Scatter Diagram Fit Formula

[David H]

What is the formula to work out if the spots on a scattergram graph can be rotated to fit in a grid square or fall beyond its limits?

[fiction-factory]

Are you referring to a linear line of best fit?
I know what a scattergraph is and what you mean by spots but I don't know why you would rotate it (the line?) (maybe to switch the x and y axes round?) nor do I know what you mean by 'fit on the grid'- you could just set your scale so that the plotted points fit on.
I also know the formula using method of least squares but don't know what formula you are referring to.
Please can you try to clarify what you mean?

[David H]

I don't think we can upload pictures but if you look at an Ordnance Survey map and then put lots of locations on it, they will often spread beyond a grid square (eg TQ) which is 100km, but when rotated will then fit inside it. I have my own map with locations and so far I've printed the map and cut the shape out they make but it's not very accurate and won't work when it's a close fit so need a mathematical formula.

To give an example, if you put a spot in Amersham, St Albans, Eastbourne and Ashford (Kent) they all fall outside TQ but if you then rotate the quadrangle (or pentagon if five locations) it may well fit inside the TQ square. It isn't even related to the diagonal length as if you have a rectangle shorter than it over all if a bit sticks out it can't then be rotated at any angle to fit the 100km (or any other size) square.

It is physically impossible to cut out a pentagon for my map that is accurate enough to see if it can fit or not physically but will know exactly given a formula. It's probably between A level and degree level maths, I didn't get O level so haven't a scooby.

[fiction-factory]

Okay thanks. I assumed you were talking about scatter graphs to plot relationships/correlation between two variables. I'll look again at your question later but on first reading I am not sure I understand what you are asking. My Maths goes beyond A level but I don't seem to have the patience for these things now, but there other qualified mathematicians on here such as jim360, Prudie, Buenchico , vascop etc who may be able to help if I push this back onto Latest Posts

[David H]

Thanks. You can get a rough idea by cutting out the shape made by the extreme points and turning it round on the grid, but that only works when it's not a close fit. That can only be done with an exact calculation. I've done related subjects when I did statistics but this was a level or two above it.

[Hypognosis]

Sounds like a matrix transformation thing. I've only the vaguest recollection of these and that is how rubbish I was at them.

We did need to know it was about a map because that introduces an immediate problem which is that lines of longitude are not parallel while lines of latitude are.

So you're rotating something which isn't square, in reality.

"Base map constructed on Transverse Mercator Projection, Airy Spheroid, OSGB (1936) Datum." Whatever that means.

[fiction-factory]

So are you wanting to know a rule for working out how much to rotate a given irregular pentagon so that it fits inside a square (the smallest possible square?)?