Understanding Correlation, R-Square, and Linear Regression in Financial Analysis

Understanding Correlation, R-Square, and Linear Regression in Financial Analysis

Continuing our review of meta quiz topics, after discussing coefficient of determination and its relationships, let's explore the connection between correlation and R-square.

In simple linear regression, where we have a function like Y = aX + b with one independent variable X, we can examine the relationship between X and Y in two ways:

1. Through Correlation:

   • Calculate using: Correlation = Covariance(X,Y) / √(Variance(X) × Variance(Y))
   • Correlation ranges between -1 and +1

2. Through R-square:

   • For simple linear regression with X and Y
   • Take the square root of R-square to get the absolute value of correlation
   • Use the slope coefficient (a) to determine if correlation is positive or negative

For example: If correlation is 0.8, then R-square = 0.8² = 0.64 This means X explains 64% of Y's variance

To find correlation from R-square:

1. Take square root of R-square (√0.64 = 0.8)
2. Look at slope coefficient (a):
   • If a is positive: correlation = +0.8
   • If a is negative: correlation = -0.8

This process helps determine both the strength and direction of the relationship between variables.