Regression & Best Fit Line

Scatter plot with line of best fit and R² value

Grades HS

Data Points (x, y) — up to 15

6 valid points

Line of Best Fit (Least Squares)

ŷ = 1.96x + 0.14

Slope (m)1.96

Intercept (b)0.14

R (correlation)0.9993

R² (explained var.)0.9986

Strong positive correlation(|r| > 0.7)

Step-by-step (n = 6 points)

Σx = 21Σy = 42Σxy = 181.3Σx² = 91x̄ = 3.5ȳ = 7

m = (n·Σxy − Σx·Σy) / (n·Σx² − (Σx)²)

= (6×181.3 − 21×42) / (6×91 − 21²)

b = (Σy − m·Σx) / n

Scatter Plot with Line of Best Fit

Predict: enter x → get ŷ

ŷ = 1.96×7 + 0.14= 13.86