Understanding R-Squared in Experimental Design

This technical report discusses the implications of R-squared (R2), also known as the coefficient of determination, in the context of experimental design and statistical modeling. It outlines how R2 measures the proportion of variance in the response variable that can be attributed to the input factors. The author provides examples illustrating that R2 values below 0.5 can still yield statistically significant results, as evidenced by the Framingham Heart Study. The report emphasizes the importance of factor range in determining R2 values and suggests that a narrower range can lead to lower R2, despite potentially valid models. The author also presents simulations demonstrating the effects of varying factor levels on R2 and stresses the need for sufficient experimental runs to enhance statistical power. The conclusion advises against over-reliance on R2, recommending that researchers focus on adjusted and predicted forms of the statistic while ensuring statistical significance and practical relevance of their models.