A guide to correlation vs. regression

When it comes to product management, data should play a pivotal role in your decision-making process so that you ensure your team remains informed. In my own role as a PM, I interpret and analyze data to drive product development, marketing strategies, and UX and design improvements. However, it can be overwhelming to determine which data measurements to use.

To help you with this, today’s article focuses on two of the most important ones: correlation and regression analysis. Keep reading to learn the basic concepts and usage of both methods, as well as how to apply them in product development. By the end, you should feel comfortable to optimize your product strategy with statistical tools.

What is correlation?

Correlation indicates the presence and strength of the relationship between pairs of variables. It helps in assessing whether fluctuations in one variable correspond to fluctuations in another variable, and quantifies this association using a correlation coefficient (r).

For instance, if you want to check the relationship between the amount of time spent exercising and weight loss for a healthcare app, you could suggest that your development team calculates the correlation coefficient based on the available data. A high positive correlation would indicate that more time spent exercising is associated with greater weight loss, while a high negative correlation would suggest the opposite.

To do this, you need to know the types and key aspects of correlations. Typically, there are positive, negative, and no or zero correlations:

• Positive correlation — When one variable increases, the other variable also increases. For example, the number of hours spent exercising and weight loss often have a positive correlation; the more hours spent exercising, the greater the weight loss
• Negative correlation — When one variable increases while the other decreases. For example, studying for more hours and making fewer mistakes on a test may be negatively correlated, as increased study time often results in a decrease in the number of mistakes
• No correlation — When there’s no relationship between the two variables. For example, eating more and IQ would not correlate

The correlation coefficient measures the strength of correlation and is represented as r, ranging from -1 to +1. A correlation of +1 or -1 indicates a strong relationship, while a 0 indicates a weak one.

What is regression?

Regression analysis is a statistical model that predicts the relationship between a dependent variable and one or more independent variables. Linear regression is a common type of regression analysis that exhibits the relationship by fitting a straight line through data points.

For instance, consider the question: “Do heavier cars have lower mileage?” The relationship between car weight and miles per gallon (mpg) can be analyzed to see if heavier cars have lower mileage.

Linear regression is popular in statistical analysis due to its simplicity, efficiency, and interpretability. You can use it to analyze user behavior, sales, or customer satisfaction based on influencing factors like marketing spending, product features, or demographic data. Like all statistical modes, regression models also have associated challenges since they often oversimplify complex real-world relationships and are quite sensitive to outliers, skewing the results.

The most commonly used regression models include:

• Linear regression — Models relationships with a straight line for simple, linear patterns (e.g., predicting weight from height)
• Multiple regression — Uses multiple predictors to forecast a dependent variable (e.g., predicting product price based on marketing factors)
• Polynomial regression — Fits non-linear patterns with polynomial equations (e.g., modeling temperature variation over the course of a year)
• Logistic regression — It predicts categorical outcomes, often binary. The most common example is classifying emails as spam or not
• Ridge regression — Adds a penalty to reduce overfitting and handle multicollinearity

Other regression methods are lasso regression and elastic net regression, which apply to different objectives and data patterns. Other regression models are ridge regression, lasso regression, and elastic net regression.

Key differences between correlation and regression

The table below provides a quick overview of the fundamental differences between correlation and regression so you can determine which one makes the most sense for your use-case:

When to use correlation vs. regression in data analysis

Correlation measures the strength and direction of the relationship between two variables. You can use it to explore how strongly two variables are related and determine whether their relationship is positive or negative without implying causation. For example, if you want to assess whether hours spent studying are related to test scores, use correlation.

On the other hand, regression predicts the value of one variable based on one or more other variables and helps you understand their relationship. It’s good for modeling and examining the effects of multiple factors while controlling for others. For instance, regression can predict a person’s salary based on experience, education, and job role.

How to perform and interpret correlation and regression analysis

Correlation and regression analysis both have clearly defined processes that make it easy to implement them. Use the following steps with your team:

Correlation analysis

1. Define your variables — Identify the two variables to analyze
2. Collect and prepare data — Gather, clean, and prepare the data
3. Calculate the correlation — Compute the correlation coefficient (e.g., Pearson’s r)
4. Check the correlation coefficient — Check the value of r to analyze positive (r > 0), negative(r < 0), or no correlation (r ≈ 0)
5. Visualize your data — Create scatter plots to visualize the relationship and check for patterns or outliers

Interpreting correlation analysis

• Strong — |r| > 0.7
• Moderate — 0.3 < |r| ≤ 0.7
• Weak — |r| ≤ 0.3
• Positive or Negative — r > 0 or r < 0
• Limitations of analysis — Correlation doesn’t imply causation; it only measures the strength and direction of a relationship

Regression analysis

Performing regression analysis has a less defined process but PMs generally follow these steps:

1. Choose a problem — Identify the dependent variable (outcome) and independent variables (predictors)
2. Prepare your data — Collect, clean, and transform the data (normalize, encode)
3. Explore your data — Use statistics and visualizations to detect patterns and outliers
4. Check your assumptions — Verify assumptions like linearity and independence
5. Split data — Divide into training and testing sets
6. Build the model — Choose and fit the regression model using statistical tools like R or Python
7. Evaluate the model — Use metrics like R-squared and RMSE to assess accuracy
8. Refine your model — Adjust for outliers, perform feature engineering, and apply regularization
9. Make predictions — Test the model and interpret coefficients
10. Communicate results — Present findings and insights

Interpreting regression analysis

• Coefficients — Show relationships
• R-squared — Measures explanatory power
• P-values — Assess significance

Applications of correlation and regression

The most common application of correlation and regression is predictive analytics, which you can use to make day-to-day decisions. For example, you can lean on historical data to predict customer behavior, such as purchasing, churning, retaining, or acquiring. This information is valuable for inventory management, resource allocation, and strategic planning.

Imagine that you want to understand the factors influencing people’s purchase decisions. There could be various factors like location, demographics, etc. Understanding the relationship between each factor and product sales would help drive more sales. Regression analysis can be used to understand how each factor influences sales and to predict outcomes.

Other applications of correlation and regression include:

Real estate

As a PM for an online real estate application at a startup, I encountered a business challenge. We needed to help clients identify the most profitable real estate properties by analyzing the market conditions.

To address this, my product team used correlation analysis to understand the relationship between various factors such as neighborhood development, infrastructure, location, and property appreciation rates. By correlating these factors, we could predict which areas were likely to see significant growth in property value. This information empowered our clients to make more informed decisions.

Employee productivity tool

In the past, I designed an internal employee productivity dashboard (CXO) to improve employee efficiency. The objective was to assess the correlation between employees’ meeting time and various metrics representing their value within the organization, such as job level (e.g., Manager, Director, VP), performance ratings, and influence (measured by network centrality).

We applied correlation analysis to determine if there was a connection between time spent in meetings and employee value. Subsequently, we performed multivariate regression to model the relationships between time spent in meetings (independent variable) and the person’s value (dependent variable), alongside other factors like job level, performance rating, and influence score.

This process helped us identify our high-value contributors and diminishing returns, as well as let us optimize meeting times according to roles.

Challenges and solutions for correlation and regression

While correlation and regression can be valuable resources, you need to watch out for common challenges and mistakes. One of the biggest ones involves misinterpreting correlation as causation, which occurs when you make the false assumption that one of the variables causes the other. This frequently leads to incorrect conclusions that can have a detrimental effect on your product.

You also need to watch out for overfitting in regression models, where overly complex models capture noise rather than the underlying trends. This makes it nearly impossible to generalize the model onto new data, limiting the impact of your work.

Outliers are another issue, as outliers can skew results and lead to misleading correlations or regression coefficients if not managed properly.

To help fight against these, use scatter plots to visualize the connections between variables and detect outliers or non-linear patterns that could distort results. Statistical techniques like Lasso or Ridge regression can help prevent overfitting in regression models, ensuring they can be applied effectively to new data. Additionally, using large and representative sample sizes is essential for enhancing the analysis’s reliability and reducing the likelihood of obtaining false results.

Key takeaways

Correlation analysis helps you understand the strength of relationships between two variables by producing a correlation coefficient (r). On the other hand, regression predicts outcomes based on historical data. There are multiple types of regression and you should take some time to familiarize yourself with each so that you can determine the best one for your team.

As you begin your implementation, make sure to take steps to avoid common challenges like misinterpreting causation and overfitting. By doing so, you can make effective data-driven decisions that pave the way for continued product success. Good luck, and comment with any questions.

Featured image source: IconScout