Regression analysis

Imagine the following situation: you ran a large customer survey and ended up with a dozen metrics — overall satisfaction, NPS, support rating, delivery speed, interface usability, value for money, and so on.

A manager asks: "What should we fix first to improve the bottom-line index?" Comparing group averages and looking at simple correlations gives you hints, but it does not answer the key question: how do these factors work together?

To estimate the contribution of each factor while accounting for the others, and to identify the true drivers of a metric, you use regression analysis. It helps you move from a collection of separate charts to a model that shows exactly how different aspects of the experience "add up" into the final score.

What regression analysis is, in plain terms

Regression analysis is a set of methods that let you describe the dependence of one variable (for example, overall satisfaction or NPS) on one or several other variables (speed, quality, price, convenience) and quantitatively estimate the contribution of each factor.

Put simply, regression answers the question: "How will the target metric change if one of the factors goes up or down, all else being equal?" At the same time, it is important to remember that the model relies on the data you "feed" it and cannot prove causation; it only describes the observed structure of relationships.

The main elements of a regression model

Dependent variable. What you want to explain or predict: overall satisfaction, the CSI index, likelihood to recommend, intention to stay a customer, the eNPS score, and so on.

Independent variables. Factors that, according to your hypothesis, influence the target metric: ratings for individual aspects of the service, the experience of recent interactions, purchase frequency, customer type, service channel, and so on. How to choose a meaningful set of such factors is the subject of the articles "Quantitative Research" and "How to conduct marketing research".

Coefficients. Numbers in the model that show how the target metric changes when a factor increases by one "unit" (a point, a category, etc.), with the other variables held fixed. The sign of the coefficient shows the direction of the effect (positive or negative), and its magnitude shows the relative strength, provided the variables are scaled comparably.

Model quality. Assessed using statistical indicators: the share of explained variation (R²), the significance of individual coefficients, and residual analysis. These details go beyond a basic overview, but they help you understand how reliably the model describes the data rather than simply fitting the noise.

In surveys, the most commonly used method is linear regression, when the target metric is continuous (an average score on a scale, a satisfaction index). If the outcome is binary instead (for example, "recommends / does not recommend", "stays a customer / leaves"), logistic regression is used: it predicts the probability of an outcome and also produces coefficients that can be interpreted as the effect of a factor on the odds of a particular result.

Where regression is useful in surveys

Finding drivers of satisfaction and loyalty. Instead of looking separately at the correlation of NPS with price, speed, quality, and convenience, you build a model in which all of these factors are present at the same time. This helps you understand which of them genuinely "hold up" the index and which turn out to be secondary once you account for the rest.

Prioritizing improvements. If a regression model shows that, say, "sense of fairness" and "quality of leadership" are far more strongly related to employee engagement than "the office" and "bonuses", that provides arguments in favor of specific management decisions. Approaches to such prioritization are discussed in the articles "Factor Analysis" and "Empirical marketing".

Predicting behavioral metrics. When historical data is available, you can build models that link survey results to real behavior: churn, purchase frequency, average order value. This is already closer to predictive analytics tasks, which are discussed in the term Predictive Analysis.

A simple example: what affects support satisfaction

Suppose you ran a survey among customers who contacted support and collected the following metrics: the overall rating of the interaction, response speed, the agent's competence, courtesy, and first-contact resolution. At the descriptive-statistics level, all the factors look "more or less important".

By building a regression model with the overall rating as the dependent variable, you may discover that, all else being equal, the biggest contribution comes from "first-contact resolution" and "competence". Courtesy matters too, but its contribution is smaller, and speed stops being significant once these two variables are in the model. Such a conclusion helps you focus your efforts: investing not just "in support" in general, but specifically in agent training and in redesigning problem-resolution processes.

How to read the coefficients

In linear regression, each coefficient shows by how many units, on average, the dependent variable will change when the given factor increases by one unit, with the others unchanged. For example: if the coefficient for "first-contact resolution" equals 0.8 on a 1–5 scale, then a 1-point increase in that rating is associated, on average, with a 0.8-point increase in the overall rating. By comparing the coefficients with one another (ideally on comparable scales or after standardization), you can see the relative importance of the factors. A negative coefficient means an inverse relationship: the higher the factor, the lower the target metric. It is important to look not only at the magnitude of the coefficient, but also at its p-value or confidence interval: an insignificant coefficient may be the result of noise or an insufficient sample size.

Limitations and common mistakes

Correlation and regression do not prove causation. Even if the model shows a strong relationship between a factor and an outcome, that still does not mean changing the factor will guarantee a change in the outcome. There may be hidden variables, reverse causation, and other effects, described in more detail in the articles "Response bias" and "Statistical deviations in surveys".

Multicollinearity. If the independent variables are strongly correlated with one another (for example, "overall service rating" and "willingness to recommend"), the model may produce unstable coefficients: a small shift in the data significantly changes the estimated contributions. In such cases it is better either to merge similar questions or to choose just one of them.

Overfitting. When there are many factors but few observations, the model may "fit" the random idiosyncrasies of a particular sample and perform poorly on new data. This is especially relevant for surveys with small samples or complex questionnaires.

Working only with aggregates. Building a regression at the level of values averaged by segment (for example, average satisfaction and average order value by region) often leads to false conclusions. It is more reliable to work with individual responses rather than only with aggregated figures.

Regression is not mandatory in every survey: with a small number of questions and a clear data structure, cross-tabulation and comparisons of group averages are often enough. It makes sense to move to regression when there are several factors, they are potentially related to one another, and you specifically need to "separate" their contributions to the target metric.

How to use regression together with SurveyNinja

SurveyNinja itself focuses on collecting data and on basic analytics: summaries, cross-tabs, filters, segments. For full-fledged regression analysis, external tools are most often used. However, the combination "a survey in SurveyNinja + data export + analysis in BI/statistics tools" lets you build regression into your usual workflow.

Data export. The help section "Viewing the survey report" describes how to export survey results in CSV/XLSX formats. These files can be loaded into Excel, Power BI, Python, or R to build regression models with the level of detail you need.

Linking with CRM and product-analytics data. Through SurveyNinja's API and integrations, you can combine survey responses with internal metrics (purchase frequency, churn, LTV). This lets you build models that link subjective ratings to real customer behavior. Approaches to such tasks are discussed in articles on brand health tracking and empirical marketing.

Prioritization in reports. Even without full-fledged regression, some of the ideas can be implemented through gap and comparison analysis: looking at how the target metric changes across different levels of satisfaction with individual aspects, and comparing the importance of factors by the difference between "poor" and "good" ratings. This is described, for example, in the article "CSI Index".

Practical recommendations

Start with a simple model. Do not try to include all the questionnaire items in the regression at once. Pick 5–7 key factors based on common sense, descriptive statistics, and preliminary correlations, and then gradually make the model more complex as needed.

Use regression as a tool for testing hypotheses, not for generating them. State in advance which relationships you expect to see, and test them in the model. This reduces the risk of interpreting random effects as "discoveries".

Combine quantitative and qualitative approaches. Regression suggests which factors are related to the target metric, but it does not explain why. To understand the reasons, it is useful to complement models with interviews, focus groups, and analysis of open-ended responses, which is discussed in detail in the term Qualitative Analysis.

Check that you have enough data. For stable coefficient estimates you need enough observations: a rule of thumb is at least 10–15 respondents per independent variable. With a small sample, regression gives unreliable or insignificant results; in such cases it is wiser to limit yourself to descriptive statistics and simple comparisons by segment.

Regression analysis is not a magic box that will tell you on its own to "fix support, and NPS will rise by 15 points". It is a tool that helps structure your data, quantitatively estimate the contribution of factors, and narrow down the range of hypotheses. The more responsibly you approach defining the problem, preparing the data, and interpreting the results, the more useful regression becomes for making decisions based on survey results.