Simple Linear Regression and Correlation Explained for Marketers
Discover how to accurately predict marketing trends with precision. Validate data relationships and make data-informed decisions.
Simple linear regression is a powerful way to understand and predict marketing outcomes, but accurate predictions depend on more than just plotting a line. Certain conditions, known as assumptions, must be met in order for results to be accurate. It is also important to know how variables relate to each other so you do not come to the wrong conclusions.
In this guide, we’ll look into the assumptions of simple linear regression, introduce correlation, and the correlation coefficient. Finally, we will use an example to show how everything fits together.
What is Simple Linear Regression?
Simple linear regression predicts one variable (the outcome) based on another (the influencing factor). For example, you might use the amount spent on Google Ads to predict how many conversions you’ll get.
Linear regression works by plotting the data on a scatter plot and finding the best-fitting straight line. This line, called the “regression line,” shows the general trend of the relationship between the variables.
While it appears simple, some requirements need to be in place for the model to work well.
Assumptions of Simple Linear Regression
To get accurate and meaningful results, your data must meet these key assumptions:
1. Linearity
The relationship between the variables should be linear, meaning that the data points should form a straight-line pattern when plotted. This doesn’t mean every point must sit exactly on the line, but the overall trend should follow a straight direction, either upward or downward. For example, if you’re examining how ad spend affects conversions, an increase in ad spend should consistently lead to more conversions (or fewer, in the case of a negative relationship). If the data forms a curve or fluctuates unpredictably, simple linear regression might not work accurately.
2. Minimum Sample Size
A larger sample size leads to more reliable results. While there’s no fixed rule, at least 20 data points are generally recommended for simple linear regression. Fewer data points may not provide enough information to establish a clear relationship, which can make the results unstable or misleading.
3. Homogeneity of Variance (Homoscedasticity)
This assumption means that the spread of data points around the regression line (variance) should stay consistent across all levels of the independent variable. In simpler terms, the “errors” (differences between the predicted and actual values) should be roughly the same size, whether you’re looking at high or low values of the independent variable. If the spread gets larger or smaller at different points, it could distort your model. For example, if higher ad spend leads to highly unpredictable conversion numbers, your model might not be reliable.
4. Normality
The data should follow a normal distribution. A normal distribution is the shape of your dataset, which shows that the data around the mean is more frequent (mean, median, and mode are the same value). It looks like a symmetrical bell-shaped curve when graphed. In practice, you can check this by plotting a histogram of the residuals. If the histogram looks roughly bell-shaped, this assumption is likely satisfied. This assumption ensures that the model’s predictions are consistent and reliable.
5. Independence
Each data point should be independent of others. For example, in a time-series dataset, the value for one day shouldn’t directly influence the value for the next. If data points are dependent on each other, the results of your regression analysis could be misleading.
Measuring the Strength of Relationships
It’s important to understand how your variables relate to each other before applying linear regression. This is where correlation plays a key role.
What is correlation?
Correlation measures the strength and direction of the relationship between two variables. By examining correlation, you can determine if it’s worth proceeding with a regression analysis.
Types of Correlation
Positive Correlation
When two variables increase together, they have a positive correlation. For example, as ad spend increases, conversions might also increase. On a scatter plot, you’ll notice the data points forming an upward slope to the right.
Negative Correlation
When one variable increases while the other decreases, the correlation is negative. For instance, as customer complaints rise, customer satisfaction scores might drop. On a scatter plot, this relationship appears as a downward slope to the right.
No Correlation
If there’s no consistent pattern between two variables, it indicates no correlation. For example, ad spend and website design changes might show no relationship. On a scatter plot, the points appear scattered randomly without forming a clear slope.
Why Correlation Matters
Understanding correlation helps you identify whether a relationship exists and whether it’s strong enough to proceed with linear regression. If your variables show little or no correlation, using regression might not provide meaningful predictions. Conversely, strong positive or negative correlations suggest that linear regression could yield valuable insights.
By plotting your data in a scatter plot, you can visually assess the direction and strength of the correlation before moving forward.
What is the Correlation Coefficient?
After identifying a correlation between your variables, the next step is to measure how strong or weak that relationship is. This helps you determine how confident you can be in using the data for your marketing decisions. The correlation coefficient is a number between -1 and 1 that quantifies the strength and direction of the relationship.
What the Numbers Mean
- 1 or Close to 1 (High Positive Correlation): A very strong positive relationship
- 0 (No Correlation): No relationship. The variables don’t affect each other.
- -1 or Close to -1 (High Negative Correlation): A very strong inverse relationship. When one variable increases, the other almost always decreases.
For linear regression to work, the correlation coefficient should be significantly different from 0, indicating a clear relationship.
You can use the scale above as a reference when presenting results to stakeholders or making decisions. High correlation coefficients indicate a strong relationship, while low coefficients suggest a weaker but still meaningful connection. It’s up to you to decide whether to act on a weaker correlation or explore other variables for better results.
Calculating the Correlation Coefficient
There’s a formula to calculate the correlation coefficient, so you don’t need to do it manually. Tools like Excel, Google Sheets, and Tableau can quickly compute it for you. These platforms make it simple to analyse your data without needing advanced statistical knowledge.
Why Correlation Coefficient Matters in Marketing
In marketing, understanding the strength of relationships between variables can guide smarter decisions. For instance:
- Confident Predictions: A strong correlation means you can reliably predict outcomes for future campaigns.
- Resource Allocation: Knowing the strength of a relationship helps you decide where to focus time and budget.
- Justifying Strategies: Presenting correlation coefficients makes your data analysis more credible when explaining marketing decisions to a team or client.
Example: Google Ads and Conversions
Let’s put this into practice with an example. You’re running a Google Ads campaign and want to know if your ad spend correlates with the number of conversions.
Observing the Data
- Dependent Variable: Conversions (what you want to predict).
- Independent Variable: Ad Spend (the influencing factor).
As you can see in the scatter plot above, there’s a positive correlation—as ad spend increases, conversions generally go up.
What’s Next?
In this article, we’ve discussed the importance of meeting assumptions and understanding correlation before applying linear regression. In the next guide, we’ll take this dataset and demonstrate how to apply linear regression in Tableau. You’ll see how to interpret the regression line, evaluate model accuracy, and make predictions.
With a strong foundation in these concepts, you’ll be ready to start using linear regression effectively in your own marketing analyses.
