  We present the magnetic field dependencies of transport properties for
$R$PtBi ($R$ = Gd, Dy, Tm, and Lu) half-Heusler compounds. Temperature and
field dependent resistivity measurements of high quality $R$PtBi single
crystals reveal an unusually large, non-saturating magnetoresistance (MR) up to
300 K under a moderate magnetic field of $H$ = 140 kOe. At 300 K, the large MR
effect decreases as the rare-earth is traversed from Gd to Lu and the magnetic
field dependence of MR shows a deviation from the conventional $H^{2}$
behavior. The Hall coefficient ($R_{H}$) for $R$ = Gd indicates a sign change
around 120 K, whereas $R_{H}$ curves for $R$ = Dy, Tm, and Lu remain positive
for all measured temperatures. At 300 K, the Hall resistivity reveals a
deviation from the linear field dependence for all compounds. Thermoelectric
power measurements on this family show strong temperature and magnetic field
dependencies which are consistent with resistivity measurements. A highly
enhanced thermoelectric power under applied magnetic field is observed as high
as $\sim$100 $\mu$V/K at 140 kOe. Analysis of the transport data in this series
reveals that the rare-earth-based Half-Husler compounds provide opportunities
to tune MR effect through lanthanide contraction and to elucidate the mechanism
of non-trivial MR.
