# How can I determine the accuracy of a hand-drawn line of best fit?

Here's the situation:

• Users have manually drawn a straight line of best fit through a set of data points. I have the equation (y = mx + c) for this line.

• I have used least-squares regression to determine the optimal line of best fit for the same data.

How can I assess the quality of the user-drawn LOBF? My first thought was just to work out the uncertainty between the two gradients and the two y-intercepts, but that produces dramatic errors when the true value of either the gradient or the y-intercept is close to zero. Any suggestions, please?

$$\sum_{i=1}^n\bigg( Y_{true, i}-Y_{predicted, i} \bigg)^2$$
If you want to automate this task for a computer to do it, calculate the slope and intercept of your guesses line of best fit. Pick two points on your line, $$(x_0,y_0)$$ and $$(x_1,y_1)$$.
$$y-y_0 = \dfrac{ y_1-y_0 }{ x_1-x_0 } \bigg( x-x_0 \bigg)$$
When you do the algebra to solve for $$y$$ in terms of $$x$$, you will have the equation for the line you’ve fitted by eyeballing it. You then can use this to make predictions to feed into the square error formula.