An R2 near 1 indicates that a regression line fits the data well, while an R2 close to 0 indicates a regression line does not fit the data very well.

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Using such intervals communicates the uncertainty within the model introduced by the scatter of the data instead of using the regression line that makes the relationship appear far more deterministic than it really is.

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Important cases where the computational definition of R2 can yield negative values, depending on the definition used, arise where the predictions which are being compared to the corresponding outcomes have not been derived from a model-fitting procedure using those data, and where linear regression is conducted without including an intercept.

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R2 is most often seen as a number between 0 and 1, used to describe how well a regression line fits a set of data.

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To examine this phenomenon further, I ran multiple regression analyses with the party score as the dependent variable and various institutional data points (controlling for tuition, proportion of students receiving Pell grants, overall enrollment, average SAT scores and whether schools were public or private) as the independent variables.

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He knows this because he has actual data on sales (available from Amazon) and the sales rank, and he knows how to plot a regression line in Excel.

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