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.

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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, σX = 1.6, MeanY = 25, σY = 1.7, r = 0.95

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

• 𝑦 − Mean𝑦 = 𝑟 × 𝜎_𝑦/𝜎_𝑥 × (𝑥 − Mean𝑥)
• 𝑦 − 25 = 0.95 × 1.7/1.6 × (𝑥−30)
• 𝑦 = 1.009375𝑥 − 5.28125
• 𝑦 = 1.01𝑥−5.28

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

• 𝑥 − Mean𝑥 = 𝑟 × 𝜎_𝑥/𝜎_𝑦 × (𝑦 − Mean𝑦)
• 𝑥 − 30 = 0.95 × 1.6/1.7 × (𝑦−25)
• 𝑥 = 0.89𝑦 + 7.65

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IGNOU Solved Assignments: Q7 - MAPC MPC006 Statistics in Psychology - MPC006/ASST/TMA/2014-15