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We present a sample of 824 solar and late-type stars with X-ray luminosities and rotation periods. This is used to study the relationship between rotation and stellar activity and derive a new estimate of the convective turnover time. From an unbiased subset of this sample the power-law slope of the unsaturated regime, LX/Lbol∝Roβ, is fit as β = −2.70 ± 0.13. This is inconsistent with the canonical β = −2 slope to a confidence of 5σ, and argues for an additional term in the dynamo number equation. From a simple scaling analysis this implies ΔΩ/Ω∝Ω0.7, i.e., the differential rotation of solar-type stars gradually declines as they spin down. Supersaturation is observed for the fastest rotators in our sample and its parametric dependencies are explored. Significant correlations are found with both the corotation radius and the excess polar updraft, the latter theory providing a stronger dependence and being supported by other observations. We estimate mass-dependent empirical thresholds for saturation and supersaturation and map out three regimes of coronal emission. Late F-type stars are shown never to pass through the saturated regime, passing straight from supersaturated to unsaturated X-ray emission. The theoretical threshold for coronal stripping is shown to be significantly different from the empirical saturation threshold (Ro < 0.13), suggesting it is not responsible. Instead we suggest that a different dynamo configuration is at work in stars with saturated coronal emission. This is supported by a correlation between the empirical saturation threshold and the time when stars transition between convective and interface sequences in rotational spin-down models.