Select plausible transformations from scatterplot shape

Here x denotes the horizontal explanatory variable and y the vertical response variable. For two positive original coordinates, use this trial guide: increasing and concave up → x², log₁₀(y), 1/y; increasing and concave down → log₁₀(x), 1/x, y²; decreasing and concave up → log₁₀(x), 1/x, log₁₀(y), 1/y; decreasing and concave down → x², y². A turn, no consistent direction, or a nonpositive original coordinate gives no trial set from this positive-scale guide. Each entry changes one axis only. These are candidates to test, not a guarantee of linearity or an exhaustive list of all mathematical transformations

Use the plotted direction and curvature to choose a trial transformation