change proto-methods to use proto-slot-value (forgot the change!)
[CommonLispStat.git] / src / stat-models / regression.lisp
blob772ee6941822087ad6defb748ecc5af32c6f9a66
1 ;;; -*- mode: lisp -*-
2 ;;;
3 ;;; Copyright (c) 2008--, by A.J. Rossini <blindglobe@gmail.com>
4 ;;; See COPYRIGHT file for any additional restrictions (BSD license).
5 ;;; Since 1991, ANSI was finally finished. Modified to match ANSI
6 ;;; Common Lisp.
8 ;;;; Originally from:
9 ;;;; regression.lsp XLISP-STAT regression model proto and methods
10 ;;;; XLISP-STAT 2.1 Copyright (c) 1990, by Luke Tierney
11 ;;;; Additions to Xlisp 2.1, Copyright (c) 1989 by David Michael Betz
12 ;;;; You may give out copies of this software; for conditions see the file
13 ;;;; COPYING included with this distribution.
14 ;;;;
15 ;;;; Incorporates modifications suggested by Sandy Weisberg.
17 ;;; This version uses lisp-matrix for underlying numerics.
19 (in-package :lisp-stat-regression-linear)
21 ;;; Regresion Model Prototype
23 ;; The general strategy behind the fitting of models using prototypes
24 ;; is that we need to think about want the actual fits are, and then
25 ;; the fits can be used to recompute as components are changes. One
26 ;; catch here is that we'd like some notion of trace-ability, in
27 ;; particular, there is not necessarily a fixed way to take care of the
28 ;; audit trail. save-and-die might be a means of recording the final
29 ;; approach, but we are challenged by the problem of using advice and
30 ;; other such features to capture stages and steps that are considered
31 ;; along the goals of estimating a model.
33 ;; Note that the above is a stream-of-conscience response to the
34 ;; challenge of reproducibility in the setting of prototype "on-line"
35 ;; computation.
37 (defvar regression-model-proto nil
38 "Prototype for all regression model instances.")
40 (defproto regression-model-proto
41 '(x y intercept betahat basis weights
42 included
43 total-sum-of-squares
44 residual-sum-of-squares
45 predictor-names
46 response-name
47 case-labels
48 doc)
50 *object*
51 "Normal Linear Regression Model")
56 (defun xtxinv (x)
57 "In: X
58 Out: (XtX)^-1
60 X is NxP, so result is PxP. Represents Var[\hat\beta], the vars for
61 \hat \beta from Y = X \beta + \eps. Done by Cholesky decomposition,
62 using LAPACK's dpotri routine to invert, after factorizing with dpotrf.
64 <example>
65 (let ((m1 (rand 7 5)))
66 (xtxinv m1))
67 </example>"
68 (check-type x matrix-like)
69 (minv-cholesky (m* (transpose x) x)))
72 ;; might add args: (method 'gelsy), or do we want to put a more
73 ;; general front end, linear-least-square, across the range of
74 ;; LAPACK solvers?
75 (defun lm (x y &optional rcond (intercept T))
76 "fit the linear model:
77 y = x \beta + e
79 and estimate \beta. X,Y should be in cases-by-vars form, i.e. X
80 should be n x p, Y should be n x 1. Returns estimates, n and p.
81 Probably should return a form providing the call, as well.
83 R's lm object returns: coefficients, residuals, effects, rank, fitted,
84 qr-results for numerical considerations, DF_resid. Need to
85 encapsulate into a class or struct."
86 (check-type x matrix-like)
87 (check-type y vector-like) ; vector-like might be too strict?
88 ; maybe matrix-like?
89 (assert (= (nrows y) (nrows x)) ; same number of observations/cases
90 (x y) "Can not multiply x:~S by y:~S" x y)
91 (let ((x1 (if intercept
92 (bind2 (ones (matrix-dimension x 0) 1)
93 x :by :column)
94 x)))
95 (let ((betahat (gelsy (m* (transpose x1) x1)
96 (m* (transpose x1) y)
97 (if rcond rcond (*
98 (coerce (expt 2 -52) 'double-float)
99 (max (nrows x1)
100 (ncols y))))))
101 (betahat1 (gelsy x1
103 (if rcond rcond
104 (* (coerce (expt 2 -52) 'double-float)
105 (max (nrows x1)
106 (ncols y)))))))
107 ;; need computation for SEs,
108 (format t "")
109 (list betahat ; LA-SIMPLE-VECTOR-DOUBLE
110 betahat1 ; LA-SLICE-VECVIEW-DOUBLE
111 (xtxinv x1); (sebetahat betahat x y) ; TODO: write me!
112 (nrows x) ; surrogate for n
113 (ncols x1) ; surrogate for p
114 ;; (v- (first betahat) (first betahat1))
115 ))))
120 (defun regression-model
121 (x y &key
122 (intercept T)
123 (print T)
124 (weights nil)
125 (included (repeat t (vector-dimension y)))
126 predictor-names
127 response-name
128 case-labels
129 (doc "Undocumented Regression Model Instance")
130 (debug T))
131 "Args: (x y &key (intercept T) (print T) (weights nil)
132 included predictor-names response-name case-labels)
133 X - list of independent variables or X matrix
134 Y - dependent variable.
135 INTERCEPT - T to include (default), NIL for no intercept
136 PRINT - if not NIL print summary information
137 WEIGHTS - if supplied should be the same length as Y; error
138 variances are
139 assumed to be inversely proportional to WEIGHTS
140 PREDICTOR-NAMES, RESPONSE-NAME, CASE-LABELS
141 - sequences of strings or symbols.
142 INCLUDED - if supplied should be the same length as Y, with
143 elements nil to skip a in computing estimates (but not
144 in residual analysis).
145 Returns a regression model object. To examine the model further assign the
146 result to a variable and send it messages.
147 Example (data are in file absorbtion.lsp in the sample data directory):
148 (def m (regression-model (list iron aluminum) absorbtion))
149 (send m :help) (send m :plot-residuals)"
150 (let ((x (cond
151 ((typep x 'matrix-like) x)
152 #| assume only numerical vectors -- but we need to ensure coercion to float.
153 ((or (typep x 'sequence)
154 (and (consp x)
155 (numberp (car x)))
156 (make-vector (length x) :initial-contents x)))
158 (t (error "not matrix-like.");x
159 ))) ;; actually, might should barf.
160 (y (cond
161 ((typep y 'vector-like) y)
163 ((and (consp x)
164 (numberp (car x))) (make-vector (length y) :initial-contents y))
166 (t (error "not vector-like."); y
167 ))) ;; actually, might should barf.
168 (m (send regression-model-proto :new)))
169 (format t "~%")
170 (send m :doc doc)
171 (send m :x x)
172 (send m :y y)
173 (send m :intercept intercept)
174 (send m :weights weights)
175 (send m :included included)
176 (send m :predictor-names predictor-names)
177 (send m :response-name response-name)
178 (send m :case-labels case-labels)
179 (if debug
180 (progn
181 (format t "~%")
182 (format t "~S~%" (send m :doc))
183 (format t "X: ~S~%" (send m :x))
184 (format t "Y: ~S~%" (send m :y))))
185 (if print (send m :display))
191 (defmeth regression-model-proto :isnew ()
192 (send self :needs-computing t))
194 (defmeth regression-model-proto :save ()
195 "Message args: ()
196 Returns an expression that will reconstruct the regression model."
197 `(regression-model ',(send self :x)
198 ',(send self :y)
199 :intercept ',(send self :intercept)
200 :weights ',(send self :weights)
201 :included ',(send self :included)
202 :predictor-names ',(send self :predictor-names)
203 :response-name ',(send self :response-name)
204 :case-labels ',(send self :case-labels)))
206 ;;; Computing and Display Methods
208 ;; [X|Y]t [X|Y]
209 ;; = XtX XtY
210 ;; YtX YtY
211 ;; so with (= (dim X) (list n p))
212 ;; we end up with p x p p x 1
213 ;; 1 x p 1 x 1
215 ;; and this can be implemented by
217 (setf XY (bind2 X Y :by :row))
218 (setf XYtXY (m* (transpose XY) XY))
220 ;; which is too procedural. Sigh, I meant
222 (setf XYtXY (let ((XY (bind2 X Y :by :row)))
223 (m* (transpose XY) XY)))
225 ;; which at least looks lispy.
227 (defmeth regression-model-proto :compute ()
228 "Message args: ()
229 Recomputes the estimates. For internal use by other messages"
230 (let* ((included (if-else (send self :included) 1d0 0d0))
231 (x (send self :x))
232 (y (send self :y))
233 (intercept (send self :intercept)) ;; T/nil
234 (weights (send self :weights)) ;; vector-like or nil
235 (w (if weights (* included weights) included))
236 (n (matrix-dimension x 0))
237 (p (if intercept
238 (1- (matrix-dimension x 1))
239 (matrix-dimension x 1))) ;; remove intercept from # params -- right?
240 (tss 0)
241 (res (make-vector (nrows x) :type :column :initial-element 0d0)) ; (compute-residuals y yhat)
242 (tol 0.000001
243 ;; (* 0.001 (reduce #'* (mapcar #'standard-deviation (list-of-columns x))))
245 (format t
246 "~%REMVME: regr-mdl-prto :compute~%x= ~A~%y= ~A~% tss= ~A~% tol= ~A~% w= ~A~% n= ~A~% res= ~A~%"
247 x y tss tol w n p res)
249 ;; (send self :beta-coefficents (lm x y)) ;; FIXME!
250 ;; (send self :xtxinv (xtxinv x)) ;; not settable?
252 (setf (proto-slot-value 'total-sum-of-squares) tss)
253 (setf (proto-slot-value 'residual-sum-of-squares)
255 ;; (m* (ones 1 n) (v* res res))
258 (defmeth regression-model-proto :needs-computing (&optional set)
259 "Message args: ( &optional set )
261 If value given, sets the flag for whether (re)computation is needed to
262 update the model fits."
263 (send self :nop)
264 (if set (setf (proto-slot-value 'betahat) nil))
265 (null (proto-slot-value 'betahat)))
267 (defmeth regression-model-proto :display ()
268 "Message args: ()
270 Prints the least squares regression summary. Variables not used in the fit
271 are marked as aliased."
272 (let ((coefs (vector-like->list (send self :coef-estimates)))
273 (se-s (send self :coef-standard-errors))
274 (x (send self :x))
275 (p-names (send self :predictor-names)))
276 (if (send self :weights)
277 (format t "~%Weighted Least Squares Estimates:~2%")
278 (format t "~%Least Squares Estimates:~2%"))
279 (when (send self :intercept)
280 (format t "Constant ~10f ~A~%"
281 (car coefs) (list (car se-s)))
282 (setf coefs (cdr coefs))
283 (setf se-s (cdr se-s)))
284 (dotimes (i (array-dimension x 1))
285 (cond
286 ((member i (send self :basis))
287 (format t "~22a ~10f ~A~%"
288 (select p-names i) (car coefs) (list (car se-s)))
289 (setf coefs (cdr coefs) se-s (cdr se-s)))
290 (t (format t "~22a aliased~%" (select p-names i)))))
291 (format t "~%")
292 (format t "R Squared: ~10f~%" (send self :r-squared))
293 (format t "Sigma hat: ~10f~%" (send self :sigma-hat))
294 (format t "Number of cases: ~10d~%" (send self :num-cases))
295 (if (/= (send self :num-cases) (send self :num-included))
296 (format t "Number of cases used: ~10d~%" (send self :num-included)))
297 (format t "Degrees of freedom: ~10d~%" (send self :df))
298 (format t "~%")))
300 ;;; Slot accessors and mutators
302 (defmeth regression-model-proto :doc (&optional new-doc append)
303 "Message args: (&optional new-doc)
305 Returns the DOC-STRING as supplied to m.
306 Additionally, with an argument NEW-DOC, sets the DOC-STRING to
307 NEW-DOC. In this setting, when APPEND is T, don't replace and just
308 append NEW-DOC to DOC."
309 (send self :nop)
310 (when (and new-doc (stringp new-doc))
311 (setf (proto-slot-value 'doc)
312 (if append
313 (concatenate 'string
314 (proto-slot-value 'doc)
315 new-doc)
316 new-doc)))
317 (proto-slot-value 'doc))
320 (defmeth regression-model-proto :x (&optional new-x)
321 "Message args: (&optional new-x)
323 With no argument returns the x matrix-like as supplied to m. With an
324 argument, NEW-X sets the x matrix-like to NEW-X and recomputes the
325 estimates."
326 (when (and new-x (typep new-x 'matrix-like))
327 (setf (proto-slot-value 'x) new-x)
328 (send self :needs-computing t))
329 (proto-slot-value 'x))
331 (defmeth regression-model-proto :y (&optional new-y)
332 "Message args: (&optional new-y)
334 With no argument returns the y vector-like as supplied to m. With an
335 argument, NEW-Y sets the y vector-like to NEW-Y and recomputes the
336 estimates."
337 (when (and new-y
338 (typep new-y 'vector-like))
339 (setf (proto-slot-value 'y) new-y) ;; fixme -- pls set slot value to a vector-like!
340 (send self :needs-computing t))
341 (proto-slot-value 'y))
343 (defmeth regression-model-proto :intercept (&optional (val nil set))
344 "Message args: (&optional new-intercept)
346 With no argument returns T if the model includes an intercept term,
347 nil if not. With an argument NEW-INTERCEPT the model is changed to
348 include or exclude an intercept, according to the value of
349 NEW-INTERCEPT."
350 (when set
351 (setf (proto-slot-value 'intercept) val)
352 (send self :needs-computing t))
353 (proto-slot-value 'intercept))
355 (defmeth regression-model-proto :weights (&optional (new-w nil set))
356 "Message args: (&optional new-w)
358 With no argument returns the weight vector-like as supplied to m; NIL
359 means an unweighted model. NEW-W sets the weights vector-like to NEW-W
360 and recomputes the estimates."
361 (when set
362 #| ;; probably need to use "check-type" or similar?
363 (and set nil
364 (or (= new-w nil)
365 (typep new-w 'vector-like)))
367 (setf (proto-slot-value 'weights) new-w)
368 (send self :needs-computing t))
369 (proto-slot-value 'weights))
371 (defmeth regression-model-proto :total-sum-of-squares ()
372 "Message args: ()
374 Returns the total sum of squares around the mean.
375 This is recomputed if an update is needed."
376 (if (send self :needs-computing)
377 (send self :compute))
378 (proto-slot-value 'total-sum-of-squares))
380 (defmeth regression-model-proto :residual-sum-of-squares ()
381 "Message args: ()
383 Returns the residual sum of squares for the model.
384 This is recomputed if an update is needed."
385 (if (send self :needs-computing)
386 (send self :compute))
387 (proto-slot-value 'residual-sum-of-squares))
389 (defmeth regression-model-proto :basis ()
390 "Message args: ()
392 Returns the indices of the variables used in fitting the model, in a
393 sequence.
394 This is recomputed if an update is needed."
395 (if (send self :needs-computing)
396 (send self :compute))
397 (proto-slot-value 'basis))
399 (defmeth regression-model-proto :included (&optional new-included)
400 "Message args: (&optional new-included)
402 With no argument, NIL means a case is not used in calculating
403 estimates, and non-nil means it is used. NEW-INCLUDED is a sequence
404 of length of y of nil and t to select cases. Estimates are
405 recomputed."
406 (when new-included
408 (and new-included
409 (= (length new-included) (send self :num-cases)))
411 (setf (proto-slot-value 'included) (copy-seq new-included))
412 (send self :needs-computing t))
413 (if (proto-slot-value 'included)
414 (proto-slot-value 'included)
415 (repeat t (send self :num-cases))))
417 (defmeth regression-model-proto :predictor-names (&optional (names nil set))
418 "Message args: (&optional (names nil set))
420 With no argument returns the predictor names. NAMES sets the names."
421 (if set (setf (proto-slot-value 'predictor-names) (mapcar #'string names)))
422 (let ((p (matrix-dimension (send self :x) 1))
423 (p-names (proto-slot-value 'predictor-names)))
424 (if (not (and p-names (= (length p-names) p)))
425 (setf (proto-slot-value 'predictor-names)
426 (mapcar #'(lambda (a) (format nil "Variable ~a" a))
427 (iseq 0 (- p 1))))))
428 (proto-slot-value 'predictor-names))
430 (defmeth regression-model-proto :response-name (&optional (name "Y" set))
431 "Message args: (&optional name)
433 With no argument returns the response name. NAME sets the name."
434 (send self :nop)
435 (if set (setf (proto-slot-value 'response-name) (if name (string name) "Y")))
436 (proto-slot-value 'response-name))
438 (defmeth regression-model-proto :case-labels (&optional (labels nil set))
439 "Message args: (&optional labels)
440 With no argument returns the case-labels. LABELS sets the labels."
441 (if set (setf (proto-slot-value 'case-labels)
442 (if labels
443 (mapcar #'string labels)
444 (mapcar #'(lambda (x) (format nil "~d" x))
445 (iseq 0 (- (send self :num-cases) 1))))))
446 (proto-slot-value 'case-labels))
449 ;;; Other Methods
450 ;;; None of these methods access any slots directly.
453 (defmeth regression-model-proto :num-cases ()
454 "Message args: ()
455 Returns the number of cases in the model."
456 (nelts (send self :y))) ; # cases in data, must accomodate weights or masking!
458 (defmeth regression-model-proto :num-included ()
459 "Message args: ()
460 Returns the number of cases used in the computations."
461 (sum (if-else (send self :included) 1 0)))
463 (defmeth regression-model-proto :num-coefs ()
464 "Message args: ()
465 Returns the number of coefficients in the fit model (including the
466 intercept if the model includes one)."
467 (if (send self :intercept)
468 (+ 1 (ncols (send self :x)))
469 (ncols (send self :x))))
471 (defmeth regression-model-proto :df ()
472 "Message args: ()
473 Returns the number of degrees of freedom in the model."
474 (- (send self :num-included) (send self :num-coefs)))
476 (defmeth regression-model-proto :x-matrix ()
477 "Message args: ()
478 Returns the X matrix for the model, including a column of 1's, if
479 appropriate. Columns of X matrix correspond to entries in basis."
480 (let ((m (select (send self :x)
481 (iseq 0 (- (send self :num-cases) 1))
482 (send self :basis))))
483 (if (send self :intercept)
484 (bind2 (repeat 1 (send self :num-cases)) m)
485 m)))
487 (defmeth regression-model-proto :leverages ()
488 "Message args: ()
489 Returns the diagonal elements of the hat matrix."
490 (let* ((x (send self :x-matrix))
491 (raw-levs
492 (m* (m* (m* x
493 (send self :xtxinv))
495 (repeat 1 (send self :num-coefs)))))
496 (if (send self :weights)
497 (m* (send self :weights) raw-levs)
498 raw-levs)))
500 (defmeth regression-model-proto :fit-values ()
501 "Message args: ()
502 Returns the fitted values for the model."
503 (m* (send self :x-matrix)
504 (send self :coef-estimates)))
506 (defmeth regression-model-proto :raw-residuals ()
507 "Message args: ()
508 Returns the raw residuals for a model."
509 (v- (send self :y) (send self :fit-values)))
511 (defmeth regression-model-proto :residuals ()
512 "Message args: ()
513 Returns the raw residuals for a model without weights. If the model
514 includes weights the raw residuals times the square roots of the weights
515 are returned."
516 (let ((raw-residuals (send self :raw-residuals))
517 (weights (send self :weights)))
518 (if weights (* (sqrt weights) raw-residuals) raw-residuals)))
520 (defmeth regression-model-proto :sum-of-squares ()
521 "Message args: ()
522 Returns the error sum of squares for the model."
523 (send self :residual-sum-of-squares))
525 (defmeth regression-model-proto :sigma-hat ()
526 "Message args: ()
527 Returns the estimated standard deviation of the deviations about the
528 regression line."
529 (let ((ss (send self :sum-of-squares))
530 (df (send self :df)))
531 (if (/= df 0) (sqrt (/ ss df)))))
533 ;; for models without an intercept the 'usual' formula for R^2 can give
534 ;; negative results; hence the max.
535 (defmeth regression-model-proto :r-squared ()
536 "Message args: ()
537 Returns the sample squared multiple correlation coefficient, R squared, for
538 the regression."
539 (max (- 1 (/ (send self :sum-of-squares) (send self :total-sum-of-squares)))
542 (defmeth regression-model-proto :coef-estimates ()
543 "Message args: ()
545 Returns the OLS (ordinary least squares) estimates of the regression
546 coefficients. Entries beyond the intercept correspond to entries in
547 basis."
548 (let ((x (send self :x)))
549 (princ x)))
551 (let ((n (matrix-dimension (send self :x) 1))
552 (indices (flatten-list
553 (if (send self :intercept)
554 (cons 0 (+ 1 (send self :basis)))
555 (list (+ 1 (send self :basis))))))
556 (x (send self :x)))
557 (format t "~%REMOVEME2: Coef-ests: ~% Sweep Matrix: ~A ~% array dim 1: ~A ~% Swept indices: ~A ~% basis: ~A"
558 x n indices (send self :basis))
559 (coerce (compound-data-seq (select m (1+ n) indices)) 'list))) ;; ERROR
562 (defmeth regression-model-proto :xtxinv ()
563 "Message args: ()
564 Returns ((X^T) X)^(-1) or ((X^T) W X)^(-1)."
565 (xtxinv (send self x)))
567 (defmeth regression-model-proto :coef-standard-errors ()
568 "Message args: ()
569 Returns estimated standard errors of coefficients. Entries beyond the
570 intercept correspond to entries in basis."
571 (let ((s (send self :sigma-hat)))
572 (if s (* (send self :sigma-hat) (sqrt (diagonalf (send self :xtxinv)))))))
574 (defmeth regression-model-proto :studentized-residuals ()
575 "Message args: ()
576 Computes the internally studentized residuals for included cases and externally studentized residuals for excluded cases."
577 (let ((res (send self :residuals))
578 (lev (send self :leverages))
579 (sig (send self :sigma-hat))
580 (inc (send self :included)))
581 (if-else inc
582 (/ res (* sig (sqrt (max .00001 (- 1 lev))))) ; vectorize max
583 (/ res (* sig (sqrt (+ 1 lev)))))))
585 (defmeth regression-model-proto :externally-studentized-residuals ()
586 "Message args: ()
587 Computes the externally studentized residuals."
588 (let* ((res (send self :studentized-residuals))
589 (df (send self :df)))
590 (if-else (send self :included)
591 (* res (sqrt (/ (- df 1) (- df (v* res res)))))
592 res)))
594 (defmeth regression-model-proto :cooks-distances ()
595 "Message args: ()
596 Computes Cook's distances."
597 (let ((lev (send self :leverages))
598 (res (/ (v* (send self :studentized-residuals)
599 (send self :studentized-residuals))
600 (send self :num-coefs))))
601 (if-else (send self :included) (* res (/ lev (- 1 lev) )) (* res lev))))
604 (defun plot-points (x y &rest args)
605 "need to fix."
606 (error "Graphics not implemented yet."))
611 ;; Can not plot points yet!!
612 (defmeth regression-model-proto :plot-residuals (&optional x-values)
613 "Message args: (&optional x-values)
614 Opens a window with a plot of the residuals. If X-VALUES are not supplied
615 the fitted values are used. The plot can be linked to other plots with the
616 link-views function. Returns a plot object."
617 (plot-points (if x-values x-values (send self :fit-values))
618 (send self :residuals)
619 :title "Residual Plot"
620 :point-labels (send self :case-labels)))
624 (defmeth regression-model-proto :plot-bayes-residuals
625 (&optional x-values)
626 "Message args: (&optional x-values)
628 Opens a window with a plot of the standardized residuals and two
629 standard error bars for the posterior distribution of the actual
630 deviations from the line. See Chaloner and Brant. If X-VALUES are not
631 supplied the fitted values are used. The plot can be linked to other
632 plots with the link-views function. Returns a plot object."
634 (let* ((r (/ (send self :residuals)
635 (send self :sigma-hat)))
636 (d (* 2 (sqrt (send self :leverages))))
637 (low (- r d))
638 (high (+ r d))
639 (x-values (if x-values x-values (send self :fit-values)))
640 (p (plot-points x-values r
641 :title "Bayes Residual Plot"
642 :point-labels (send self :case-labels))))
643 (map 'list #'(lambda (a b c d) (send p :plotline a b c d nil))
644 x-values low x-values high)
645 (send p :adjust-to-data)
649 ;;;; Other code
652 (defun print-lm (lm-obj)
653 "transcribed from R"
654 (p (rank lm-obj)
655 (when (= p 0)
656 ;; EVIL LOGIC! Just to store for now.
657 (let ()
658 (n (length (residuals lm-obj)))
659 (w (if (weights lm-obj)
660 (weights lm-obj)
661 (ones n 1)))
662 (r (if (weights lm-obj)
663 (residuals lm-obj)
664 (v.* (residuals lm-obj)
665 (mapcar #'sqrt (weights lm-obj)))))
666 (rss (sum (v.* r r)))
667 (resvar (/ rss (- n p)))
668 ;; then answer, to be encapsulated in a struct/class
669 ;; instance,
670 (aliased (is.na (coef lm-obj)))
671 (residuals r)
672 (df (list 0 n (length aliased)))
673 (coefficients (list 'NA 0d0 4d0))o
674 (sigma (sqrt resvar))
675 (r.squared 0d0)
676 (adj.r.squared 0d0)))
678 ;;otherwise...
679 (when (not (= p 0))
680 (let ((n (nrows (qr lm-obj)))
681 (rdf (- n p))
682 ))))
684 (lm *xv+1* *y2*)
685 (lm (transpose *xv*) *y2*)
687 (princ "Linear Models Code setup")