Linear Regression - Derivation of Equations - Numerical

The numerical below is an example of the process of deriving the Linear Regression Equations. This approach can be extended to similar cases by replacing the data.

With the help of following data, determine both the regression equations: Psychology (X): Mean= 30, Standard deviation=1.6 Sociology (Y): Mean= 25, Standard deviation= 1.7 Coefficient of correlation = 0.95

How to calculate the Linear Regression Equations?

    Step 1: Organize Data - Define the variables

  • Given: MeanX = 30, ΟƒX = 1.6, MeanY = 25, ΟƒY = 1.7, r = 0.95

    Step 2: Derive the line of regression of y on x

  • 𝑦 − Mean𝑦 = π‘Ÿ × πœŽ_𝑦/𝜎_π‘₯ × (π‘₯ − Meanπ‘₯)
  • 𝑦 − 25 = 0.95 × 1.7/1.6 × (π‘₯−30)
  • 𝑦 = 1.009375π‘₯ − 5.28125
  • 𝑦 = 1.01π‘₯−5.28

    Step 3: Derive the line of regression of x on y

  • π‘₯ − Meanπ‘₯ = π‘Ÿ × πœŽ_π‘₯/𝜎_𝑦 × (𝑦 − Mean𝑦)
  • π‘₯ − 30 = 0.95 × 1.6/1.7 × (𝑦−25)
  • π‘₯ = 0.89𝑦 + 7.65

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