# Regression analysis: The ultimate guide

In this guide, we’ll cover the fundamentals of regression analysis, from what it is and how it works to its benefits and practical applications.

When you rely on data to drive and guide business decisions, as well as predict market trends, just gathering and analyzing what you find isn’t enough — you need to ensure it’s relevant and valuable.

The challenge, however, is that so many variables can influence business data: market conditions, economic disruption, even the weather! As such, it’s essential you know which variables are affecting your data and forecasts, and what data you can discard.

And one of the most effective ways to determine data value and monitor trends (and the relationships between them) is to use regression analysis, a set of statistical methods used for the estimation of relationships between dependent variables and independent variables.

In this guide, we’ll cover the fundamentals of regression analysis, from what it is and how it works to its benefits and practical applications.

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## What is regression analysis?

Regression analysis is a statistical method of analyzing different factors, and understanding which can influence an objective (e.g. the success of a product launch, business growth, a new marketing campaign), and which factors can be ignored.

It can also help leaders understand how given variables impact each other, including external factors, and the results. For example, when forecasting financial performance, regression analysis can determine how changes in certain drivers within the business can influence revenue or expenses in the future. You might find that there’s a high correlation between the number of marketers employed by the company, the leads generated, and the opportunities closed. Yet when leads increase but the number of marketers employed stays constant, it no longer impacts opportunities closed. However, as the number of marketers increases, it both increases leads and opportunities closed.

Regression models enable you to determine which data points to focus on to bring about a specific result. For example, hiring more marketers rather than increasing leads generated per marketer.

## How does regression analysis work?

Regression analysis starts with variables that are categorized into two types: independent and dependent variables. Your selection depends on the outcomes you’re analyzing.

### Understanding variables:

#### 1. Dependent variables

This is the main variable that you want to analyze and predict. For example, operational (O) data such as your quarterly or annual sales. On the other hand, you could look at experience (X) data such as your net promoter score (NPS) or customer satisfaction score (CSAT).

Dependent variables are also called response variables, outcome variables, or left-hand-side variables (they appear on the left-hand side of a regression equation.

As for identifying dependent variables, there are three easy ways to do so:

First, is the variable measured as an outcome of the study? Second, is the variable dependent on another in the study? And finally, do you measure the variable only after other variables are altered?

#### 2. Independent variables

Independent variables are the factors that could affect your dependent variables. For example, a price rise in the second quarter.

You can identify independent variables with the following list of questions:

First, is the variable manipulated, controlled, or used as a subject grouping method by the researcher? Second, does this variable come after the other variable in time? Finally, are you trying to understand whether or how this variable affects another?

Independent variables are often referred to differently in regression depending on the purpose of the analysis, some other descriptors include:

Explanatory variables

Explanatory variables are those which explain an event or an outcome in your study. For example, explaining why your sales dropped or increased.

Predictor variables

Predictor variables are used to predict the value of the dependent variable. For example, predicting how much sales will increase when new product features are rolled out.

Experimental variables

These are variables in the regression equation that can be manipulated or changed directly by researchers to assess the impact. For example, assessing how different product pricing (\$10 vs \$15 vs \$20) will impact the likelihood to purchase.

Subject variables

Subject variables are variables that you can’t change directly, but vary across the sample. For example, age, gender, or income of consumers.

Unlike experimental variables, you can’t randomly assign or change subject variables, but you can design your regression analysis to determine the different outcomes of groups of participants with the same characteristics. For example, ‘how do price rises impact sales based on income?’

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## Carrying out regression analysis

First and foremost, plot your results. Doing so makes interpreting regression results much easier as you can clearly see the correlations between dependent and independent variables.

Let’s say you carried out a regression analysis to understand the relationship between the number of ads placed and revenue generated.

On the Y-axis, revenue generated. On the X-axis, the number of digital ads. By plotting the information on the graph, and drawing a line (called the regression line) through the middle of the data, you can see the relationship between the number of digital ads placed and revenue generated.

This regression line is the line that provides the best description of the relationship between your independent variables and your dependent variable. In this example, we’ve used a simple linear regression model.

Statistical analysis software can draw this line for you and precisely calculate the regression line. The software then provides a formula for the slope of the line, adding further context to the relationship between your independent and dependent variables.

### Simple linear regression analysis

Simple linear regression is used when your regression model is only measuring the impact of one independent variable.

A simple linear model basically uses a single straight line to determine the relationship between your independent variable and independent variable.

This regression model is mostly used when you want to determine the relationship between two variables (like price increases and sales) or the value of the dependent variable at certain points of the independent variable (for example the sales levels at a certain price rise).

While this linear regression is useful, it does require you to make some assumptions.

For example, it requires you to assume that:

1. The data was collected using a statistically valid sample collection method that is representative of the target population
2. There are no relationships between the variables that are hidden
3. That the relationship between the independent variable and dependent variable is linear — as in the best fit along the data points is a straight line and not a curved one

### Multiple linear regression analysis

As the name suggests, multiple linear regression is a regression equation that uses multiple independent variables to predict the outcome of the dependent variable.

It’s an extension of the simple linear regression model in that it looks at the impact of several variables against each other. However, like simple linear regression, multiple regression analysis also makes some basic assumptions.

For example, it assumes:

• There is a linear relationship between the dependent and independent variables (it creates a straight line and not a curve)
• The independent variables aren’t highly correlated in their own right

An example of multiple linear regression would be how the market impacts the share price of a company. In this example, the linear equation sets the share price as the dependent variable.

Now, there are several independent variables that can affect the price — sales figures, brand reputation, the economic climate. But with multiple linear regression models you can estimate how these variables will influence the share price, and to what extent.

### Multivariate linear regression

Multivariate linear regression is an extension of multiple regression with one dependent variable and multiple independent variables. Based on the number of independent variables, we try to predict the output or outcome.

For example, if an organization wants to establish or estimate how much it has to pay a new hire, it can use multivariate linear regression, taking into account several variables, e.g. education level, experience, job location, skills required, to determine their wage.

Through multivariate linear regression, you can look at relationships between variables in a holistic way and quantify the relationships between them. As you can clearly visualize those relationships, you can make adjustments to dependent and independent variables to see which conditions influence them. Overall, multivariate linear regression provides a more realistic picture than looking at a single variable.

However, multivariate techniques are complex and involve high-level mathematics that require a statistical program to analyze the data.

### Logistic regression

Logistic regression is a process of modeling the probability of a discrete outcome given an input variable. For example, the most common logistic regression models have a binary outcome.

So, what is a binary outcome? Well, it’s when there are only two possible scenarios, either the event happens (1) or it doesn’t (0). Independent variables are those variables or factors that may influence the outcome (or dependent variable).

Logistic regression is best used when you’re working with binary data, e.g. yes/no outcomes, pass/fail outcomes, and so on. In other words, if the data fits into one of two categories or is dichotomous in nature.

## Benefits of using regression analysis

Across the globe, businesses are increasingly relying on quality data and insights to drive decision-making — but to make accurate decisions, it’s important that the data collected and statistical methods used to analyze it are reliable and accurate.

Using the wrong data or the wrong assumptions can result in poor decision making, lead to missed opportunities to improve efficiency and savings, and — ultimately — damage your business long term.

There are several benefits to using regression analysis to judge how changing variables will affect your business and to ensure you focus on the right things when forecasting.

Here are just a few of those benefits:

### Make accurate predictions

Regression analysis is commonly used when forecasting and forward planning for a business. For example, when predicting sales for the year ahead, a number of different variables will come into play to determine the eventual result.

Regression analysis can help you determine which of these variables are likely to have the biggest impact based on previous events and help you make more accurate forecasts and predictions.

### Identify inefficiencies

Using a regression equation a business can identify areas for improvement when it comes to efficiency, either in terms of people, processes, or equipment.

For example, regression analysis can help a car manufacturer determine order numbers based on external factors like the economy or environment.

Using the initial regression equation, they can use it to determine how many members of staff and how much equipment they need to meet orders.

### Drive better decisions

Improving processes or business outcomes is always on the minds of owners and business leaders, but without actionable data, they’re simply relying on instinct, and this doesn’t always work out.

This is particularly true when it comes to issues of price. For example, to what extent will raising the price (and to what level) affect next quarter’s sales?

There’s no way to know this without data analysis. Regression analysis can help provide insights into the correlation between price rises and sales based on historical data.

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## A real-life example of how regression analysis is used

Marketing and advertising spending are common topics for regression analysis when trying to assess the value of ad spend and marketing spend on revenue.

A typical example is using a regression equation to assess the correlation between ad costs and conversions of new customers.

In this instance, our dependent variable (the factor we’re trying to assess the outcomes of) will be our conversions.

The independent variable (the factor we’ll change to assess how it changes the outcome) will be the daily ad spend.

The regression equation will try to determine whether an increase in ad spend has a direct correlation with the number of conversions we have.

The analysis is relatively straightforward — using historical data from an ad account, we can use daily data to judge ad spend vs conversions and how changes to the spend alter the conversions.

By assessing this data over time, we can make predictions not only on whether increasing ad spend will lead to increased conversions but also what level of spending will lead to what increase in conversions. This can help to optimize campaign spend and ensure marketing delivers good ROI.

But this is an example of a simple linear model. If you wanted to carry out a more complex regression equation, we could also factor in other independent variables such as seasonality.

By increasing the number of independent variables, we can get a better understanding of whether ad spend in isolation is resulting in an increase in conversions, or whether it’s in combination with another set of variables.

Using this predicted value of each independent variable, we can more accurately predict how spend will change the conversion rate of advertising.

## Regression analysis tools

Regression analysis is an important tool when it comes to better decision-making and improved business outcomes. And what better way to get the data you need to drive meaningful change than with Stats iQ™?

Qualtrics Stats iQ sits at the intersection of powerful statistical analysis and intuitive ease of use, empowering everyone from beginners to expert analysts to uncover meaning from data, identify hidden trends and produce predictive models. No statistical training required.

Stats iQ automatically runs the right statistical tests and visualizations and then translates the results into simple language that anyone can put into action. With prediction at your fingertips, you can isolate key experience drivers, understand what influences the business, apply the most appropriate regression methods, identify data issues, and much more.

You can also use several regression equations, including linear regression and logistic regression, to gain deeper insights into business outcomes and make more accurate, data-driven decisions.

And with Stats iQ, you don’t have to worry about the regression equation because our statistical software will run the appropriate equation for you automatically based on the variable type you want to monitor.

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