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Regression analysis is a powerful statistical method that allows you to examine the relationship between two or more variables of interest.
While there are many types of regression analysis, at their core they all examine the influence of one or more independent variables on a dependent variable.
Regression analysis is one of the most important and widely used statistical techniques out there. But for many people, it remains kind of confusing and mysterious.
Well, we’re here to lift the veil on regression analysis and explain exactly what it does in simple terms! Read on for my beginner’s guide to understanding regression analysis.
What is Regression Analysis?
Regression analysis is a statistical method used to estimate the relationship between a dependent variable and one or more independent variables.
In other words, it helps us understand how the value of the dependent variable changes when we change the value of the independent variables. The aim is to determine the “causal effect” of the independent variables on the dependent variable.
Some key terms

Dependent variable The variable we are trying to explain or predict Also called the “outcome variable”

Independent variables The variables we think have an effect on the dependent variable Also called “predictor variables” or “explanatory variables”

Regression coefficient: The metrics that quantify the effect each independent variable has on the dependent variable.
The regression coefficients tell us the size and direction (positive or negative) of the effect.
Why Use Regression Analysis?
There are a few key reasons regression analysis is so popular:

Determine the strength of relationships between variables. The regression coefficients show us how strongly each independent variable influences the dependent variable.

Make predictions. We can use the regression equation to predict values of the dependent variable given values of the independent variables.

Identify the most important independent variables. The size of the regression coefficients tells us which independent variables have the biggest effect.

Assess impacts of changes. By changing the values for the independent variables in our equation, we can estimate the impact on the dependent variable.
Types of Regression Analysis
The two most common types of regression analysis are:

Simple linear regression: Estimates the relationship between a single independent variable and the dependent variable.

Multiple linear regression: Estimates the relationship between multiple independent variables and the dependent variable.
More advanced regression techniques include logistic regression and nonlinear regression. But linear regression models are by far the most common, especially for beginners.
How Does Linear Regression Analysis Work?
Linear regression uses a straight line equation to estimate the relationship between the independent and dependent variables.
The linear regression equation takes the form:
y = a + b1*x1 + b2*x2 + ... + bn*xn
Where:
 y = Dependent variable
 a = Intercept
 b1 to bn = Regression coefficients
 x1 to xn = Independent variables
To perform a linear regression, statistics software calculates the values for the intercept (a) and regression coefficients (b1, b2, etc.) that produce the “best fit” line through the data points.
The most common method is ordinary least squares, which minimizes the sum of the squared residuals (aka the differences between the actual data values and the values predicted by the line).
Once we’ve fit the regression line, we can use the equation to make predictions! We just plug in the values for the independent variables and calculate the estimate for the dependent variable.
Interpreting Regression Coefficients
The key results from a regression analysis are the regression coefficients for each independent variable. These tell us:

Direction of the effect: A positive coefficient means the dependent variable increases when that independent variable increases. A negative coefficient means the dependent variable decreases when that independent variable increases.

Size of the effect: The actual value of the coefficients indicates the size of the effect each independent variable has on the dependent variable. Larger coefficients mean the independent variable has a larger impact.

Statistical significance: Does the independent variable have a real, statistically significant impact on the dependent variable? Or is the effect just random chance? Pvalues help assess the significance. Lower pvalues indicate higher significance.
RealWorld Regression Analysis Examples
Here are some examples of how regression analysis is used by businesses, researchers, and policy analysts:

Estimate how sales are impacted by advertising spend, price changes, promotions, etc.

Forecast stock returns based on financial ratios like P/E, debt ratios, dividend yield, etc.

Analyze how different factors contribute to employee turnover.

Estimate the effect of class size on student test scores.

Predict the impact of fiscal policy changes on economic growth.
As you can see, regression analysis is applied in tons of different contexts to estimate the causal effect of some factors on key outcomes of interest. It provides critical insights for decision making.
Limitations of Regression Analysis
While an invaluable statistical tool, regression analysis does have some important limitations to be aware of:

Correlation doesn’t equal causation. Regression analysis estimates relationships between variables, but does not definitively prove causation. There may be other confounding factors affecting your dependent variable.

Outliers can skew results. Highly influential outliers can distort the best fit regression line. Always plot your data visually to check for outliers.

Assumptions may be violated. Linear regression analysis relies on certain assumptions that must be validated, such as linearity, normality, homoscedasticity, and lack of multicollinearity. Violating these assumptions can invalidate results.
So regression analysis must always be applied thoughtfully, with careful consideration of the methodology and business context. The estimates provide helpful guidance, but human judgement is still critical.
Let’s Break It Down…
Hopefully this breakdown clarified what regression analysis is all about! To recap:

Regression analysis estimates the relationships between a dependent variable and one or more independent variables.

The most common types are simple linear and multiple linear regression.

It provides the direction and size of effects, helps make predictions, and identifies the most influential factors.

Regression coefficients and pvalues are key outputs to interpret.

Limitations include lack of definitive causation proof, outliers, and assumptions that may be violated.
Used correctly, regression analysis is an invaluable tool for quantitative analysis and datadriven decision making. And now you know the basics to understand the regression results you encounter day to day!
What is regression analysis and what does it mean to perform a regression?
Regression analysis is a reliable method of identifying which variables have impact on a topic of interest. The process of performing a regression allows you to confidently determine which factors matter most, which factors can be ignored, and how these factors influence each other.
In order to understand regression analysis fully, it’s essential to comprehend the following terms:
 Dependent Variable: This is the main factor that you’re trying to understand or predict.
 Independent Variables: These are the factors that you hypothesize have an impact on your dependent variable.
In our application training example above, attendees’ satisfaction with the event is our dependent variable. The topics covered, length of sessions, food provided, and the cost of a ticket are our independent variables.
Regression analysis provides detailed insight that can be applied to further improve products and services.
Here at Alchemer, we offer handson application training events during which customers learn how to become super users of our software.
In order to understand the value being delivered at these training events, we distribute followup surveys to attendees with the goals of learning what they enjoyed, what they didn’t, and what we can improve on for future sessions.
The data collected from these feedback surveys allows us to measure the levels of satisfaction that our attendees associate with our events, and what variables influence those levels of satisfaction.
Could it be the topics covered in the individual sessions of the event? The length of the sessions? The food or catering services provided? The cost to attend? Any of these variables have the potential to impact an attendee’s level of satisfaction.
By performing a regression analysis on this survey data, we can determine whether or not these variables have impacted overall attendee satisfaction, and if so, to what extent.
This information then informs us about which elements of the sessions are being well received, and where we need to focus attention so that attendees are more satisfied in the future.
Regression analysis
What is regression analysis?
Regression analysis is a statistical technique used for studying the relationship between two or more variables of interest. It has multiple variations depending on its intended use and how many variables are present, and it can help a company in strategic decisionmaking.
What are some key aspects of regression analysis?
Some key aspects of regression analysis include: a. Dependent variable: The variable of interest, also known as the response or target variable, which is being predicted or explained by the independent variables. b.
Why do companies use regression analysis?
Companies often use regression analysis for the following reasons: An organization can use regression analysis to predict a specific dependent variable. To make variable predictions, use data for the independent variables and review its effects on the dependent variable.
How do you perform a regression analysis?
You can perform regression and determine the factors that have the most impact, the ones to overlook and how they influence each another. It’s essential to differentiate between the dependent and independent variables, which you hypothesize to impact the dependent variable.