differences between correlation and regression

Key similarities 

  • Both quantify the direction and strength of the relationship between two numeric variables.
  • When the correlation (r) is negative, the regression slope (b) will be negative. 
  • When the correlation is positive, the regression slope will be positive. 
  • The correlation squared (r2 or R2) has special meaning in simple linear regression. It represents the proportion of variation in Y explained by X.

Key differences 

  • Regression attempts to establish how X causes Y to change and the results of the analysis will change if X and Y are swapped. With correlation, the X and Y variables are interchangeable.
  • Regression assumes X is fixed with no error, such as a dose amount or temperature setting. With correlation, X and Y are typically both random variables*, such as height and weight or blood pressure and heart rate. 
  • Correlation is a single statistic, whereas regression produces an entire equation.

Similarities:

  • Both quantify the direction of a relationship between two variables.
  • Both quantify the strength of a relationship between two variables.

Differences:

  • Regression is able to show a cause-and-effect relationship between two variables. Correlation does not do this.
  • Regression is able to use an equation to predict the value of one variable, based on the value of another variable. Correlation does not does this.
  • Regression uses an equation to quantify the relationship between two variables. Correlation uses a single number.

References

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