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R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Sun, 07 Dec 2008 08:37:28 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/07/t1228664318cmyqg4959sjuldi.htm/, Retrieved Sun, 19 May 2024 10:44:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30101, Retrieved Sun, 19 May 2024 10:44:46 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

175

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMP     [Standard Deviation-Mean Plot] [step 1] [2008-12-07 15:37:28] [e515c0250d6233b5d2604259ab52cebe] [Current]

Feedback Forum

2008-12-10 15:19:52 [Ken Van den Heuvel] [reply] 
De SMP analyse splitst onze data in sequentiële stukjes. Voor elk stukje heeft de module een gemiddelde ( mean) en een standaard afwijking ( standard deviation) berekent.  
 
Elk stukje stelt 1 jaar voor. De bolletjes in de grafiek stellen deze verschillende jaren voor.  
 
Als we een lijn zouden trekken door de sd mean plot bekomen we een lijn met een positieve helling. Als de werkloosheid stijgt, zal de standaard fout dus ook stijgen. 
 
Beta = 0.048 en dus positief, er is dus een positieve helling. Beta is significant verschillend van 0. 
De p-value is 0.00382. De kans dat ons resultaat op toeval berust is dus slechts 0,38%. 
 
Uit de tabel kunnen we afleiden dat Lambda gelijk is aan 0.47. We ronden dit af tot een wat meer bruikbaar resultaat van 0.5 (in onze uiteindelijke formule verheffen we Yt immers tot de macht Lambda, een macht van 0,5 kan vervolgens als een vierkantswortel geschreven worden. 
2008-12-14 14:32:25 [Chi-Kwong Man] [reply] 
Grafiek 1 ziet eruit als een scatterplot omdat je niet weet wanneer het gebeurd is, dus moeten we de outliers beoordelen (rechter of linkerkant), dit doen we door een lijn door te trekken. Aan de hand van de beta-coëfficiënt (0.048) kunnen we vaststellen dat de helling van de scatterplot positief is. De kans dat deze resultaat op toeval berust is slechts 0,38%. De lambda bedraagt hier 0,47. Dit ronden we af naar 0,5 om later te gebruiken. De 2 voorwaarden om lambda te gebruiken zijn: beta moet significant verschillend zijn van 0 en dat er geen echte outliers zijn op de scatterplot.
2008-12-15 12:20:47 [Kristof Augustyns] [reply] 
Hier zie je een scatterplot. De helling hiervan is positief. 
De bolletjes die je ziet geven de verschillende jaren aan. 
Bij het tekenen van een rechte door die bolletjes, bekomen we een mooie rechte van links onder naar rechts boven. 
Stijging werkloosheid = stijging standaardfout. 
Beta is positief dus een stijgende helling. 
p-value is 0.00382 en dit wil zeggen dat er 0,38% kans is dat het resultaat berust op toeval. 
Het is hier dus juist gezegd.
2008-12-15 16:51:47 [Lindsay Heyndrickx] [reply] 
Hier is een correcte berekening gemaakt. De SMP analyse splitst onze data in sequentiële stukjes. Voor elk stukje heeft de module een gemiddelde ( mean) en een standaard afwijking ( standard deviation) berekend.  
Elk stukje stelt 1 jaar voor. De bolletjes in de grafiek stellen deze verschillende jaren voor.  
In de tabellen heeft de p-waarde betrekking op de beta coefficient. De beta coefficient is significant verschillend van nul want de kans dat het op toeval berust is maar 0.03(p-waarde). De lambda is hier 0.46 en wordt afgerond naar 0.5 om beter met te kunnen werken. 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30101&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30101&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30101&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	227.733333333333	29.1940010442162	106
2	363.65	36.3267119348834	139.3
3	328.916666666667	93.5458451857438	273.6
4	205.45	30.3247123946491	89.5
5	188.333333333333	27.3773739803621	86
6	181.25	26.1571995999016	85.2
7	353.341666666667	36.2089506346236	110.8
8	285.308333333333	46.6051783766048	138.5
9	275.125	35.0509272345255	108.8
10	285.85	30.7409262296136	86.7
11	460.166666666667	56.0969831198748	147.3
12	373.95	53.1021228817215	150.3
13	385.1	35.1442999387072	115.5
14	471.358333333333	64.2130184808676	179.1
15	394.208333333333	40.6847628018454	138.7
16	407	46.6030432092544	147.6
17	378.575	49.9696839912143	132
18	336.633333333333	51.5290973993129	146.3
19	287.841666666667	33.2699826033054	112.7
20	297.566666666667	30.476438987082	117
21	281.666666666667	40.7140434412173	131.1
22	283.033333333333	28.4860837901065	109
23	408.85	48.934882520271	128.5
24	499.333333333333	37.5159925494408	109.6
25	484.008333333333	48.4390236808249	133.1
26	430.433333333333	37.4665022103584	108.4
27	507.583333333333	53.8722703730919	196.2
28	782.975	48.4555489832973	137.4
29	728.8	53.3077684940777	187
30	685.558333333333	72.5442618285032	222.9
31	604.716666666667	50.4040372360882	144

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 227.733333333333 & 29.1940010442162 & 106 \tabularnewline
2 & 363.65 & 36.3267119348834 & 139.3 \tabularnewline
3 & 328.916666666667 & 93.5458451857438 & 273.6 \tabularnewline
4 & 205.45 & 30.3247123946491 & 89.5 \tabularnewline
5 & 188.333333333333 & 27.3773739803621 & 86 \tabularnewline
6 & 181.25 & 26.1571995999016 & 85.2 \tabularnewline
7 & 353.341666666667 & 36.2089506346236 & 110.8 \tabularnewline
8 & 285.308333333333 & 46.6051783766048 & 138.5 \tabularnewline
9 & 275.125 & 35.0509272345255 & 108.8 \tabularnewline
10 & 285.85 & 30.7409262296136 & 86.7 \tabularnewline
11 & 460.166666666667 & 56.0969831198748 & 147.3 \tabularnewline
12 & 373.95 & 53.1021228817215 & 150.3 \tabularnewline
13 & 385.1 & 35.1442999387072 & 115.5 \tabularnewline
14 & 471.358333333333 & 64.2130184808676 & 179.1 \tabularnewline
15 & 394.208333333333 & 40.6847628018454 & 138.7 \tabularnewline
16 & 407 & 46.6030432092544 & 147.6 \tabularnewline
17 & 378.575 & 49.9696839912143 & 132 \tabularnewline
18 & 336.633333333333 & 51.5290973993129 & 146.3 \tabularnewline
19 & 287.841666666667 & 33.2699826033054 & 112.7 \tabularnewline
20 & 297.566666666667 & 30.476438987082 & 117 \tabularnewline
21 & 281.666666666667 & 40.7140434412173 & 131.1 \tabularnewline
22 & 283.033333333333 & 28.4860837901065 & 109 \tabularnewline
23 & 408.85 & 48.934882520271 & 128.5 \tabularnewline
24 & 499.333333333333 & 37.5159925494408 & 109.6 \tabularnewline
25 & 484.008333333333 & 48.4390236808249 & 133.1 \tabularnewline
26 & 430.433333333333 & 37.4665022103584 & 108.4 \tabularnewline
27 & 507.583333333333 & 53.8722703730919 & 196.2 \tabularnewline
28 & 782.975 & 48.4555489832973 & 137.4 \tabularnewline
29 & 728.8 & 53.3077684940777 & 187 \tabularnewline
30 & 685.558333333333 & 72.5442618285032 & 222.9 \tabularnewline
31 & 604.716666666667 & 50.4040372360882 & 144 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30101&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]227.733333333333[/C][C]29.1940010442162[/C][C]106[/C][/ROW]
[ROW][C]2[/C][C]363.65[/C][C]36.3267119348834[/C][C]139.3[/C][/ROW]
[ROW][C]3[/C][C]328.916666666667[/C][C]93.5458451857438[/C][C]273.6[/C][/ROW]
[ROW][C]4[/C][C]205.45[/C][C]30.3247123946491[/C][C]89.5[/C][/ROW]
[ROW][C]5[/C][C]188.333333333333[/C][C]27.3773739803621[/C][C]86[/C][/ROW]
[ROW][C]6[/C][C]181.25[/C][C]26.1571995999016[/C][C]85.2[/C][/ROW]
[ROW][C]7[/C][C]353.341666666667[/C][C]36.2089506346236[/C][C]110.8[/C][/ROW]
[ROW][C]8[/C][C]285.308333333333[/C][C]46.6051783766048[/C][C]138.5[/C][/ROW]
[ROW][C]9[/C][C]275.125[/C][C]35.0509272345255[/C][C]108.8[/C][/ROW]
[ROW][C]10[/C][C]285.85[/C][C]30.7409262296136[/C][C]86.7[/C][/ROW]
[ROW][C]11[/C][C]460.166666666667[/C][C]56.0969831198748[/C][C]147.3[/C][/ROW]
[ROW][C]12[/C][C]373.95[/C][C]53.1021228817215[/C][C]150.3[/C][/ROW]
[ROW][C]13[/C][C]385.1[/C][C]35.1442999387072[/C][C]115.5[/C][/ROW]
[ROW][C]14[/C][C]471.358333333333[/C][C]64.2130184808676[/C][C]179.1[/C][/ROW]
[ROW][C]15[/C][C]394.208333333333[/C][C]40.6847628018454[/C][C]138.7[/C][/ROW]
[ROW][C]16[/C][C]407[/C][C]46.6030432092544[/C][C]147.6[/C][/ROW]
[ROW][C]17[/C][C]378.575[/C][C]49.9696839912143[/C][C]132[/C][/ROW]
[ROW][C]18[/C][C]336.633333333333[/C][C]51.5290973993129[/C][C]146.3[/C][/ROW]
[ROW][C]19[/C][C]287.841666666667[/C][C]33.2699826033054[/C][C]112.7[/C][/ROW]
[ROW][C]20[/C][C]297.566666666667[/C][C]30.476438987082[/C][C]117[/C][/ROW]
[ROW][C]21[/C][C]281.666666666667[/C][C]40.7140434412173[/C][C]131.1[/C][/ROW]
[ROW][C]22[/C][C]283.033333333333[/C][C]28.4860837901065[/C][C]109[/C][/ROW]
[ROW][C]23[/C][C]408.85[/C][C]48.934882520271[/C][C]128.5[/C][/ROW]
[ROW][C]24[/C][C]499.333333333333[/C][C]37.5159925494408[/C][C]109.6[/C][/ROW]
[ROW][C]25[/C][C]484.008333333333[/C][C]48.4390236808249[/C][C]133.1[/C][/ROW]
[ROW][C]26[/C][C]430.433333333333[/C][C]37.4665022103584[/C][C]108.4[/C][/ROW]
[ROW][C]27[/C][C]507.583333333333[/C][C]53.8722703730919[/C][C]196.2[/C][/ROW]
[ROW][C]28[/C][C]782.975[/C][C]48.4555489832973[/C][C]137.4[/C][/ROW]
[ROW][C]29[/C][C]728.8[/C][C]53.3077684940777[/C][C]187[/C][/ROW]
[ROW][C]30[/C][C]685.558333333333[/C][C]72.5442618285032[/C][C]222.9[/C][/ROW]
[ROW][C]31[/C][C]604.716666666667[/C][C]50.4040372360882[/C][C]144[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30101&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30101&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	227.733333333333	29.1940010442162	106
2	363.65	36.3267119348834	139.3
3	328.916666666667	93.5458451857438	273.6
4	205.45	30.3247123946491	89.5
5	188.333333333333	27.3773739803621	86
6	181.25	26.1571995999016	85.2
7	353.341666666667	36.2089506346236	110.8
8	285.308333333333	46.6051783766048	138.5
9	275.125	35.0509272345255	108.8
10	285.85	30.7409262296136	86.7
11	460.166666666667	56.0969831198748	147.3
12	373.95	53.1021228817215	150.3
13	385.1	35.1442999387072	115.5
14	471.358333333333	64.2130184808676	179.1
15	394.208333333333	40.6847628018454	138.7
16	407	46.6030432092544	147.6
17	378.575	49.9696839912143	132
18	336.633333333333	51.5290973993129	146.3
19	287.841666666667	33.2699826033054	112.7
20	297.566666666667	30.476438987082	117
21	281.666666666667	40.7140434412173	131.1
22	283.033333333333	28.4860837901065	109
23	408.85	48.934882520271	128.5
24	499.333333333333	37.5159925494408	109.6
25	484.008333333333	48.4390236808249	133.1
26	430.433333333333	37.4665022103584	108.4
27	507.583333333333	53.8722703730919	196.2
28	782.975	48.4555489832973	137.4
29	728.8	53.3077684940777	187
30	685.558333333333	72.5442618285032	222.9
31	604.716666666667	50.4040372360882	144

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	25.0818554501784
beta	0.0488516650103526
S.D.	0.0155384837695400
T-STAT	3.14391453728042
p-value	0.00382792717820019

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 25.0818554501784 \tabularnewline
beta & 0.0488516650103526 \tabularnewline
S.D. & 0.0155384837695400 \tabularnewline
T-STAT & 3.14391453728042 \tabularnewline
p-value & 0.00382792717820019 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30101&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]25.0818554501784[/C][/ROW]
[ROW][C]beta[/C][C]0.0488516650103526[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0155384837695400[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.14391453728042[/C][/ROW]
[ROW][C]p-value[/C][C]0.00382792717820019[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30101&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30101&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	25.0818554501784
beta	0.0488516650103526
S.D.	0.0155384837695400
T-STAT	3.14391453728042
p-value	0.00382792717820019

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.596066412617832
beta	0.532942026074987
S.D.	0.115396834084912
T-STAT	4.61834183148243
p-value	7.31833172336402e-05
Lambda	0.467057973925013

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.596066412617832 \tabularnewline
beta & 0.532942026074987 \tabularnewline
S.D. & 0.115396834084912 \tabularnewline
T-STAT & 4.61834183148243 \tabularnewline
p-value & 7.31833172336402e-05 \tabularnewline
Lambda & 0.467057973925013 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30101&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.596066412617832[/C][/ROW]
[ROW][C]beta[/C][C]0.532942026074987[/C][/ROW]
[ROW][C]S.D.[/C][C]0.115396834084912[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.61834183148243[/C][/ROW]
[ROW][C]p-value[/C][C]7.31833172336402e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]0.467057973925013[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30101&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30101&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.596066412617832
beta	0.532942026074987
S.D.	0.115396834084912
T-STAT	4.61834183148243
p-value	7.31833172336402e-05
Lambda	0.467057973925013

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
(n <- length(x))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code