L. R. , What is L R ? I was asked that one day. He was not ready for the answer.

One Day, On the tailgate of my survey truck I had plans waiting to be look at , and calculators here and there with Data Collectors, scales ,triangles erasers pen , pencils the every day survey items. this day was no different . But wait it was, sewer on one street a storm sewer on the next and  grade had to be set on a drainage ditch. It was one of those jobs that was taken so soon ,like here are the plans ,he has  equipment waiting on YOU. In my day and time this was no big deal I wasn't brought in the day of Auto Cadd  so this wasn't no dog and pony show to me. I had seen this movie many times. Now I had a new I Man that thought he was smarter than the average bear , then what comes out of he mouth  as he picks up my HP 32s calculator, which he had never seen before. What does this key do.? Of course I asked what key ? He then said the one with L R above it . My answer , everything you will do today . He said this little key. I said YEP!!

So then began his lessons on HP calculators and Linear Regression. Stay tune to here more.

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I guess no one seems to know... tell us!

Linear Regression function

Hi Survenator,   As luck would have it, I did tell the whole story. As I was about to save it. I was correcting one last thing, I hit the space bar  and  Abracadabra !! it was all gone. So goes the life and times of a Surveyor. So I will begin again.

Hi everyone, As I was saying this day was like any other day in our line of work. Many times you will be working  were the grades that are set or calculated. Many times you will have  grades on a plan or some one will calculate or you will down load them to be staked. There are those of you who use HP calculators,  some come with  L R keys some don't, the one's that don't, usually can be program to do this. Everyone else will calculate grades by using % percent. This is a every simple math equation,  the differences divide by the length, times 100 will tell you the %  of a base 100% value. A lot of times these calculation are set and never checked and they need to be. You say, that's not my problem I did not calculate them ,the office did this. Where as, if you would have check them, even randomly, you may have found this mistake and saved the day. Maybe I found so many errors, that I never trusted this one system, so I always had a system of checks. Be it on the plans or from the office. So as you start the day you are going to lay out a sewer line. This MH is 0+00 on the plans, It will be set over a existing line were the flow line is 500.00 MSL it will be a spur line to a new MH at 2+00 the grade will be .50% , this means the grade will rise .50 ft every 100 ft. so the elevation at 2+00 will be 501.00 MSL , This calculation is 1 /200=0.005, this is 5 thousandths of a foot  as this foot has 200 parts.So every 1 ft. this line will increase 0.005 times. So in calculating this grade the %  is 0.50 percent as 1/200 =0.005 x100=0.50% this is how the grade was determined on the plans. So you will need to check this grade.The MH is 0+00. This is the center of the MH.  At 0+02 is where the first pipe will be set. So 0.005 x 2=0.01 +500.00= 500.01.This is the grade at 0+02, then at 0+25, 0.005 x 25=0.125 + 500.00=500.125, then at 0+50 ,  0.005x50=0.25+500=500.25. So on and so on this is how grade is calculated using percent.  A much easier way is using Linear Regression, this L R key. This is used, with the statistic registers to accumulate the sums of the values of X and Y.    First I will clear my values in the calculator .Then ENTER the ELEV first, then the Station, so elev  500.00 ENTER 0.00 the sta. then press the accumulation key the value of 1 will be in the display, this is the beginning value, then elev  501.00  ENTER  200.00 the sta., the value of 2 will be in the display, this is the END,  then press LR this will bring up the L R soft key menu. press the value of R , this is the Correlation coefficient for (x,y) data, this will range from ─ 1 to + 1, a + 1 is a perfect fit. Since you only have 2 values this must be the answer in this case or something is wrong. But now you math is done. Key in the dist. press LR  press the Y value and there is your elev., so 50 press LR, then Y value= 500.25,then 75, press  LR then Y=500.375, then 100 press LR then Y=500.50. Lets reverse this so now you have a elev. on this line that you want to know the station, elev.of 500.62 what is this station 500.62 Press LR and the value of X = 124.00 so now you know that elev of 500.62 is at 1+24 this is just two of the ways Linear regression can be used. It is also used in the program STARNET in which some of you may know. And this is on your calculator.  A program to solve grades fast. As fast as an entered program and this one is already there. this is also known as best fit or least square fits. I will continue with  comparing this to a grade program next.


Thanks to Mr. Jim and Survenator for your Replys


Hello everyone, I would like to add this link, to this Discussion on Linear regression , what is Linear regression and what are non- linear regression models. This site I use a lot for many different things in surveying.



HI Everyone , Earlier I spoke of some of the HP calculators not having Linear Regression or other types of regression models. Linear meaning a strait line Not all variable can relate to each other in a linear fashion  But by transformation of x and y variable it is possible  to linearize the fit,and to come up with four different model of regression. Linear,Logarithmic,Exponential and Power. This link here will go over the different non-linear types.


Linear is the most simplest case of regression.Hp 35s has automatic regression by using logarithm function to transform data along with linear values.

Now this program will mimic the four models that is listed above as the best Linearized Regression  program for the HP 35.  Best Curve Fits.



Hi Everyone, This is a link  using L R In traverse adjustment. There are many traverse adjustment programs using this regression of least squares fits.Starnet is a well known one, but there are many more.




 this is a few to take a look at.

Reply by Billy Brooks

Hi Everyone , As you see regression can be programed . A simpler version is also in your Hp 35s manual on chapter 16 Statistics Programs. Manly linear regression will be use is Surveying, the
others in Engineering but also if your a student, then you may have need for this. Now i will look at how a grade program compares to linear regression function.I will use my grade program which I call Percent or Rate.It is a simple program that i will use, A given percent %, multiplies it times the
distance and this sum is then added to the beginning elev. to be equal to that station or if the percent is not known than the beginning station and the beginning elev is Entered and then the
ending station and elev is Entered it will solve the percent, then continues with the program for the
desired station.

First XEQ the program G Enter , the program will run and ask for the beginning station, We will use the above problem to compare. the beginning station is 0+00R/S then beginnin elevation =
500.00 R/S then the program will asked P? 0 for rate or Enter% .We will choose Rate, so 0.000 R/S Now the program will ask for ending Station and Elevation. First , station, 200 R/S then elev. 501.00 R/S then P= .50% . Now the program will ask station, when R/S is applied. So R/S, it will
asked station to stake, first station was 0+02 ,so 2.0 R/S=500.01 then R/S station to stake, next
0+25 , so 25, R/S = 500.125. Now since the display is two lines you will see both station at the top and elevation on the bottom line. The program works the same, if when asked for percent or rate you answer in percent then it will calculate using percent that was entered.. This program is a good
tool to have if you have a lot of grade that you calculate or even to check your plans.It will not solve
the station to elevation, but this also simple. Take the difference in the elevation that you have
increased to, we used 500.62 this means you have went up in elev. 0.62 ft from the beginning elev.
of 500.00, Now divide that by the rate per foot ,this was 0.005 per ft. 0.62/0.005 =124. so the
station of 500.62 Elev. = 1+24 The program does also take up a lot of memory in your
calculator.but this may not be a problem. The calculator as plenty of memory for other programs.If
you do not have access to a program like this, then that is when the linear regression function is a
plus .Because with it you do not need this program because linear regression is already on your
calculator.. I did not go over Inverse model or Quadratic model, but they are explained on the
https://www.educalc.net/2104083.page above, for those of you need to know them.


Hi everyone,Here is a Grade Program I talked about above, to work with your LR function, both are very good to use. This program lets you use Rate or Percent when asked either input 0 are input percent as positive or negative .enter beginning station, R/S then beginning elevation, R/S then if you do not know the percent enter 0 R/S and program will ask for ending station R/S and ending elevation R/S and percent will be calculated then R/S will ask for station to stake. If enter percent then program will ask station to stake. I have used this program a lot.This program is my version written

by Billy Brooks for the HP 35s

HP 35s ver. GRADES LBL G

1. LBL G

2. CLx


4.SF 10


6. PSE



9. SF10

10. B = BEG STA



13.STO D

14. SF 10

15. E = BEG ELEV



18.STO Z

19. SF 10


21. PSE

22.SF 10

23. INPUT 0 (zero )

24. PSE

25. OR PER%


27.SF 10


29 PSE

30.PER +/- (+ or - )



33. X ╪ 0 ?

34. GTO G057

35.SF 10




39. STO X

40. SF 10




44. STO N

45. RCL N

46.RCL Z

47. ─

48.RCL X

49. RCL D

50. ─

51. ÷ ( or / )

52. 100

53. x ( times)

54. STO P

55. VIEW P

56. GTO G057

57. SF 10


59. PSE


61. RCL B

62. ─

63. RCL P

64.% ( key % )

65. RCL Z

66. +

67.RCL S


69.SF 10






75.GTO G057



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