Question

In a linear regression setting with \(Y\) and \((X_1, X_2, X_3,...., X_n)\). The correlation coefficient between \(X_2\) and \(Y\) was found to be \(-0.90\).

  1. Relationship between \(X_2\) and \(Y\) is strong
  2. Relationship between \(X_2\) and \(Y\) is weak
  3. Relationship between \(X_2\) and \(Y\) is neutral

Answer

Relationship between \(X_2\) and \(Y\) is strong.

The correlation coefficient(\(\rho\)) ranges from \([-1,1]\). As the value of \(\rho\) approaches 1, the strength of positive relationship (between \(X\) and \(Y\)) increases whereas if \(\rho\) approaches -1, the strength of negtaive relationship increases.

If \(\rho\) is equal to zero, then \(X\) and \(Y\) are said to be uncorrelated. This also implies that \(X\) and \(Y\) are independent, although vice versa is not true, as \(\rho\) measures only the strength of linear relationship.

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