. The dataset consists of 200 rows of data, each representing a market with the following attributes:
TV: advertising dollars spent on TV for a single product in a given market (in thousands of dollars)Radio: advertising dollars spent on RadioNewspaper: advertising dollars spent on NewspaperSales: sales of a single product in a given market (in thousands of widgets)
We will try to predict sales using the three other features.
Import necessary packages¶
We will use the following packages for this tutorial:
pandasto load and manipulate datanumpyto work with arrays of datamatplotlibandseabornfor plotting and visualizationsklearnfor machine learning and data analysis tools
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns
Load the data¶
Download the dataset from here. Click on the folder icon on the left panel of colab and create a folder named datasets. Then upload the dataset to the datasets folder.
We will use the pd.read_csv() function to read the dataset into a pandas dataframe. We will also use the head() function to display the first five rows of the dataframe.
data = pd.read_csv('datasets/Advertising.csv')
data.head()
| TV | Radio | Newspaper | Sales | |
|---|---|---|---|---|
| 0 | 230.1 | 37.8 | 69.2 | 22.1 |
| 1 | 44.5 | 39.3 | 45.1 | 10.4 |
| 2 | 17.2 | 45.9 | 69.3 | 12.0 |
| 3 | 151.5 | 41.3 | 58.5 | 16.5 |
| 4 | 180.8 | 10.8 | 58.4 | 17.9 |
Explor the data¶
At first, we will try to understand the data by exploring it. We will use the info() function to get a brief information about the dataframe.
data.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 200 entries, 0 to 199 Data columns (total 4 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 TV 200 non-null float64 1 Radio 200 non-null float64 2 Newspaper 200 non-null float64 3 Sales 200 non-null float64 dtypes: float64(4) memory usage: 6.4 KB
From the output, we can see that the dataframe has 200 rows and 4 columns. The columns are named TV, Radio, Newspaper, and Sales. The Sales column is the target variable and the other three columns are the features. The info() function also shows that there are no missing values (null values) in the dataframe and all the values are numerical (float64).
Next, we will use the describe() function to get some statistical information about the dataframe.
data.describe()
| TV | Radio | Newspaper | Sales | |
|---|---|---|---|---|
| count | 200.000000 | 200.000000 | 200.000000 | 200.000000 |
| mean | 147.042500 | 23.264000 | 30.554000 | 15.130500 |
| std | 85.854236 | 14.846809 | 21.778621 | 5.283892 |
| min | 0.700000 | 0.000000 | 0.300000 | 1.600000 |
| 25% | 74.375000 | 9.975000 | 12.750000 | 11.000000 |
| 50% | 149.750000 | 22.900000 | 25.750000 | 16.000000 |
| 75% | 218.825000 | 36.525000 | 45.100000 | 19.050000 |
| max | 296.400000 | 49.600000 | 114.000000 | 27.000000 |
From the output, we can see that the average sales revenue is 15.13 thousand dollars with a standard deviation of 5.29 thousand dollars. The minimum sales revenue is 1.6 thousand dollars and the maximum sales revenue is 27 thousand dollars. The average advertising budget for TV, Radio, and Newspaper are 147, 23, and 30 thousand dollars respectively.
Also, we got a brief idea about the distribution of the data from the describe() function. For example, the maximum advertising budget for TV is 296 thousand dollars and the minimum is 0.7 thousand dollars. The average advertising budget for TV is 147 thousand dollars and the standard deviation is 85 thousand dollars. The 25th percentile, 50th percentile, and 75th percentile values are 74, 149, and 218 thousand dollars respectively meaning that 25% of the markets have an advertising budget of less than 74 thousand dollars, 50% of the markets have an advertising budget of less than 149 thousand dollars, and 75% of the markets have an advertising budget of less than 218 thousand dollars for TV. The same information can be obtained for the other features.
sns.boxplot(data=data, orient='v')
plt.show()
From the boxplots, we can see that there are two outliers in the Newspaper feature. The outliers are the two points above the maximum value. We will remove these two points from the dataset.
Remove outliers¶
We will use update the dataframe by taking only the rows where the budget for Newspaper is less than 90 thousand dollars, as the outliers are above 90 thousand dollars.
data = data[data['Newspaper'] < 90]
sns.boxplot(data=data, orient='v')
plt.show()
From the boxplots, we can see that there are no outliers in the Newspaper feature.
Pairplot¶
Next, we will draw a pairplot to visualize the relationship between the features and the target variable. The pairplot will also show the correlation between the features and the distribution of the data.
sns.pairplot(data=data, diag_kind="kde")
plt.show()
From the pairplot, we can conclude the following:
- No or very little linear relationship between TV and Radio
- Low linear relationship between TV and Newspaper
- Moderate linear relationship between Radio and Newspaper
- High linear relationship between TV and Sales, Radio and Sales, and Newspaper and Sales
- A small curvilnear relationship between TV and Sales as well as Radio and Sales
Correlation matrix¶
To get a numerical idea about the correlation between the features and the target variable, we will draw a correlation matrix.
matrix = data.corr()
sns.heatmap(matrix, annot=True, cmap='Blues')
plt.show()
This plot further quantifies the relationship between the features and the target variable, and confirms our observations from the pairplot.
Prepare the data¶
Before we can train a machine learning model, we need to prepare the data.
Created: May 24, 2023