data={{0.707,1.517}, {0.774,1.665}, {0.837,1.798},{0.894,1.925}, {0.949,2.038}, {1.0,2.150}, {1.049,2.260}, {1.095,2.359}, {1.140,2.464}, {1.183,2.545}, {1.225,2.634}, {1.265,2.728}, {1.304,2.817}, {1.342,2.885}, {1.378,2.979},{1.414,3.038}}

original=ListPlot[data,Frame -> True,
                                             FrameLabel -> {"Raíz longitud (m)","Periodo (s)"},
				  ImageSize->Large,
                                       PlotStyle -> {PointSize[0.02]}]

model=LinearModelFit[data,x,x]

Plot[model["BestFit"], {x, 0, 2}]

Show[ListPlot[data], Plot[model["BestFit"], {x, 0, 2}]]