Best-fit and Worst-fit Lines

Once points and error bars are plotted, two straight lines are drawn.The best-fit line is the straight line that best represents the data. It should pass through all the error bars, with the points scattered evenly on either side.The worst-fit line is the steepest or the shallowest straight line that still passes through all the error bars. A steep worst-fit line is often drawn from the bottom of the first error bar to the top of the last; a shallow one from the top of the first to the bottom of the last. Check it still passes through every bar in between.Draw the best-fit line as a solid line and the worst-fit line as a dashed line, and label both.Reading a gradient: draw a large triangle on each line covering more than half of the line, and use points read from the line, not data points, unless they lie exactly on it:gradient = Δy ÷ ΔxWorked example: The best-fit line passes through (0, 0.2) and (5.0, 10.2).
Gradient = (10.2 − 0.2) ÷ (5.0 − 0) = 10.0 ÷ 5.0 = 2.0.
The steep worst-fit line passes through (1.0, 1.7) and (5.0, 10.7).
Gradient = (10.7 − 1.7) ÷ (5.0 − 1.0) = 9.0 ÷ 4.0 = 2.25.Read the y-intercept of each line where it crosses x = 0 (only if the x-axis starts at zero; otherwise use y = mx + c with a point on the line). Comparing the best-fit and worst-fit values gives the uncertainties, as the next lesson shows.