Correlation vs Regression
May 25, 2023 2023-05-25 13:49Correlation vs Regression
Correlation vs Regression
Correlation
Correlation measures the strength and direction of the linear relationship between two variables. It quantifies how closely the values of one variable are associated with the values of another variable.
For example, let’s consider a dataset that includes the number of hours studied (X) and the corresponding exam scores (Y) of a group of students. By calculating the correlation coefficient, we can determine the strength and direction of the relationship between hours studied and exam scores. A correlation coefficient of +0.8 indicates a strong positive correlation, meaning that as the number of hours studied increases, the exam scores tend to increase as well. Conversely, a correlation coefficient of -0.6 indicates a moderate negative correlation, suggesting that as the number of hours studied increases, the exam scores tend to decrease.
Correlation does not imply causation, meaning that even though two variables may be strongly correlated, it does not necessarily mean that one variable is causing the changes in the other. It simply measures the degree of association between the variables.
Regression
Regression, on the other hand, helps us understand the relationship between variables by estimating the value of one variable (dependent variable) based on the values of one or more other variables (independent variables). It allows us to make predictions or model the relationship between variables.
Building upon the previous example, regression analysis can be used to create a predictive model to
estimate the exam score (dependent variable) based on the number of hours studied (independent variable). By fitting a regression line or curve to the data, we can make predictions about the exam
scores for different amounts of study time.
Differences between Correlation and Regression
Purpose
Correlation is used to measure the strength and direction of the relationship between two
variables. It provides a numerical value that represents the degree of association.
Regression is used to model and predict the value of one variable (dependent variable) based on the values of one or more other variables (independent variables). It aims to understand the relationship and estimate the effect of independent variables on the dependent variable.
Nature of Variables
Correlation can be calculated for any two variables, regardless of their roles (e.g., both variables can be considered independent or dependent).
Regression explicitly differentiates between the independent variable(s) (predictors) and the dependent variable (the one being predicted).
Analysis
Correlation measures the degree of association between variables using correlation coefficients (such as Pearson;s correlation coefficient or Spearman’s rank correlation coefficient).
Regression involves fitting a mathematical model (such as linear regression, polynomial regression, or multiple regression) to the data and estimating coefficients that represent the relationship between the variables.
Predictions
Correlation does not involve making predictions. It focuses solely on quantifying the relationship between variables.
Regression allows for making predictions by utilizing the estimated model and coefficients
to estimate the value of the dependent variable based on given values of the independent variable(s).
Causality
Correlation does not imply causality. A strong correlation between variables does not
necessarily mean that one variable causes changes in the other. It only indicates a statistical association.
Regression does not establish causality, it can provide insights into the relationship between variables and identify variables that have a significant impact on the dependent variable. However, additional analysis and experimentation are required to establish causality.
Statistical Testing
Correlation measures the degree of association between variables and can indicate whether the association is statistically significant. However, it does not provide formal hypothesis testing.
Regression analysis allows for hypothesis testing to determine the statistical significance of the relationship between variables. It provides statistical measures like p-values and confidence intervals to assess the significance of the coefficients and the overall model fit.
