Given a large set of data measurements each containing 8 constituent values, and a "target" reading which contains 8 values as well (examples below), how do you find the measurement in the large data set that is most closely representative of the target values?
$$ Measurements \begin{array}{c|lcr} n & \text{x1} & \text{x2} & \text{x3} & \text{x4} & \text{x5} & \text{x6} & \text{x7} & \text{x8} \\ \hline 1 & 1.01 & 0.125 & 0.5114 & 0.154 & 0.814 & 0.14 & 0.84 & 0.14 \\ 2 & 1.2 & 0.241 & 0.544 & 0.254 & 0.5154 & 0.74 & 0.24 & 0.64 \\ 3 & 1.31 & 0.2 & 0.5124 & 0.754 & 0.514 & 0.94 & 0.54 & 0.574 \end{array} $$ $$ Target \begin{array}{c|lcr} & \text{x1} & \text{x2} & \text{x3} & \text{x4} & \text{x5} & \text{x6} & \text{x7} & \text{x8} \\ \hline & .514 & 0.125 & 0.714 & 0.24 & 0.014 & 0.414 & 0.184 & 0.714 \end{array} $$
My initial thought was to plot each measurement and use linear regression to determine the function which represents the 8 data values for each measurement, and then use cross correlation to determine which measurement had the closest relationship to the target, but I wasn't sure if this is the correct mathematics to be using. Any help would be appreciated!