What Is Regression Analysis? (Plus Steps and Types)
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Regression analysis is a statistical tool used in finance, business and other fields to determine the relationship between two variables. For instance, you can use this tool to assess whether sales increase during certain seasons or if marking up the price of a product affects the number of customers who purchase it. Learning regression analysis can help you make stronger and more effective business decisions. In this article, we explain what regression analysis is and why professionals use it, discuss how regression analysis works and list the types of regression analysis.
What is regression analysis?
The answer to the question, "What is regression analysis?" is it's a set of statistical methods used to measure the correlation between a dependent variable and one or more independent variables. Regression analysis assesses how strongly related the two variables are to help you create a stronger business plan, forecast and decision. For instance, it can help you better understand the relationship between variables that impact a company sales or budgeting goals.
Professionals in many industries often use regression analysis for two main reasons:
Make variable predictions
If you want to predict a certain dependent variable, you can use a regression analysis. To do this, input the data for independent variables and review the effects it has on the dependent variable. For instance, if you want to predict your employer's sales income for the quarter (the dependent variable), you can use a regression analysis filling in the details for the number of salespeople the company has on staff, the number of days in their sales quarter and the cost of their services (independent variables) to find out what the company's sales income may look like.
Estimate a variable effect
Another reason professionals use regression analysis is to estimate how one independent variable might impact the outcome of the dependent variable. For instance, if your coworker suggests that the organisation's outdated website (independent variable) is having a direct effect on the sales of the company, you may perform a regression analysis on the hypothesis to determine if it may be accurate.
How does regression analysis work?
Regression analysis can give a value to one dependent variable and multiple independent variables and address how they interact with one another. For instance, if you have a hypothesis that a magazine sells more copies if it has an aesthetically pleasing cover, you can determine if there's a relationship between those two variables using these regression analysis steps:
1. Consider creating two sets of data
Creating two sets of data is the first step in analysing the correlation between the number of magazines sold (dependent variable) and how beautiful their cover looked (independent variable). Using the first set of data, take a random selection of magazines and note the number of copies the company has sold upon release. Then, for each of the magazines in your first data set, conduct a survey to the buyers asking them this question, "Do you like the magazine's cover?" Their responses to this question create the second data set that you can use to study the regression analysis.
2. Graph the results
For this study, since there are only two sets of data and one independent variable you're assessing, you can easily visualise the results using a graph. Label the y-axis of your graph as the dependent variable, which is the number of magazines sold, and the x-axis as your independent variable, which is the number of buyers who liked the cover. Then, combine the sets of data and translate their results into a graph using the corresponding axes.
3. Determine the correlation of the variables
Once you've graphed the variables, you may start to see some correlations in the data. For instance, you might notice an increasing slope, perhaps alluding to a positive correlation between how the buyers like the covers and the number of magazines sold, or you may notice a downwards slope, which may be telling you that a beautiful cover had a negative impact on the number of magazines sold.
It's also possible that the data may be so random that there's no correlation at all. If that's the case, consider gathering more data and see if your results change. You may also change your hypothesis altogether.
4. Draw a regression line
Once you've graphed your data, if you're having difficulty seeing a correlation, or you want to examine the correlation further, you can draw a line through the middle of your data. While you can draw this physically using a straight edge and an estimated guess, there's also a mathematical program that can help you create a more accurate graph and line through the centre.
The line you've drawn through the middle of your data is known as the regression line. This line can help you understand the negative or positive direction of the data. If you're using mathematical software, the line can provide you with an exact formula that allows you to calculate and predict different variables in the future.
Types of regression analysis
Here are a few types of regression analysis:
Simple regression analysis
You can use this method to determine the correlation between a dependent variable and a single independent variable. For instance, you can assess the relationship between how much money an individual makes and their educational level. You can also use this method to determine the correlation between the volume of crop production and the amount of rainfall in a single season.
In a simple regression analysis formula, the letter A represents the dependent variable and the value of Y when x = 0. The letter B represents the slope of the correlation and the letter U represents the residual error. The formula to predict how data may look in the future is:
Y = a + b(x) + u
Multiple regression analysis
In comparison, you can use this method to determine the correlation between a dependent variable and two or more independent variables. For instance, you might assess the relationship between how much money an individual makes and both their education and experience or the volume of crop production compared to farm location, natural disasters and rainfall. Conducting a multiple regression analysis is more complex, but it can provide you with more specific and realistic results than simple regression analysis.
The formula for multiple regression analysis is similar to the simple regression analysis, though it uses more independent variables and slopes:
Y = a + b(x1) + c(x2) + d(x3) + u
Linear regression is similar to simple regression analysis. The only difference is that it has a predictor variable and a dependent variable related to each other directly or linearly. You can determine the best fit line with linear regression and create a predictor error between the predicted value and what's actually observed. The drawback of this type of regression analysis is the vulnerability to outliers in the data. An outlier is a data point that differs significantly from other observations. Thus, companies only use linear regression for small pools of predictions or information.
Multiple linear regression
As with linear regression, multiple linear regression shows the linear or direct correlation between variables, though it involves multiple dependent variables. Although multiple linear regression may involve more than one dependent variable, it's also best used for smaller sets of data versus big data. This can prevent accuracy issues with outliers.
Ridge regression is a machine learning analysis you can utilise when the data expect a big correlation between independent variables. Usually, the least square estimates generate unbiased values, especially with multi-collinear data. If the collinear relation is very high, the analysis may generate a bias value.
Logistic regression can help you measure the relationship between independent and target variables, though it doesn't correlate between independent variables. You typically have a large data set when using logistic regression, and the dependent variable is often discrete. With logistical regression, the target variable usually only has two values, and a sigmoid curve shows the correlation.
The acronym LASSO stands for least absolute shrinkage and selection operator (LASSO). This type of linear regression uses regularisation and objective functions by prohibiting the coefficient size. Unlike ridge regression, LASSO regression allows you to get closer to zero and you can choose a set of features from your database to create LASSO regression models. Since only required features get used in LASSO regression and all other features get marked zero, you can usually avoid overfitting the model. LASSO regression also often requires standardisation.
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