Table of Contents

## What regression analysis is and how it works

Regression analysis is the process by which a data scientist assesses the relationship between two or more variables. In other words, regression analysis helps us to know how much one variable affects another variable. Regression analysis can help us predict future outcomes, like what our grades will be in college or what we will earn over time at a job. Sometimes a marketing team will want to predict whether a customer is likely to make a purchase, so that they can target the right messages and ads. Other times, researchers want to know if people in similar jobs are most likely to make similar wages. We can also use regression analysis to determine which factors (or variables) contribute most heavily to an outcome. For example, a researcher might ask how much pressure on the gas pedal is needed for the car to go 60 miles per hour. The variables are gas pedal pressure, time and speed.

In regression analysis, we have a dependent variable (our Y-axis) and an independent variable (our X-axis). The dependent variable changes as the independent variable changes (correlates). For example, we can measure the weight of a person and then see how that changes as we increase their height.

## The different types of regressions

There are several different types of regression models, depending on the goal of the analysis. For example, linear regression is used to predict an outcome based on a single independent variable. In other words, we can use this type of regression to predict how much an outcome will change as one variable changes. For example, we could predict how much a person’s salary will change as their experience increases, or how much a firm’s stock value will change as the economy improves. Multiple regression is used to predict an outcome based on two or more independent variables. In other words, we can use this type of regression to predict how much an outcome will change as one variable changes, and the other independent variable changes at the same time.

We can also combine linear regression with multiple regression. This is called schedule-based regression analysis. In this type of analysis, we include a constant and a separate term for each independent variable in the model. For example, we can estimate how much an employee’s salary will change as their experience increases by including both experience and age as independent variables in our model. This approach allows us to predict how much a different outcome will change as one independent variable changes and other independent variables change at the same time. For example, we could predict how much a person’s salary will change as their experience increases and the growth rate of the economy improves at the same time.

## The benefits of using regression analysis in business

Businesses use regression analysis to look at their performance and determine what drives their success. For example, a market research team might want to know if product quality is more important than product design when it comes to selling a new product. A manufacturing team might want to find out if the plant manager or the employees drive greater productivity levels. Businesses use regression analysis to determine which factors are most important when it comes to improving their performance and creating more value for their customers.

Regression analysis helps businesses predict the future, so they can be successful. A well-designed regression model will predict future outcomes based on past data. By knowing what has happened in the past, businesses can create a vision for the future and then take specific actions to make that vision a reality.

Regression analysis can also be used to break down performance management into specific areas. By using regression analysis, managers can look at different areas of their performance and make changes to improve them. A process leader might show that the number of defects in the manufacturing line can be lowered by increasing the number of employees working on the line to improve efficiency. In another example, a sales manager might show that advertising has an effect on future sales levels and that better advertising leads to more sales.

## How to choose the right regression for your data set

We need to have confidence that the regression model we choose is correct. To do this, a data scientist needs to know three things: what the model is, what type of data set it is on and whether it is a linear or non-linear model. For example, let’s say we had the results of this survey:

How many of the following food do you like?

One Two Three Four Five Don’t Know/No Answer

Chicken 5 12 9 13 2 0

Beef 37 6 23 15 3 0

For this survey, we could create a scatter plot of the data and come up with a line of best fit (shown on the graph below). Let’s say that we need to use this model to predict what people like in chicken. We would then look at their responses to beef.

Looking at the data we can see that any person who chose one for chicken, we could predict that they would choose two for beef.

But if we look at people who said “Three” for chicken, then we would need to predict that they would choose nine for beef.

## Tips for interpreting regression results correctly

One of the first things we need to do when interpreting regression results is to determine whether our model is linear or non-linear. If we have a non-linear model, it may be more difficult to analyze the results and make a clear determination. If the variables in our model are not independent of each other, we may also want to control for this interaction. For example, if we’re working with customer satisfaction and customer satisfaction is related to customer loyalty, it may be best to remove the interaction between them so that we can analyze both of them independently.

In our example, we’ve got a model that is a linear regression. We can tell this by checking to see if we are using the fit and y-intercept in the formula for our least squares estimate, as shown below:

Just as with any calculation, it’s important to interpret what you’re doing with your results. When interpreting your results, it’s important to consider the variables that you have entered into your model. A common problem with interpreting results is to forget that you have one or more variables in your model. This happens when you’ve entered the whole population into your model, instead of subgroups of that population.

When we perform a linear regression, it is important to remember that the relationship between our independent and dependent variables isn’t really a straight line. Rather, as another function of the independent variable lies between our correlation lines. The correlation between two variables is an indicator of their association but can be inaccurate due to other factors.