“…Streamflow reconstructions have traditionally been performed using multiple linear regression models, or modifications thereof, and the predictors used in these regression models are typically tree ring chronologies or their principal components. The regression models used in these studies include stepwise multiple linear regression (Barnett et al, 2010;Earle, 1993;Watson et al, 2009;Woodhouse, 2001;Woodhouse & Lukas, 2006); standard multiple linear regression or canonical regression, often in the form of principal components regression (PCR) (Barnett et al, 2010;Cook & Jacoby, 1983;Cook et al, 2013;Day & Sandifer, 2015;Gedalof et al, 2004;Ma et al, 2014;Maxwell et al, 2011;Meko & Graybill, 1995;Meko et al, 2001;Stockton & Jacoby, 1976;Timilsena et al, 2007;Watson et al, 2009); or hierarchical Bayesian regression (Bracken et al, 2016;Devineni et al, 2013;Rao et al, 2018). With the exception of Devineni et al (2013), Rao et al (2018), and Bracken et al (2016), the reconstructions in these studies are done using variations of ordinary least squares (OLS) regression for reconstructing flow at each single-site individually (point-by-point regression) rather than multiple sites simultaneously and accounting for spatial correlation across the sites by explicitly estimating the inherent correlation structure either physically or statistically.…”