Linear Regression (slope, intercept, R^2)
Least-squares fitted line (slope, intercept), R^2, residual standard error, the slope t-test with a two-tailed p-value, and an optional prediction at a given x, for paired x / y series. Per OpenIntro Statistics Ch. 8.
Formula and source
Least squares: slope = sum((x - xbar)(y - ybar)) / sum((x - xbar)^2); intercept = ybar - slope * xbar. R^2 = r^2. Residual sum of squares RSS = Syy - slope * Sxy; residual standard error = sqrt(RSS / (n - 2)). Slope t-test for slope = 0: t = slope / (RSE / sqrt(Sxx)) on n - 2 df, two-tailed p = 2 * (1 - tcdf(|t|, n - 2)). Prediction y-hat = intercept + slope * x.
OpenIntro Statistics 4th ed. Chapter 8 (introduction to linear regression) by name; the Student-t CDF via the regularized incomplete beta function per Numerical Recipes in C 2nd ed. ยง6.4.
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