A regression analysis provides us with the ability to mathematically model the data we collect in lab. In turn, this allows us to make predictions about the results of additional experiments. Blindly accepting the results of such an analysis without carefully examining the data and the model, however, can lead to serious errors.
By now, you know that Data Set 1 can be explained adequately using the model
Y = 0.500*X + 3.00
although there appears to be substantial uncertainty in the values for X, for Y, or for both X and Y. The data in Data Set 2 are nonlinear and adequately modeled using the following 2nd-order polynomial equation
Y = -0.1276*X2 + 2.7808*X - 5.9957
with an R2 of 1. With the exception of one data point, which appears to have an unknown source of determinate error, the data in Data Set 3 are linear. Removing this data point (X = 13.00, Y = 12.74) and fitting a linear trendline gives the following model equation
Y = 0.3454*X + 4.0056
with an R2 of 1.
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