Fitting a line is easy; grading it is the skill. The grade is $R^2 = r^2$ — R-squared equals r squared — the coefficient of determination, where $r$ is the correlation and $R^2$ is the SHARE of the variation in $y$ that the line accounts for. Both are naked numbers; $R^2$ lives between 0 and 1 and is usually quoted as a percentage.

Now the surprise this lesson is built on. A correlation of $r = 0.8$ sounds like a strong 80%. It is not: $R^2 = 0.64$, so the line explains 64% of the variation and 36% is still doing whatever it likes. Squaring a number below one always shrinks it, and the shrink is the honest part — it is why researchers quote $R^2$ and salespeople quote $r$.

Two more graders finish the chapter. Percent error, $PE = \dfrac{|x_{\text{meas}} - x_{\text{acc}}|}{x_{\text{acc}}}$, compares ONE reading with a known true value: $x_{\text{meas}}$ is what the instrument said, $x_{\text{acc}}$ is the accepted value, and the accepted value goes on the bottom every time — it is the thing you claim to know. And the weighted mean, $\bar{x} = \dfrac{n_1\bar{x}_1 + n_2\bar{x}_2}{n_1 + n_2}$, combines two group averages: here subscript 1 means group one and subscript 2 means group two, $n$ is a group's SIZE and $\bar{x}$ with a subscript is that group's mean. Averaging the two averages is the classic wound — it hands a section of 10 the same vote as a section of 90.