::Free Statistics and Forecasting Software::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This R module demonstrates with real data that gas consumption as usually measured by drivers is quite variable, and with no apparent trend, until a nonparametric smoother reveals a very distinct seasonal pattern. Ask students if they see anything in the data. The first graph you see is the raw data, and in the next graph the smoothed fit is displayed. The point of the demo is that nonparametric smoothing is easy to understand and useful, and should be taught in intro stats courses. The program can also be used to demonstrate the trial-and-error approach to choosing the degree of smoothing, by varying the parameter 'span'.

Click here to edit the underlying code of this R Module.

Span
Smooth?
TRUEFALSE
Chart options
Width:
Height:

Click here to edit the underlying code of this R Module.

---

Source code of R module
1	x <- c(1999.38
2	,1999.39
3	,1999.41
4	,1999.42
5	,1999.44
6	,1999.45
7	,1999.46
8	,1999.47
9	,1999.49
10	,1999.5
11	,1999.51
12	,1999.52
13	,1999.53
14	,1999.54
15	,1999.54
16	,1999.58
17	,1999.6
18	,1999.64
19	,1999.66
20	,1999.59
21	,1999.67
22	,1999.68
23	,1999.69
24	,1999.71
25	,1999.72
26	,1999.73
27	,1999.74
28	,1999.76
29	,1999.77
30	,1999.78
31	,1999.79
32	,1999.81
33	,1999.82
34	,1999.84
35	,1999.84
36	,1999.86
37	,1999.88
38	,1999.89
39	,1999.91
40	,1999.92
41	,1999.94
42	,1999.95
43	,1999.96
44	,1999.98
45	,2000
46	,2000.02
47	,2000.03
48	,2000.04
49	,2000.05
50	,2000.16
51	,2000.17
52	,2000.19
53	,2000.21
54	,2000.21
55	,2000.24
56	,2000.25
57	,2000.26
58	,2000.27
59	,2000.28
60	,2000.29
61	,2000.31
62	,2000.34
63	,2000.36
64	,2000.36
65	,2000.39
66	,2000.4
67	,2000.42
68	,2000.43
69	,2000.45
70	,2000.46
71	,2000.47
72	,2000.51
73	,2000.54
74	,2000.56
75	,2000.57
76	,2000.59
77	,2000.62
78	,2000.63
79	,2000.67
80	,2000.67
81	,2000.68
82	,2000.7
83	,2000.71
84	,2000.73
85	,2000.74
86	,2000.76
87	,2000.77
88	,2000.78
89	,2000.8
90	,2000.81
91	,2000.83
92	,2000.84
93	,2000.86
94	,2000.87
95	,2000.88
96	,2000.88
97	,2000.9
98	,2000.91
99	,2000.92
100	,2000.93
101	,2000.94
102	,2000.96
103	,2000.97
104	,2000.98
105	,2001.01
106	,2001.03
107	,2001.04
108	,2001.06
109	,2001.07
110	,2001.08
111	,2001.09
112	,2001.12
113	,2001.13
114	,2001.16
115	,2001.19
116	,2001.2
117	,2001.21
118	,2001.23
119	,2001.24
120	,2001.26
121	,2001.26
122	,2001.27
123	,2001.3
124	,2001.31
125	,2001.33
126	,2001.34
127	,2001.36
128	,2001.36
129	,2001.38
130	,2001.4
131	,2001.41
132	,2001.43
133	,2001.45
134	,2001.46
135	,2001.48
136	,2001.5
137	,2001.51
138	,2001.53
139	,2001.55
140	,2001.57
141	,2001.58
142	,2001.59
143	,2001.61
144	,2001.62
145	,2001.67
146	,2001.69
147	,2001.72
148	,2001.73
149	,2001.74
150	,2001.76
151	,2001.77
152	,2001.78
153	,2001.8
154	,2001.81
155	,2001.82
156	,2001.84
157	,2001.89
158	,2001.9
159	,2001.91
160	,2001.92
161	,2001.94
162	,2001.96
163	,2001.98
164	,2002.01
165	,2002.02
166	,2002.04
167	,2002.06
168	,2002.07
169	,2002.09
170	,2002.1
171	,2002.12
172	,2002.14
173	,2002.15
174	,2002.16
175	,2002.17
176	,2002.19
177	,2002.2
178	,2002.21
179	,2002.24
180	,2002.24
181	,2002.27
182	,2002.28
183	,2002.29
184	,2002.31
185	,2002.35
186	,2002.37
187	,2002.4
188	,2002.34
189	,2002.44
190	,2002.5
191	,2002.56
192	,2002.6
193	,2002.64
194	,2002.65
195	,2002.67
196	,2002.69
197	,2002.7
198	,2002.72
199	,2002.72
200	,2002.74
201	,2002.76
202	,2002.77
203	,2002.78
204	,2002.8
205	,2002.82
206	,2002.84
207	,2002.84
208	,2002.87
209	,2002.89
210	,2002.9
211	,2002.91
212	,2002.92
213	,2002.93
214	,2002.99
215	,2003.01
216	,2003.04
217	,2003.05
218	,2003.07
219	,2003.08
220	,2003.1
221	,2003.13
222	,2003.15
223	,2003.18
224	,2003.19
225	,2003.2
226	,2003.22
227	,2003.23
228	,2003.24
229	,2003.25
230	,2003.26
231	,2003.27
232	,2003.29
233	,2003.3
234	,2003.32
235	,2003.33
236	,2003.34
237	,2003.36
238	,2003.36
239	,2003.37
240	,2003.39
241	,2003.41
242	,2003.42
243	,2003.43
244	,2003.46
245	,2003.47
246	,2003.48
247	,2003.49
248	,2003.51
249	,2003.54
250	,2003.55
251	,2003.56
252	,2003.58
253	,2003.61
254	,2003.66
255	,2003.68
256	,2003.68
257	,2003.7
258	,2003.72
259	,2003.73
260	,2003.74
261	,2003.76
262	,2003.81
263	,2003.82
264	,2003.84
265	,2003.85
266	,2003.86
267	,2003.88
268	,2003.88
269	,2003.89
270	,2003.91
271	,2003.92
272	,2003.94
273	,2003.95
274	,2003.96
275	,2003.99
276	,2004.02
277	,2004.05
278	,2004.03
279	,2004.07
280	,2004.08
281	,2004.09
282	,2004.11
283	,2004.15
284	,2004.17
285	,2004.19
286	,2004.21
287	,2004.24
288	,2004.26
289	,2004.27
290	,2004.28
291	,2004.3
292	,2004.31
293	,2004.33
294	,2004.34
295	,2004.36
296	,2004.38
297	,2004.39
298	,2004.41
299	,2004.43
300	,2004.44
301	,2004.46
302	,2004.48)
303	y <- c(10.69
304	,9.09
305	,11.29
306	,10.59
307	,9.97
308	,9.65
309	,9.18
310	,10.49
311	,9.27
312	,10.4
313	,8.9
314	,9.17
315	,10.4
316	,9.53
317	,8.19
318	,10.04
319	,9.37
320	,10.46
321	,10.09
322	,7.38
323	,10.56
324	,9.83
325	,9.57
326	,10.46
327	,12.2
328	,7.64
329	,10.26
330	,9.43
331	,9.94
332	,11.19
333	,10.17
334	,9.61
335	,10.28
336	,12.06
337	,9.73
338	,10.1
339	,10.63
340	,10.64
341	,11.24
342	,9.4
343	,11.78
344	,9.75
345	,12.3
346	,11.35
347	,10.97
348	,11.77
349	,11.09
350	,11.43
351	,10.92
352	,11.91
353	,11.17
354	,10.04
355	,10.32
356	,9.6
357	,9.56
358	,10.27
359	,8.69
360	,10.91
361	,9.64
362	,9.09
363	,10.39
364	,10.15
365	,10.2
366	,9.28
367	,10.66
368	,9.37
369	,10.14
370	,10.43
371	,10.24
372	,9.28
373	,10.38
374	,9.85
375	,10.81
376	,12.2
377	,9.47
378	,9.49
379	,8.9
380	,9.76
381	,9.62
382	,9.6
383	,9.99
384	,10.48
385	,9.56
386	,9.19
387	,9.94
388	,9.57
389	,10.4
390	,9.26
391	,10.69
392	,10.35
393	,10
394	,9.34
395	,10.45
396	,10.76
397	,9.74
398	,7.34
399	,11.21
400	,10.67
401	,9.22
402	,10.34
403	,10.66
404	,9.96
405	,12.11
406	,10.71
407	,10.09
408	,10.25
409	,9.96
410	,11.73
411	,9.71
412	,10.1
413	,10.29
414	,11.05
415	,10.35
416	,12
417	,10.56
418	,10.43
419	,8.19
420	,11.38
421	,9.95
422	,10.51
423	,8.61
424	,10.29
425	,10.11
426	,10.12
427	,9.84
428	,10.05
429	,10.13
430	,9.97
431	,10.13
432	,9.87
433	,9.92
434	,9.44
435	,9.71
436	,9.77
437	,9.82
438	,10.31
439	,8.82
440	,9.62
441	,9.64
442	,10.69
443	,9.08
444	,9.59
445	,9.57
446	,8.17
447	,9.99
448	,9.09
449	,9.66
450	,9.21
451	,9.44
452	,10.04
453	,9.3
454	,10.24
455	,10.15
456	,10.2
457	,11.36
458	,9.5
459	,9.96
460	,10.15
461	,11.02
462	,10.05
463	,10.65
464	,10.31
465	,11.42
466	,10.08
467	,10.44
468	,10.39
469	,10.74
470	,10.99
471	,11.02
472	,10.55
473	,10.72
474	,10.54
475	,10.67
476	,10.35
477	,9.68
478	,10.78
479	,9.8
480	,11.09
481	,10.45
482	,10.66
483	,10.65
484	,9.9
485	,9.55
486	,9.91
487	,10.26
488	,10.14
489	,9.82
490	,10.27
491	,10.12
492	,9.52
493	,9.05
494	,10.26
495	,9.4
496	,8.99
497	,8.98
498	,9.49
499	,10.42
500	,9.31
501	,9.13
502	,9.71
503	,10.3
504	,9.75
505	,9.05
506	,10.91
507	,10.09
508	,11.15
509	,10.69
510	,10.36
511	,10.56
512	,10.52
513	,10.32
514	,9.78
515	,12.11
516	,10.75
517	,11.12
518	,10.32
519	,12.33
520	,10.03
521	,11.4
522	,12.47
523	,13.57
524	,10.2
525	,10.2
526	,10.84
527	,9.61
528	,10.35
529	,10
530	,9.76
531	,10.3
532	,9.86
533	,10.52
534	,10.49
535	,10.14
536	,10.11
537	,6.86
538	,9.58
539	,10.17
540	,8.9
541	,10.54
542	,9.49
543	,10.23
544	,9.04
545	,10.47
546	,11.88
547	,10.55
548	,8.86
549	,11.71
550	,9.88
551	,9.07
552	,9.63
553	,10.5
554	,10.16
555	,7.65
556	,8.56
557	,10.51
558	,8.9
559	,9.7
560	,9.83
561	,9.73
562	,9.03
563	,10.18
564	,9.45
565	,11.27
566	,10.35
567	,10.76
568	,11.2
569	,11.08
570	,9.17
571	,12.67
572	,11.09
573	,10.32
574	,10.71
575	,10.88
576	,8.44
577	,10.15
578	,10.06
579	,9.76
580	,12.45
581	,10.02
582	,8.89
583	,10.66
584	,10.71
585	,10.52
586	,10.58
587	,10.15
588	,11.1
589	,9.96
590	,11.31
591	,9.51
592	,6.98
593	,10.55
594	,7.22
595	,10.16
596	,8.03
597	,9.77
598	,10.36
599	,9.63
600	,10.6
601	,9.6
602	,8.75
603	,10.32
604	,10.23)
605	merc.df <- as.data.frame(cbind(x,y))
606	colnames(merc.df) <- c("date1","lp100km")
607	span <- as.numeric(par1)
608	if (par2 == "TRUE") smooth <- TRUE else smooth <- FALSE
609	x=merc.df$date1
610	y=merc.df$lp100km
611	yl=loess(y~x,span=span)
612	bitmap(file="noloessplot.png")
613	plot(yl,col="darkgreen",type="p",main="5 years gas consumption, 1999-2004 (raw data)",xlab="decimal date",ylab="litres per 100 km")
614	dev.off()
615	if (smooth==TRUE)
616	{
617	bitmap(file="loessplot.png")
618	plot(yl,col="darkgreen",type="p",main="5 years gas consumption, 1999-2004 (incl. LOESS)",xlab="decimal date",ylab="litres per 100 km")
619	mn=mean(yl$y)
620	lines(yl$x,yl$fitted,col="red",lwd=3)
621	lines(yl$x,mn*rep(1,length(yl$x)),col="black",lwd=3)
622	dev.off()
623	bitmap(file="resplot.png")
624	plot(yl$x,yl$residuals,col="darkgreen",ylab="residuals from
625	smooth",xlab="decimal date",main="Residuals of (Data - Smooth)")
626	lines(yl$x,0*rep(1,length(yl$x)),col="black",lwd=3)
627	rl=loess(yl$residuals~yl$x,span=span)
628	lines(rl$x,rl$fitted,col="red",lwd=3)
629	dev.off()
630	}

Cite this software as:

Weldon Larry, (2008), Time Series Smoothing Example (v1.0.2) in Free Statistics Software (v1.1.23-r2), Office for Research Development and Education, URL http://www.wessa.net/rwasp_gas.wasp/

The R code is based on :

Weldon Larry, Stat Ed Programs for Demos in R, Simon Fraser University, URL http://www.stat.sfu.ca/~weldon/title.doc

Weldon Larry, R Programs for Statistics Education, Simon Fraser University, URL http://www.stat.sfu.ca/~weldon/Programs

Weldon Larry, Instructions for using R programs for Statistics Education, Simon Fraser University, URL http://www.stat.sfu.ca/~weldon/instructions.doc

To cite Wessa.net in publications use:
Wessa, P. (2008), Free Statistics Software, Office for Research Development and Education,
version 1.1.23-r2, URL http://www.wessa.net/

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