ANOVA

Summaries

ANOVA – Analysis of Variance – a procedure to analyze (Decompose) the total variability

Total Sum of Square (SST) – sum(Y-Y_mean)²

Regression Sum of Squares (RSS) – sum (Y^ – Y_mean)²

Sum of Squared Error (SSE) – Sum(Y-Y^)²

SST = RSS + SSE

Mean Regression Sum of Squares (MSR) = RSS/k (k=DOF)

Mean Square Error (MSE) = SSE / n-k+1

Coefficient of determination = correlation² (for one variable regression) = (SST – SSE)/SST

Standard Error of Estimate (SEE)

SEE = sqrt(SSE/n-2)

F-statistic: explain the dependence of a variable on a group of variables.

F=MSR/MSE = (RSS/k)/(SSE/n-(k+1))

Same function as t-test for 1 variable. F = t²

*** Always make sure using the correct DOF