How can you use regression analysis to understand cause-and-effect relationships?

Understanding the cause-and-effect relationships in your data is like unraveling a mystery where numbers hold the key to the narrative. Regression analysis is a statistical tool that allows you to examine the relationship between a dependent variable and one or more independent variables. Imagine you're investigating whether temperature affects ice cream sales. In this case, sales are the dependent variable, and temperature is the independent variable. Regression analysis helps you quantify how much sales are expected to increase with each degree rise in temperature, assuming all other factors remain constant. It's a powerful way to predict outcomes and make informed decisions based on empirical evidence.

1 Basics First

Before diving into the intricacies of regression analysis, it's essential to grasp its foundational concepts. At its core, regression seeks to establish a mathematical equation that describes the relationship between variables. The dependent variable, also known as the 'outcome', is what you want to predict, while independent variables, or 'predictors', are the factors you suspect have an effect on the outcome. For your ice cream sales example, a simple linear regression would create a formula that represents the line of best fit through the data points on a graph, showing how sales change with temperature.

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Mark Stouse

CausalAI | Business Effectiveness | Fiduciary Responsibility | Delaware 2023 | Speaker | “Best of LinkedIn” | AI Professor | NACD | HSE | Pavilion | Forbes | MASB | ANA | Author
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One thing to really grasp is that an accurate causal model is the one that most closely represents the situation in Real Life. It will never be perfectly complete or accurate; the absence of any number of “unknown unknowns” from the model ensures that.

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2 Types of Regression

Depending on the nature of your data and the specific questions you want to answer, you may choose from several types of regression. Linear regression is the most straightforward and is used when the relationship between variables is a straight line. However, when the relationship is more complex, you might need polynomial or logistic regression. Polynomial regression can model curves in the data, while logistic regression is used when the outcome is a categorical variable, such as 'yes' or 'no'. Selecting the appropriate type of regression is crucial for accurate analysis.

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Mark Stouse

CausalAI | Business Effectiveness | Fiduciary Responsibility | Delaware 2023 | Speaker | “Best of LinkedIn” | AI Professor | NACD | HSE | Pavilion | Forbes | MASB | ANA | Author
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While the math in multivariable regression is probabilistic, the logic in the average data analyst is rooted in the application of regression to the physical sciences, hence the existence of the 95% Confidence Score as a standard. However, when regression is used in business, the significant presence of human behavior as a variable often means that a max confidence score is in the 50s. To offset this, it’s crucial to recalculate the model far more frequently than in classic regression, and this also means that linear regression models create a very strong feedback loop between causal forecast and actuals. Nonlinear and logarithmic regression are used in business to compute S-curves and show the points of diminishing returns.

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3 Data Preparation

Quality data analysis begins with thorough data preparation. You must ensure your data is clean, which means it's free from errors and missing values that could skew your results. Additionally, it's important to check for outliers—data points that are significantly different from others—as they can disproportionately influence the regression model. Once your data is prepped, you can use software like R or Python for analysis. These tools have built-in functions for performing various types of regression, making the process more efficient and less prone to calculation errors.

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4 Interpreting Results

Interpreting the results of regression analysis involves looking at the coefficients of the equation generated by your statistical software. These coefficients tell you the strength and direction of the relationship between your variables. For instance, a positive coefficient indicates that as the independent variable increases, so does the dependent variable. It's also vital to assess the statistical significance of your results to ensure that the relationships you observe are not due to random chance but are likely reflective of true effects in your data.

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Marian Jacklich, MS, CPA

Sr. Business Consultant
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Of course, remember that correlation is not the same as causation. While there may be a dependent relationship between your variables, to truly ascertain if one variable is causing another variables changes, you need to actually create an experiment. You don’t use historical data for the experiment, you need to design then use new changing and controlled events so that you can document the changes.

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5 Assumptions Check

Regression analysis relies on certain assumptions about your data. It's important to verify these assumptions to ensure the validity of your results. Key assumptions include linearity, independence of errors, homoscedasticity (constant variance of errors), and normal distribution of errors. If these assumptions are violated, your model may not accurately represent the data. Various diagnostic plots and statistical tests can help you check these assumptions. If any assumption does not hold, you may need to transform your data or use a different type of regression model.

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6 Moving Forward

Once you have a valid regression model, you can use it to make predictions and inform decision-making. For instance, you can forecast future ice cream sales based on predicted temperatures. It's also possible to adjust your model as you collect more data or as conditions change. Regression analysis is not only about understanding past trends but also about anticipating future ones. By continuously refining your model, you maintain its relevance and accuracy in helping you make data-driven decisions.

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7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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Mark Stouse

CausalAI | Business Effectiveness | Fiduciary Responsibility | Delaware 2023 | Speaker | “Best of LinkedIn” | AI Professor | NACD | HSE | Pavilion | Forbes | MASB | ANA | Author
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Causal.ai is a strong development in causal analytics that merges aspects of machine learning with multivariable regression to strength causal inference.

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How can you use regression analysis to understand cause-and-effect relationships?

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4

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1 Basics First

2 Types of Regression

3 Data Preparation

4 Interpreting Results

5 Assumptions Check

6 Moving Forward

7 Here’s what else to consider

Data Analytics

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How can you use regression analysis to understand cause-and-effect relationships?

1

2

3

4

5

6

7

1 Basics First

2 Types of Regression

3 Data Preparation

4 Interpreting Results

5 Assumptions Check

6 Moving Forward

7 Here’s what else to consider

Data Analytics

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