so, I need to make y axis be exponential and also my observation should be exponential too. Here is code
set yrange[2.8:4.2]
# forecasts with 95 pc conf. interval
plot \
'-' using 1:2 title "log_m" w lines lw 0.5, \
'-' using 1:2 title "forecast" w lines, \
'-' using 1:2:3 title "95-interval" w errorbars
2019.333333 3.496507561
2019.416667 3.433987204
2019.5 3.465735903