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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sun, 18 Dec 2011 07:35:43 -0500

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/2011/Dec/18/t1324211765usuljy7620x7jam.htm/, Retrieved Sun, 05 May 2024 19:27:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156772, Retrieved Sun, 05 May 2024 19:27:03 +0000

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Estimated Impact

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

-     [Kendall tau Correlation Matrix] [] [2010-12-05 17:44:33] [b98453cac15ba1066b407e146608df68]
- RMPD  [Multiple Regression] [] [2011-12-09 11:34:14] [14511500b645ce5186c706473940fe45]
-   PD      [Multiple Regression] [] [2011-12-18 12:35:43] [8a7469f165590e0a048f07fe1c69d604] [Current]

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Dataseries X:

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272545	1747	69	483	32033	186099	3	116	38	144
179444	1209	64	429	20654	113854	4	127	34	133
222373	1844	69	673	16346	99776	16	106	42	162
218443	2683	104	1137	35926	106194	2	133	38	148
167843	1228	51	374	10621	100792	1	64	27	88
70849	631	28	179	10024	47552	3	89	35	129
506574	4627	123	2251	43068	250931	0	122	33	128
33186	381	19	111	1271	6853	0	22	18	67
216660	2063	59	740	34416	115466	7	117	34	132
213274	1758	44	595	20318	110896	0	82	33	120
307153	2132	109	800	24409	169351	0	147	46	169
237633	2128	114	660	20648	94853	7	184	55	210
164292	1667	68	635	12347	72591	8	113	37	122
364402	2965	79	1172	21857	101345	4	171	55	191
244103	2098	84	674	11034	113713	10	87	44	162
384448	4904	178	1692	33433	165354	0	199	59	223
325587	2242	68	811	35902	164263	6	139	36	140
323652	2977	157	1168	22355	135213	4	92	39	144
176082	1438	55	507	31219	111669	3	85	29	111
266736	2347	87	689	21983	134163	8	193	51	199
278265	2522	70	837	40085	140303	0	160	49	187
442703	2889	103	1270	18507	150773	1	144	39	144
180393	1447	41	462	16278	111848	5	84	25	89
189897	1717	54	601	24662	102509	9	208	52	208
234247	3362	121	1242	31452	96785	1	154	45	165
237452	2898	125	1025	32580	116136	0	139	38	146
267268	2828	127	1062	22883	158376	5	127	41	158
270787	1972	86	618	27652	153990	0	148	43	154
155915	1495	51	559	9845	64057	0	99	32	117
342564	2840	69	1062	20190	230054	0	135	41	158
282172	2299	76	913	46201	184531	3	171	47	183
216584	1909	76	643	10971	114198	6	149	50	186
318563	2091	84	779	34811	198299	1	178	48	185
98672	971	37	322	3029	33750	4	137	37	141
386258	3293	95	1243	38941	189723	4	151	41	156
273950	2764	56	1186	4958	100826	0	127	42	159
425120	3682	120	1324	32344	188355	0	151	44	161
227636	1918	83	640	19433	104470	2	89	36	139
115658	947	33	284	12558	58391	1	46	17	55
349863	3433	194	1210	36524	164808	2	153	42	163
324178	3246	79	1490	26041	134097	10	122	39	145
178083	1692	67	667	16637	80238	9	111	41	148
195153	1735	73	635	28395	133252	5	108	36	115
177694	1771	61	479	16747	54518	6	142	47	174
153778	2496	82	1022	9105	121850	1	45	45	73
455168	5501	151	2068	11941	79367	2	131	41	147
78800	918	42	330	7935	56968	2	66	26	82
208051	2228	76	648	19499	106314	0	180	52	201
348077	4051	118	1367	22938	191889	10	165	47	181
175523	2081	54	868	25314	104864	3	146	45	164
224591	1875	74	588	28524	160791	0	137	40	158
24188	496	24	218	2694	15049	0	7	4	12
372238	2537	314	833	20867	191179	8	157	44	163
65029	744	17	255	3597	25109	5	61	18	67
101097	1161	64	454	5296	45824	3	41	14	52
279012	3027	58	1108	32982	129711	1	120	37	134
317644	2526	84	662	38975	210012	5	228	61	230
340471	3705	185	1119	42721	194679	5	137	39	145
358958	2667	141	1058	41455	197680	0	150	42	153
252529	2175	83	822	23923	81180	12	127	36	139
370628	3949	140	1302	26719	197765	10	161	46	178
304468	3165	117	1145	53405	214738	12	73	28	101
265870	2939	113	1185	12526	96252	11	97	43	169
264889	2610	88	931	26584	124527	8	142	42	163
228595	1426	66	557	37062	153242	2	125	37	139
216027	1646	65	436	25696	145707	0	87	30	116
198798	1971	132	596	24634	113963	6	128	35	137
238146	2746	145	837	27269	134904	9	148	44	167
234891	2308	81	848	25270	114268	2	116	36	135
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239314	2537	68	865	17828	102204	13	154	45	173
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342846	2695	92	1077	30927	165278	3	133	36	140
207650	1809	107	524	18487	181712	6	125	41	154
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182357	1791	64	644	17696	75881	0	110	37	134
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145943	1369	69	653	9648	68580	5	99	26	99
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80953	870	25	437	7905	55792	0	27	8	28
150216	1966	54	822	4527	25157	0	77	27	101
167878	1459	59	423	41517	100922	6	137	38	139
369718	3795	205	1489	21261	118845	1	137	37	143
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275997	3087	74	1099	15049	82390	1	135	36	140
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189252	1624	36	555	30391	111542	3	139	36	140
222504	1607	51	552	39932	162519	5	127	35	127
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287748	2714	136	853	40312	117495	8	176	51	198
294320	2325	65	848	32616	195894	0	130	41	155
186856	1999	179	640	11338	80684	0	59	36	138
43287	602	14	214	7409	19630	4	64	19	71
185468	2146	80	716	18213	88634	4	36	23	84
235352	2325	146	795	45873	139292	0	98	44	167
268077	2617	48	1170	39844	128602	0	125	40	155
305195	2688	90	1048	28317	135848	0	124	40	150
143356	1207	72	399	24797	178377	0	83	30	112
154165	3102	88	906	7471	106330	0	127	41	161
307000	1869	68	609	27259	178303	4	143	40	149
298039	2304	88	688	23201	116938	0	115	45	164
23623	398	11	156	238	5841	0	0	1	0
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61857	530	25	192	3913	24610	4	30	11	32
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21054	387	16	146	338	6622	0	0	0	0
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216299	2059	42	716	18700	80716	2	151	43	163
357602	2792	82	1021	36809	157384	0	187	52	198
198104	1395	61	481	24959	122975	0	171	53	205
410803	3590	80	1582	37343	191469	4	167	48	187
316105	2387	97	820	21849	231257	0	145	48	187
397297	3334	124	1153	49809	258287	3	175	50	186
187992	1250	35	473	21654	122531	0	137	40	151
102424	1121	42	401	8728	61394	0	100	36	131
286327	2880	335	954	20920	86480	4	150	40	155
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143860	1759	54	546	1037	18284	15	149	42	160
391854	4138	132	1728	42570	147581	2	161	46	172
157429	1831	77	689	17672	72558	4	112	39	143
258751	1787	48	590	34245	147341	2	135	41	151
282399	2535	94	897	16786	114651	1	124	46	158
217665	1816	113	613	20954	100187	0	45	32	125
366774	3873	116	1548	16378	130332	9	120	39	145
236660	2181	88	759	31852	134218	1	126	39	145
173260	2035	63	716	2805	10901	3	78	21	79
323545	2960	99	955	38086	145758	11	136	45	174
168994	1915	57	720	21166	75767	5	179	50	192
253330	2648	86	1023	34672	134969	2	118	36	132
301703	2633	105	818	36171	169216	1	147	44	159
1	2	0	0	0	0	9	0	0	0
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0	0	0	0	0	0	0	0	0	0
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0	0	0	0	0	0	0	0	0	0
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969	29	2	0	0	0	0	0	0	0
206501	1822	68	591	17372	75882	2	71	34	125

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net
R Engine error message	Error in dimnames(data) <- dimnames : length of 'dimnames' [1] not equal to array extent Calls: array Execution halted

\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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
R Engine error message & Error in dimnames(data) <- dimnames : 
  length of 'dimnames' [1] not equal to array extent
Calls: array
Execution halted
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156772&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[ROW][C]R Engine error message[/C][C]Error in dimnames(data) <- dimnames : 
  length of 'dimnames' [1] not equal to array extent
Calls: array
Execution halted
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156772&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156772&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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net
R Engine error message	Error in dimnames(data) <- dimnames : length of 'dimnames' [1] not equal to array extent Calls: array Execution halted

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code