HP 48G Linear Regression Best Fit Line

12122021, 02:47 AM
(This post was last modified: 12122021 08:35 AM by Rodger Rosenbaum.)
Post: #21




RE: HP 48G Linear Regression Best Fit Line
Note that the first thing in the little program I gave in the previous post is the LR function.
If the data are entered into the statistics registers in the usual way, the advantage of doing it this way is that you can have access to the two ways of fitting. If you execute LR, you get the ordinary least squares result; if you run the ORTH program, you get orthogonal least squares; comparison of the two is easy. 

12182021, 10:13 PM
(This post was last modified: 12182021 10:15 PM by MNH.)
Post: #22




RE: HP 48G Linear Regression Best Fit Line
(12112021 05:38 PM)Rodger Rosenbaum Wrote: The result will be the slope and intercept for the line which minimizes the SSE with the deviation from the line in the orthogonal direction. My results are: 120.175378956 80799.308982 which looks strange to me, probably because I don't know a lot about statistics. My ΣDAT is y 29945.480 30002.951 30006.678 30058.926 30114.903 30119.876 30221.977 x 921.773 922.245 982.237 921.687 923.001 983.350 924.059 In the matrix editor I entered the 'x' data in column 1 and the 'y' data in column 2. Is that correct? The actual survey data is PT # Northing Easting Elevation Description 248 29945.480 921.773 0.000 PROP_COR 249 30002.951 922.245 0.000 PROP_COR 250 30006.678 982.237 0.000 PROP_COR 251 30058.926 921.687 0.000 PROP_COR 252 30114.903 923.001 0.000 PROP_COR 253 30119.876 983.350 0.000 PROP_COR 254 30221.977 924.059 0.000 PROP_COR Please see the attached file (thumbnail) to see the relationship of the points. North is straight up. 

12192021, 12:10 AM
Post: #23




RE: HP 48G Linear Regression Best Fit Line  
12192021, 12:31 AM
Post: #24




RE: HP 48G Linear Regression Best Fit Line  
12192021, 12:46 AM
Post: #25




RE: HP 48G Linear Regression Best Fit Line
(12192021 12:10 AM)MNH Wrote:(12112021 05:38 PM)Rodger Rosenbaum Wrote: << LR SWAP DROP DUP CORR DUP SIGN 4 ROLLD SQ / SWAP INV  I am using this on a HP49g+, so the byte count may be different than what you get on your simulated HP48G. I get: Bytes: 90. Checksum: # E548h I triple checked the program and what you have is correct. 

12192021, 12:48 AM
(This post was last modified: 12192021 01:33 AM by Rodger Rosenbaum.)
Post: #26




RE: HP 48G Linear Regression Best Fit Line
(12192021 12:31 AM)MNH Wrote:(12112021 12:13 PM)Rodger Rosenbaum Wrote: The slope and intercept for the orthogonal fit are: I'm using the standard analytic geometry slope/intercept form y = mx + b, where m is the slope and b is the intercept: https://www.chilimath.com/lessons/interm...ceptform/ This is also what the LR function uses. It shouldn't be too hard to convert to what you need. 

12192021, 01:08 AM
Post: #27




RE: HP 48G Linear Regression Best Fit Line
(12182021 10:13 PM)MNH Wrote:(12112021 05:38 PM)Rodger Rosenbaum Wrote: The result will be the slope and intercept for the line which minimizes the SSE with the deviation from the line in the orthogonal direction. After you enter the data into ΣDAT you need to get into the statistics menu and execute the "Fit data" function (it's the 3rd function in the list). Doing this will fill in all the summary statistics such as ΣX, ΣY, ΣXY, etc. Without doing this the LR function, and the ORTH program won't work. A check for all the data being entered is this: Recall ΣDAT to the stack; you should see a two column, 7 row matrix. Execute the calculator's ABS function. This will calculate the square root of the sum of the squares (the Frobenius norm) of all the elements of the ΣDAT matrix. You should get 79589.685862 If this is ok, try the LR function (ordinary least squares) and you should get on the stack (reverse order from what ORTH will get): Intercept: 30074.5044063 Slope: (7.71315429794E3) Now clear the stack and execute ORTH; you should get on the stack: 1161.69645637 1121788.42831 I also checked the ORTH result with a method using the singular value decomposition and got exactly the same result. 

12192021, 03:19 AM
(This post was last modified: 12192021 03:20 AM by Joe Horn.)
Post: #28




RE: HP 48G Linear Regression Best Fit Line
(12192021 12:46 AM)Rodger Rosenbaum Wrote:(12192021 12:10 AM)MNH Wrote: Bytes: 98.5 Rodger, your program's numeric literals are integertype objects, which the 48G does not have. Replacing them with reals on the 49g+/50g changes the checksum to #27D3h. On a 48G, the checksum is #D883h. All are 90 bytes. <0ɸ0> Joe 

12192021, 03:54 AM
Post: #29




RE: HP 48G Linear Regression Best Fit Line
(12192021 03:19 AM)Joe Horn Wrote:(12192021 12:46 AM)Rodger Rosenbaum Wrote: I am using this on a HP49g+, so the byte count may be different than what you get on your simulated HP48G. Would the checksum on an Emu48 be the same as on a real 48G? 

12192021, 09:04 AM
Post: #30




RE: HP 48G Linear Regression Best Fit Line
(12192021 03:54 AM)Rodger Rosenbaum Wrote:(12192021 03:19 AM)Joe Horn Wrote: Rodger, your program's numeric literals are integertype objects, which the 48G does not have. Replacing them with reals on the 49g+/50g changes the checksum to #27D3h. On a 48G, the checksum is #D883h. All are 90 bytes. I hope somebody who uses it can answer that for you. Unfortunately, I don't, so I can't. <0ɸ0> Joe 

12192021, 03:23 PM
Post: #31




RE: HP 48G Linear Regression Best Fit Line
I appreciate all of the help being offered here! I may be a victim of misunderstanding the mathematical lexicon involved with finding a best fit line (BFL). I recently read on a website that a BFL is an orthogonal projection using least squares. Please look at the attached thumbnail in this thread. The BFL (248 going N. to 254) on the W. side of the street is
248 29945.480 921.773 249 30002.951 922.245 251 30058.926 921.687 252 30114.903 923.001 254 30221.977 924.059 The office software I'm using creates 2 points, which define the BFL as being N 00°28'36" E (azimuth 00°28'36" or clockwise 00°28'36" from the N.). The first of these points is near 248, the second is near 254. The orthogonal offsets to the BFL are Point: 248 Offset: 0.24655 Right Point: 249 Offset: 0.24033 Right Point: 251 Offset: 0.78342 Left Point: 252 Offset: 0.06476 Right Point: 254 Offset: 0.23177 Right I believe I need I to create a new matrix (ΣDAT) in my Emu48. I believe I entered erroneous data after examining a recent post in this thread. If my thinking is correct, the resulting slope will indicate the direction of the BFL. I have to digest all of the information presented here. Again, thank you for the help! 

12192021, 03:26 PM
Post: #32




RE: HP 48G Linear Regression Best Fit Line
(12192021 03:23 PM)MNH Wrote: I appreciate all of the help being offered here! I may be a victim of misunderstanding the mathematical lexicon involved with finding a best fit line (BFL). I recently read on a website that a BFL is an orthogonal projection using least squares. Please look at the attached thumbnail in this thread. The BFL (248 going N. to 254) on the W. side of the street is I don't see a thumbnail. 

12192021, 04:00 PM
(This post was last modified: 12192021 05:26 PM by Rodger Rosenbaum.)
Post: #33




RE: HP 48G Linear Regression Best Fit Line
Look at the two images part way down the page here:
https://stats.stackexchange.com/question...esviapca The first image shows ordinary least squares which is what the HP48G LR function returns. The second image shows what the ORTH program returns. I've got the full solution for you now. Besides entering the ORTH program, create two new variables X and Y. Put your data in those variables as single column matrices, with X and Y being reversed from what was used previously. Designate X and Y parts of your latest data like this: ............X.............Y 248 29945.480 921.773 249 30002.951 922.245 251 30058.926 921.687 252 30114.903 923.001 254 30221.977 924.059 Type in another little program called OFIT: << X TRN DUP 1. CON AUGMENT TRN ORTH * Y  >> Run it all like this: Type your data into the ΣDAT matrix (as a two column matrix), run "Fit data..." in the statistics menu, type your X and Y data in separate single column matrices and store in the X and Y variables, then run OFIT. Here's what I get when I do all this. [ .246561355 ] [ .240335279 ] [ .783442323 ] [ .064763432 ] [ .231782261 ] If you don't want to see so many digits, put "5 RND" at the end of the OFIT program. The signs may be reversed from what you wantthat's an easy fix, eh? 

12192021, 08:12 PM
Post: #34




RE: HP 48G Linear Regression Best Fit Line
(12192021 04:00 PM)Rodger Rosenbaum Wrote: Here's what I get when I do all this. That's just fabulous! Actually, even 5 digits after the decimal point is an overkill. I would never need more than 3 digits. Quote:The signs may be reversed from what you wantthat's an easy fix, eh? The signs are reversed because a negative sign would indicate a point is to the left of a line. I'll put all this code together and post my program within a week. 

12192021, 10:39 PM
Post: #35




RE: HP 48G Linear Regression Best Fit Line  
12202021, 12:15 AM
(This post was last modified: 12202021 12:18 AM by Rodger Rosenbaum.)
Post: #36




RE: HP 48G Linear Regression Best Fit Line
(12192021 10:39 PM)MNH Wrote:(12192021 04:00 PM)Rodger Rosenbaum Wrote: << X TRN DUP 1. CON AUGMENT TRN ORTH * Y  >> That's because AUGMENT is part of the HP49g+/HP50g additional functions. :) There's an easy way to deal with this. When you type in the X data normally it would be like this: [ 29945.480 ] [ 30002.951 ] [ 30058.926 ] [ 30114.903 ] [ 30221.977 ] But just type in an extra column of 1s like this: [ 29945.480 1 ] [ 30002.951 1 ] [ 30058.926 1 ] [ 30114.903 1 ] [ 30221.977 1 ] and store that in the X variable. Then the OFIT program becomes: << X ORTH * Y  >> Don't add a column of 1s when you're typing the ΣDAT data. 

12202021, 01:11 AM
Post: #37




RE: HP 48G Linear Regression Best Fit Line
(12202021 12:15 AM)Rodger Rosenbaum Wrote: ... Then the OFIT program becomes: It may make more sense to return ORTH residuals, instead of vertical residuals. Just multiply above by correction factor 1/√(1+m^2), where m = ORTH slope 1/√(1+m^2) = 1/√(1+tan(θ)^2) = cos(θ) Bonus: With ORTH residuals, ordering of X,Y does not matter. Except for sign difference, we would get the same ORTH residuals. 

12212021, 12:59 AM
Post: #38




RE: HP 48G Linear Regression Best Fit Line
When I saw the results of MNH's office software:
Point: 248 Offset: 0.24655 Right Point: 249 Offset: 0.24033 Right Point: 251 Offset: 0.78342 Left Point: 252 Offset: 0.06476 Right Point: 254 Offset: 0.23177 Right The words "Right" and "Left" led me to think that the offsets were taken in a direction parallel to the coordinate axes. I didn't notice the sentence just above that said "The orthogonal offsets to the BFL are". :( But it's easy to adjust the offsets to be orthogonal offsets with a few additions to OFIT. Here's the new OFIT: << X ORTH DUP 1. GET UNROT * Y  SWAP ATAN COS * 5. RND >> With this version I get: [ .24655 ] [ .24033 ] [ .78342 ] [ .06476 ] [ .23177 ] Which is exactly what MNH's office software gets, evidence that orthogonal offsets are what they want. :) The variance of these data is very small and because of this almost any method of regression gets results very close to any of the others. The result for the slope returned by ORTH is .008321172, but calculating it with Mathematica and 50 digit precision gets .00832117201288. Calculating this problem with the summary statistics derived by the HP48/49g+/50g is not the best way, but even so the result from the ORTH and OFIT routines is returning 8 accurate digits as determined by the Mathematica result. 

12212021, 01:51 AM
(This post was last modified: 12212021 02:15 AM by MNH.)
Post: #39




RE: HP 48G Linear Regression Best Fit Line
(12192021 04:00 PM)Rodger Rosenbaum Wrote: Type your data into the ΣDAT matrix (as a two column matrix) ... My data stored in 'ΣDAT' [[29945.480 921.773] [30002.951 922.245] [30058.926 921.687] [30114.903 923.001] [30221.977 924.059]] Quote:... run "Fit data..." in the statistics menu ... I get '672.349+0.008*X' Correlation: 0.894 Covariance: 94.090 Quote: type your X and Y data in separate single column matrices and store in the X and Y variables ... 'x' data stored in 'X' [[29945.480 1] [30002.951 1] [30058.926 1] [30114.903 1] [30221.977 1]] 'y' data stored in 'Y' [[921.773] [922.245] [921.687] [923.001] [924.059]] Quote:... then run OFIT. I get  Error: Bad Argument Type Oops! I just realized that you posted something this morning. Executing the new OFIT program, I get GET Error: Bad Argument Type 4: 0.008 3: 672.345 2: 672.345 1: 1.000 

12212021, 02:23 AM
Post: #40




RE: HP 48G Linear Regression Best Fit Line  
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