Deep Thought and the ANOVA tables: the Answer to Life, the Universe, and Everything

Comparison of Regression Analysis and Analysis of Variance

Consider the data set: "Trout.txt", it contains a pair of original variables: Pond: [1,2,3] - the particular pond the trout came from; stLength - the standard length of the trout [cm]

As an exercise into the underlying math - compare ANOVA tables from:

• one-way ANOVA of standard length (stLength) of trout as a function of the pond (Pond) used to raise them
• linear regression of length as a function of pond while treating pond as a continuous variable (I agree, this analysis makes little sense with the previous setup. Consider the numbers in "Pond" a measure of the depth of the pond in meters)
• second order polynomial regression of length as a function of pond (as a continuous variable)

Examine the ANOVA tables and understand how all terms are derived. Are any terms the same across ANOVA and 2nd order regression? Examine the formula for the second order equation, plug in values for x, and examine the resulting y values. Do you recognize these numbers? If so, understand why some ANOVA tables are identical.

Curve Fitting

Compare models with different degrees of freedom - F statistic: (SS_M for higher degree model - SS_M for lower degree model) / (MS_E for higher degree model). compare to F-Tables with numerator df = 1 and denominator df = residual df of the higher degree model