HP 48G Linear Regression Best Fit Line

[Rodger Rosenbaum]

Edit: Have a look at the next post.

If we look at the data set:

Pt.--- Northing(y)--Easting(x)

248 1529945.480 521921.773
249 1530002.951 521922.245
251 1530058.926 521921.687
252 1530114.903 521923.001
254 1530221.977 521924.059
600 1529945.482 521921.526
601 1530221.979 521923.827

Points 600 and 601 are the endpoints of the BFL. Point 600 is near to point 248, and point 601 is near to point 254.

Assume that the the data set with its more digits are typed into ΣDAT (but not points 600 and 601) letting Northing be X and Easting be Y, LR is executed to fill in the summary statistics. Now if we execute ORTH we get:

[[ .008321172 ]
[ 509190.586948 ]]

In order to get point 600, they took the Northing value of point 248 and added .oo2 to it and formed a 1x2 matrix on the stack from it like this:

[[ 1529945.482 1 ]]

Then execute ORTH and the stack looks like this:

2: [[ .008321172 ]
[ 509190.586948 ]]

1: [[ 1529945.482 1 ]]

Then press multiply and get:

1: [[ 521921.526454 ]]

Drop the last two digits and that's the value they got for the Easting, which I'm treating as the Y value.

Or do it this way: type in as the X matrix and store in the X variable (the Northing of points 600 and 601 are included):

[ 1529945.480 1 ]
[ 1530002.951 1 ]
[ 1530058.926 1 ]
[ 1530114.903 1 ]
[ 1530221.977 1 ]
[ 1529945.482 1 ]
[ 1530221.979 1 ]

The last two entries are points 600 and 601, which are points 248 and 254 with .002 added to each.

Now execute X (recall the X matrix), ORTH, * and see:

[[ 521921.526438 ]
[ 521922.004664 ]
[ 521922.470441 ]
[ 521922.936236 ]
[ 521923.827217 ]
[ 521921.526454 ]
[ 521923.827233 ]]

The last two values are the Easting of points 600 and 601 after you round to only 3 digits after the decimal point. They are identical to what the Office software got.

Now type in the Eastings and store as the Y matrix. Execute OFIT and get:

[[ .24655 ]
[ .24033 ]
[ -.78341 ]
[ .06476 ]
[ .23177 ]
[ -.00045 ]
[ -.00023 ]]

The last two values are the orthogonal offsets of points 600 and 601. Since points 600 and 601 are the endpoints of the BFL, they are necessarily ON the BFL and their orthogonal offsets from the BFL should be zero, which they essentially are! :-)