1 of 7

Simple Linear Regression Analysis

Relationship between Height (X) and Weight (Y)

2 of 7

3 of 7

Step 1: Data Summary

  • Given Data:

​

  • Mean of X (Height): x̄ = 142.0
  • Mean of Y (Weight): ȳ = 60.9
  • Σ(x - x̄)² = 1,603,652
  • Σ(x - x̄)(y - ȳ) = 688,697

4 of 7

Step 2: Calculate Slope (b₁)

  • Formula: b₁ = Σ(x - x̄)(y - ȳ) / Σ(x - x̄)²
  • b₁ = 688,697 / 1,603,652
  • b₁ ≈ 0.4

5 of 7

Step 3: Calculate Intercept (b₀)

  • Formula: ȳ = b₀ + b₁ x̄
  • 60.9 = b₀ + 0.4(142)
  • b₀ = 60.9 - 56.8
  • b₀ = 4.1

6 of 7

Step 4: Regression Equation

  • ŷ = b₀ + b₁x
  • ŷ = 4 + 0.4x
  • This means for every 1 unit increase in height, the weight increases by 0.4 kg.

7 of 7

Step 5: Interpretation

  • • b₁ = 0.4: For each 1 unit increase in height, weight ↑ by 0.4 kg.

​

  • • b₀ = 4: The intercept represents the estimated weight when height is 0.
  • • The regression line shows a positive linear relationship between height and weight.