# 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, ΟX = 1.6, MeanY = 25, ΟY = 1.7, r = 0.95

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

• π¦ − Meanπ¦ = π × π_π¦/π_π₯ × (π₯ − Meanπ₯)
• π¦ − 25 = 0.95 × 1.7/1.6 × (π₯−30)
• π¦ = 1.009375π₯ − 5.28125
• π¦ = 1.01π₯−5.28

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

• π₯ − Meanπ₯ = π × π_π₯/π_π¦ × (π¦ − Meanπ¦)
• π₯ − 30 = 0.95 × 1.6/1.7 × (π¦−25)
• π₯ = 0.89π¦ + 7.65

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