Linear Regression - Derivation of Equations - Numerical

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