PPA 207 – Quantitative Methods in PPA
Statistical Calculations to Know

Meeting One:

Mean = (∑ x_i ) / N

x = observation

N = total number observations

Weighted Mean = (∑ w_i x_i ) / (∑ w_i)

w = weight applied to observation

Standard deviation = square root [ (∑ (x_i – mean x)²) / n-1 ]

Skewness (measure of whether peak is centered in middle

of distribution)

+ value indicates peak is off to left

- indicates that off to right

significant (not a normal distribution) if

(skewness / std. deviation) > 2

Meeting Two:

Chi-square = χ² = ∑ [ (observed_i – expected_i)² / expected_i ]

 Meeting Three:

PRE formula

(errors without knowledge independent variable – errors with knowledge) / errors without knowledge

Meeting Four:

e_i = Y_i – (a + bX_i)

b = [Σ (X_i – mean X)(Y_i – mean Y)] / Σ (X_i – mean X)²

a = mean Y – (b * mean X)

Meeting Five:

R² = ESS / TSS = Explained behavior of Y / variation in Y

ESS = Σ (Y_i hat – mean Y_i)²

TSS = Σ (Y_i - mean Y_i)²

TSS = ESS + RSS

RSS = Σ e_i²

H_o: β = -0.30, H₁: β ≠ -0.30

t statistic = (b – hypothesized b) / standard error of b

Elasticity = % change in Y / % change in X = regression b * (mean X / mean Y)