![]() ![]() At the low end, the curve “doubles back” on itself the responses for the blank look to be slightly higher than the responses for the standard at x = 2. When a quadratic model is fitted to data set 3, R 2 soars to 0.9999 (see Figure 2) and analyst 3 now “wins.” Although the model choice looks excellent and the replicates are very tight, further investigation of the plot reveals a disturbing feature. R 2 has not provided enough information for making a sound decision. ![]() The plots show that the low R 2 for set 3 is likely due to an easy-to-fix problem (i.e., the wrong model was used). Figure 1 shows the results for the three data sets. Indeed, an examination of the plots themselves illustrates this fact. However, for all its popularity, this statistic is not a sufficient indicator of the adequacy of a given model or fitting technique. If the sole criterion for the decision is the value of R 2, then the second data set should be used. ![]() Figure 1 - Three separate data sets, each fitted with a straight line, and the corresponding values of R 2 a) R 2 = 0.7273, b) R 2 = 0.9143, c) R 2 = 0.7268. ![]()
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