This thesis studies anomalies and error estimates for the contiguous United States temperature and precipitation data from the U.S. Historical Climatology Network (Version 2) in the period of 1895-2010. Statistical inference procedures including Welch's t-test and non-parametric methods are presented in the context of changes of climate regimes and extremes. Four temperature and two precipitation regimes have been identified and used to analyze the US climate variations from 1895 to 2010. Analyzed are time series of temperature and precipitation, probability densities and statistical moments for the different climate regimes. Further, spatial distribution of the anomalies and errors are considered to determine the impact on different regions of the US from extreme temperature and precipitation. A ranking of the top ten extremist years is established. Drought impact from climate extremes is analyzed for Dust Bowl period and the warming after 1998. Main findings are the rigorous justification of significant differences of the different climate regimes and different climate extremes. The analysis also explains some physical causes of the frequency and spatial distribution of extreme climate anomalies, especially for droughts in the 1930s, 1950s, and after 1998.