Statistics Formula
- Mean(x')=X'=∑x/n
- Median M=(n+1)/2 n is even
then M = ((n/2)term+((n/2)+1)term)/2
- Variance = σ2=∑(x'−x)²/n
- Standard Deviation = S=σ
- Mode = The mode in a dataset is the value that is most frequent in the dataset.
Correlation
- Pearson product-moment correlation = r = Σ (xy) / sqrt [ ( Σ x² ) * ( Σ y² ) ]
- Linear correlation (sample data) = r = [ 1 / (n - 1) ] * Σ { [ (xi - x) / sx ] * [ (yi - y) / sy ] }
- Linear correlation (population data) = ρ = [ 1 / N ] * Σ { [ (Xi - μX) / σx ] * [ (Yi - μY) / σy ] }
Simple Linear Regression
- Simple linear regression line: ŷ = b0 + b1x
- Regression coefficient = b1 = Σ [ (xi - x) (yi - y) ] / Σ [ (xi - x)²]
- Regression slope intercept = b0 = y - b1 * x
- Regression coefficient = b1 = r * (sy / sx)
- Standard error of regression slope = sb1 = sqrt [ Σ(yi - ŷi)² / (n - 2) ] / sqrt [ Σ(xi - x)² ]
