What is the statistical model that we are fitting to our biomass data in this an

Question

What is the statistical model that we are fitting to our biomass data in this analysis?

Extra credit question: What fraction of the variation in biomass can be explained by this model?

we are interested in the effects of several different pesticide treatments, fertilizers, and any potential interactions between pesticides and fertilizers, on the biomass of an annual plant We set up a 2-way fully factorial design, crossing all combinations of pesticides fertilizers The experiment has a balanced design (meaning that the same number of replicate plants was used for every pesticide/fertilizer treatment combination), and we recorded the biomass of each plant at the end of the growing season. We conducted an analysis of variance in R (with biomass weight as the response variable) and obtained the following partial ANOVA table 1. Analysis of Variance Table Response: weight Source df Sum of Mean square F value p-value squares (MS) (or, is the p- value

Explanation / Answer

Statistical model that we are fitting to our biomass data in this analysis is Two way ANOVA.

The two-way ANOVA compares the mean differences between groups that have been split on two independent variables (called factors). The primary purpose of a two-way ANOVA is to understand if there is an interaction between the two independent variables on the dependent variable.

Fraction of the variation in biomass can be explained by this model = R2

R2 = 1 - (SSE/ SST)

Where SSE = Sum of square of residuals = 134.535

SST = Total Sum of squares = 142.288 + 44.174 + 62.702 + 134.535 = 383.699

R2 = 1 - (134.535 / 383.699)

R2 = 0.64937

Hence , 64.937% of the variation in biomass can be explained by this model.

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