# multiple linear regression fit
#
# example from # John Heilborn, Ed. 1981 "Science and engineering programs, Apple II Edition" Osborn/McGraw Hill p10 of 227pp  ISBN 0-9310-63-2
# xData  :=   71  73  64  65  61  70  65  72  63  67  64   % height (in)  ;  
# yData  :=  160 183 154 168 159 180 145 210 132 168 141   % weight (#)   ;  
# fit_linearRegressSingle  xData  yData  "pass  "pass  (link  d_temp  'fit_linearRegressSingle Heilborn example.txt')  
# book result :  f(x) =  constant + slope * x  
# constant		slope			coeffDeterm(=R^2)	coeffCorrel(=R)	StdErrEst
# -106.7917		4.047223		0.556260				0.745828				15.413488  
# standard result :  
#	"$d_Qtest"'fit_linearRegress/fit_linearRegress - tests SLR_Heilborn standard.txt'


Coefficients & statistics : 
+------------------+--------+
|constant          |-85.3417|
+------------------+--------+
|slope             | 3.74389|
+------------------+--------+
|coeffDeterm_Rsq   |0.305514|
+------------------+--------+
|CorrCoeff^2       |0.552733|
+------------------+--------+
|StndErrOf estimate| 14.3604|
+------------------+--------+
#
# for regression tables etc, copy-paste to LibreCalc : 
#		geany Replace spaces with tab :  search : \s+  replace : \t
#
multLinReg estimates and residuals
+--+------+----+-------+----------+---------+
|i |xGiven|yObs|yEst   |yResiduals|pct_resid|
+--+------+----+-------+----------+---------+
|0 |    71| 160|180.474|  -20.4744| -12.7965|
+--+------+----+-------+----------+---------+
|1 |    73| 183|187.962|  -4.96222|  -2.7116|
+--+------+----+-------+----------+---------+
|2 |    64| 154|154.267| -0.267222|-0.173521|
+--+------+----+-------+----------+---------+
|3 |    65| 168|158.011|   9.98889|  5.94577|
+--+------+----+-------+----------+---------+
|4 |    61| 159|143.036|   15.9644|  10.0405|
+--+------+----+-------+----------+---------+
|5 |    70| 180|176.731|   3.26944|  1.81636|
+--+------+----+-------+----------+---------+
|6 |    65| 145|158.011|  -13.0111| -8.97318|
+--+------+----+-------+----------+---------+
|7 |    72| 210|184.218|   25.7817|   12.277|
+--+------+----+-------+----------+---------+
|8 |    63| 145|150.523|  -5.52333|  -3.8092|
+--+------+----+-------+----------+---------+
|9 |    67| 168|165.499|   2.50111|  1.48876|
+--+------+----+-------+----------+---------+
|10|    64| 141|154.267|  -13.2672| -9.40938|
+--+------+----+-------+----------+---------+