(15C) Least Squares fit, Standard Deviations

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An extract from DEVELOPMENT AND CALIBRATION OF TWO AND FOUR WIRE WATER SURFACE WAVE HEIGHT MEASUREMENT SYSTEMS, Naval Postgraduate School, Thesis - MS ENGINEERING ACOUSTICS, December 1992

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APPENDIX A
I. HP-15C CALCULATOR LEAST SQUARES FIT STANDARD DEVIATIONS PROGRAM CODE
The standard deviations in all the least squares fit parameters were discussed in chapter II E. This is program code for the HP-15C hand held calculator, which can be used to solve equations (2.16 through 2.19) for data entered into the calculator using the summation key (B1 P66/67). The calculator stores the different summation values in the following register as shown in Table (A.1).
TABLE A.1. HP-15C REGISTER VALUES AFTER USING SUMMATION KEY.

Register   Value
     2       N, the number of samples
     3       summation of Xn
     4       summation of Xn²
     5       summation of Vn
     6       summation Of Vn²
     7       summation of XnVn

The standard deviations in y, slope, and intercept are displayed at program lines 040, 054, and 067 respectfully. The program code is shown below.

Program         Program        Calculator
function         line number       keys  
g[P/R]           000
f [LBL]C         001              42,21,13
RCL[5]           002              45,5
g[x²]             003              43,11
RCL[4]           004              45,4
×                 005              20
2                  006              2
ENTER           007              36
RCL[7]           008              45,7
×                  009              20
RCL[3]           010              45,3
×                  011              20
RCL[5]           012              45,5
×                  013              20
CHS              014              16
-                  015              30
RCL[2]           016              45,2
ENTER           017              36
RCL[7]           018              45,7
g[x²]             019              43,11
×                  020              20
+                  021              40
RCL[2]           022              45,2
ENTER           023              36
RCL[4]           024              45,4
×                  025              20
RCL[3]           026              45,3
g[x²]             027              43,11
-                  028              30
÷                  029              10
CHS              030              16
RCL[6]           031              45,6
+                  032              40
RCL[2]           033              45,2
ENTER           034              36
2                  035              2
-                  036              30
÷                  037              10
√x                038              11
ST0[8]          039              44,8
R/S               040              31
RCL[4]           041              45,4
ENTER           042              36
RCL[4]           043              45,4
ENTER           044              36
RCL[2]           045              45,2
x                  046              20
RCL[3]           047              45,3
g[x²]             048              43,11
-                   049              30
÷                  050              10
√x                051              11
RCL[8]           052              45,8
×                  053              20
R/S               054              31
RCL[2]           055              45,2
ENTER           056              36
RCL[2]           057              45,2
ENTER           058              36
RCL[4]           059              45,4
×                  060              20
RCL[3]           061              45,3
g[x²]             062              43,11
-                  063              30
÷                  064              10
√x                065              11
RCL[8]           066              45,8
×                 067              20
g[RTN]          068              43,32
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