통계의 간소화: 상관분석과 회귀분석의 사용 방법과 시기

Statistical tools provide a framework for accurately interpreting data. That is why statistical tools are an essential part of research. The two basic statistical operations are correlation analysis and regression analysis, which are commonly used to explore relationships between variables.

However, these concepts are often confused because of their similarity. While correlation analysis measures the strength and direction of a relationship, regression analysis goes one step further and models the relationship and predicts the outcome. Both are very useful for early-career researchers, scientists, postdocs, and academics to effectively analyze data . In this article, we will take a closer look at correlation and regression analysis and find out when to use which method.

What is correlation analysis?

Correlation analysis is a statistical measurement that refers to the process of establishing a relationship between two variables. It is the most common method of measuring the association between variables.

In correlation analysis, correlation refers to how one variable changes in response to another variable. In other words, it indicates whether the two variables increase together, decrease together, or have no relationship between them. Correlation is measured by the correlation coefficient (r), which ranges from -1 to 1.

• The closer the r value is to 0, the weaker or insignificant the relationship between the variables. An example of this would be the relationship between study time and test scores.
• An r value of 1 indicates a perfect positive correlation, meaning that when one variable increases, the other variable also increases (they move in the same direction). This is the case with temperatures in Celsius and Fahrenheit. As the Celsius temperature increases, the corresponding Fahrenheit temperature also increases.
• An r value of -1 indicates a perfect negative correlation, meaning that when one variable decreases, the other increases (the two variables move in opposite directions). You can observe this in the time it takes to reach a destination and the speed at which you move. The faster the speed, the shorter the travel time.

Correlation analysis provides insight into patterns without predicting or assuming causality. Causality here means a relationship in which changes in the independent variable directly cause changes in the dependent variable. Here are some types of correlation analysis:

1. Pearson correlation analysis:

Determines how closely two continuous variables are linearly related. Applies most accurately when the data is normally distributed.

2. Spearman correlation analysis:

Measures the relationship between ranked data. It should be used when the data does not meet the requirements of Pearson correlation analysis. This is the case when the relationship between the data is not linear but follows a consistent direction.

3. Kendall correlation analysis:

Examines the relationship between two variables by their ranks. Often used when working with small data sets or ordinal data.

It is important to note that correlation analysis only estimates the association between variables and does not indicate causality. This is why regression analysis is necessary.

What is regression analysis?

Regression analysis is a statistical method that models the relationship between one dependent variable (outcome) and one or more independent variables (predictor variables). Regression analysis allows researchers to predict the value of one variable based on the value of another variable. This helps identify factors that affect the dependent variable and estimate trends.

Regression analysis finds the best line to predict y from x. There are two ways to calculate the regression coefficients. One is to calculate y based on x(b _yx ) and the other is to calculate x based on y(b _xy ). If one coefficient is greater than 1, the other is less than 1. Their geometric mean is equal to the correlation coefficient (r), but their arithmetic mean can be greater than or equal to the r value. Here are some types of regression analysis.

1. Linear regression:

Models the relationship between a dependent variable and one independent variable using a straight line. Used when the relationship is linear. Since all real-world regression models involve multiple predictors, the term ‘linear regression’ often refers to ‘multivariate linear regression’. An example of this is when predicting a person’s weight based on height, using a straight line relationship that is not perfectly true in real-world situations.

2. Nonlinear regression:

Models relationships where the dependent variable does not change linearly with the independent variable. Use when data contains exponential, logarithmic, or other nonlinear trends. For example, you can apply this method to model the acceleration of a chemical reaction due to an increase in temperature.

3. Multiple regression:

Includes two or more independent variables that predict the dependent variable. Multiple regression is useful for investigating more complex relationships. A good example of multiple regression is predicting the value of a property based on factors such as its size, location, and age.

Regression analysis helps us predict the value of a dependent variable based on independent variables. However, it is important to understand how regression analysis differs from correlation analysis, which measures the strength and direction of the relationship between two variables. Let’s now look at the main differences between correlation analysis and regression analysis.

Now that we have a clear understanding of what types of correlation and regression analysis there are and what their basic differences are, the next step is to figure out which one to use and when!

When to use correlation analysis and when to use regression analysis

Let’s take a look at some practical examples to see how to use it.

1. Checking the relationship between height and weight in a population: In this case, you need to use correlation analysis to calculate the correlation between the two variables. A positive correlation indicates that as height increases, weight tends to increase. However, this is not a predictable situation.
2. Checking the relationship between temperature and ice cream sales: In this case, you should use correlation analysis. Although a positive correlation suggests that ice cream sales tend to increase as temperature increases, you cannot accurately predict sales with this scenario.
3. Determine Sales and Advertising Budget: To predict future sales based on advertising budgets, you should use regression analysis. Analyze past data to model how changes in advertising budgets affect sales figures.
4. Determining Employee Performance and Training Hours: To assess how training hours affect the outcome of employee performance for targeted decision making, regression analysis should be used. This will help you predict employee performance based on the length of training hours.

Common pitfalls and misconceptions

Let’s look at some common mistakes made in correlation and regression analysis, and learn how to avoid them with some examples.

A common mistake is to assume that correlation means causation. A strong correlation between two variables may exist, but that does not necessarily mean that one variable causes the other. For example, a correlation may exist between coffee consumption and productivity, but that does not necessarily mean that coffee consumption increases productivity. In this case, the increase in productivity may be the result of changes in other variables, such as the time of day. For example, people often drink more coffee during work hours, when they need to be productive even if they do not drink coffee.

Another common mistake is to incorrectly apply linear regression models to nonlinear relationships. If the relationship is nonlinear (e.g., exponential or logarithmic), using linear models can lead to inaccurate predictions. For example, consider predicting the growth of a bacterial population over time. The growth of bacteria often follows an exponential growth pattern, doubling at regular intervals. To model this accurately, you need to use nonlinear regression that is appropriate for the nature of your data.

Choosing the right method is important to properly evaluate the characteristics of your data and ensure valid results. Once you know which statistical measures to apply, you can choose one of the various platforms to perform your statistical analysis.

Choosing the right tools for accurate analysis

In order to obtain reliable results from your research, it is important to choose the right applications and tools. You can use basic software such as Microsoft Excel, or you can choose to use advanced applications such as PSPP , Matlab , and GraphPad Prism . These applications have more powerful data analysis capabilities and are suitable for working with large-scale data sets.

Do you need expert guidance on choosing the right statistical method for your research? Enago’s research paper statistical analysis service provides expert help and support to researchers who want to improve the quality of their analysis and ensure the accuracy of their research results.

Researchers can draw accurate conclusions and increase the reliability of predictions by selecting appropriate statistical tools. If you have experience using statistical tools or have questions about using correlation and regression analysis, please share them.