Line of Best Fit (1 Viewer)

[Love]

Best way and key features to draw line of best fit?

Is it necessary to pass through the first and last point on the graph? How do you determine the outliers of the graph?

Cheers!

 

[InteGrand]

"Is it necessary to pass through the first and last point on the graph?"

Someone confirm it...but pretty sure the answer is no

You don't need to pass through the first and last point on the graph.

 

[Carrotsticks]

I don't know anything about how things are marked, but it seems illogical for them to force you to draw the regression line to specifically pass through the first and last points.

EDIT: Answered above ^

 

[InteGrand]

Best way and key features to draw line of best fit?

Is it necessary to pass through the first and last point on the graph? How do you determine the outliers of the graph?

Cheers!

Theoretically speaking, the point will lie on the LOBF, where is the average of the x-coordinates of the points to be plotted, and similarly for . However, it's a waste of time to calculate these averages, as you just need a decent-looking LOBF, not THE perfect one.

To draw a decent one, try lining up your ruler (preferably a see-through one) with the points and adjusting it to see what the line you'd draw would be like. Try and draw one where, roughly speaking, the sum of distances of points above your LOBF to the LOBF is similar to those below. (E.g. if every point was above your LOBF, clearly your LOBF isn't ideal, and you should adjust it upwards.)

To identify an outlier by eye, just check if it seems to lie well off the LOBF if you ignored that point and did your LOBF based on the remaining points only. You shouldn't force a line of best fit through a clear outlier; rather, ignore it and draw the LOBF through the other points; circling the outlier point and writing something like "outlier ignored for LOBF".

 

[InteGrand]

Also, take note of whether they tell you to draw your LOBF with the condition that it pass through the origin. If they don't, you generally shouldn't force it through the origin, as even if a physical law implies the LOBF should theoretically go through the origin, experimental errors often mean that data points don't do this; the offset of the LOBF from the origin in this case is a measure of the systematic error in the experiment.

If they tell you to force the LOBF through the origin, you should of course do that.

 

[Fizzy_Cyst]

^^ Awesome explanations Integrand, addressed basically everything which needs to be addressed.

One other thing, your LOBF should only run from first valid data point to the last valid data point, there should be no extrapolation of a line of best fit (unless required by the question), if a line of best fit is to be extrapolated, you need to distinguish between LOBF and extrapolated section (i.e., LOBF in solid pencil and extrapolation in dotted pencil)

 

[Love]

Cheers guys!

 

[braintic]

^^ Awesome explanations Integrand, addressed basically everything which needs to be addressed.

One other thing, your LOBF should only run from first valid data point to the last valid data point, there should be no extrapolation of a line of best fit (unless required by the question), if a line of best fit is to be extrapolated, you need to distinguish between LOBF and extrapolated section (i.e., LOBF in solid pencil and extrapolation in dotted pencil)

The first space shuttle disaster was basically caused by scientists extrapolating a line/curve beyond the last data point ... and getting it wrong.

 

[kawaiipotato]

The first space shuttle disaster was basically caused by scientists extrapolating a line/curve beyond the last data point ... and getting it wrong.

is there a source for this? That sounds.. interesting