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R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 15 Nov 2007 03:48:50 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/15/t1195123535jujax97kt2nu1d2.htm/, Retrieved Thu, 15 Nov 2007 11:45:45 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

140 373 132 371 117 354 114 357 113 363 110 364 107 363 103 358 98 357 98 357 137 380 148 378 147 376 139 380 130 379 128 384 127 392 123 394 118 392 114 396 108 392 111 396 151 419 159 421 158 420 148 418 138 410 137 418 136 426 133 428 126 430 120 424 114 423 116 427 153 441 162 449 161 452 149 462 139 455 135 461 130 461 127 463 122 462 117 456 112 455 113 456 149 472 157 472 157 471 147 465 137 459 132 465 125 468 123 467 117 463 114 460 111 462 112 461 144 476 150 476 149 471 134 453 123 443 116 442 117 444 111 438 105 427 102 424 95 416 93 406 124 431 130 434 124 418

Text written by user:

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

-25[t] = + 25.7095903042373 + 0.3341097741355`25 `[t] -1.35075440129733M1[t] -10.0278612159084M2[t] -17.6287970771281M3[t] -22.2951234107307M4[t] -25.6281164110000M5[t] -28.6242820943263M6[t] -32.5071367509352M7[t] -35.1119548161657M8[t] -39.2175493221984M9[t] -37.7690117474795M10[t] -7.89129973075869M11[t] -0.503834316673765t + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STAT H0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	25.7095903042373	9.160825	2.8065	0.006776	0.003388
`25 `	0.3341097741355	0.023379	14.2908	0	0
M1	-1.35075440129733	2.549443	-0.5298	0.598223	0.299111
M2	-10.0278612159084	2.651237	-3.7823	0.000365	0.000183
M3	-17.6287970771281	2.657874	-6.6327	0	0
M4	-22.2951234107307	2.650749	-8.4109	0	0
M5	-25.6281164110000	2.645881	-9.686	0	0
M6	-28.6242820943263	2.645331	-10.8207	0	0
M7	-32.5071367509352	2.649651	-12.2685	0	0
M8	-35.1119548161657	2.658738	-13.2062	0	0
M9	-39.2175493221984	2.668726	-14.6952	0	0
M10	-37.7690117474795	2.674232	-14.1233	0	0
M11	-7.89129973075869	2.638944	-2.9903	0.004061	0.00203
t	-0.503834316673765	0.041013	-12.2846	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.971946355203395
R-squared	0.944679717393163
Adjusted R-squared	0.932490502581487
F-TEST (value)	77.5012773167527
F-TEST (DF numerator)	13
F-TEST (DF denominator)	59
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	4.57053009318048
Sum Squared Residuals	1232.49497462744

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	140	148.477947338808	-8.47794733880753
2	132	138.628786659252	-6.62878665925186
3	117	124.844150321055	-7.84415032105496
4	114	120.676318993185	-6.67631899318502
5	113	118.844150321055	-5.84415032105493
6	110	115.678260095190	-5.67826009519042
7	107	110.957461347772	-3.95746134777218
8	103	106.178260095190	-3.17826009519043
9	98	101.234721498349	-3.23472149834853
10	98	102.179424756394	-4.17942475639371
11	137	139.237827261557	-2.23782726155721
12	148	145.957073127371	2.04292687262891
13	147	143.434264861129	3.56573513887098
14	139	135.589762826386	3.41023717361382
15	130	127.150882874357	2.84911712564274
16	128	123.651271094758	4.34872890524165
17	127	122.487321970899	4.51267802910073
18	123	119.655541519170	3.34445848082972
19	118	114.600632997617	3.39936700238348
20	114	112.828419712254	1.17158028774573
21	108	106.882551793006	1.11744820699416
22	111	109.163694147593	1.83630585240698
23	151	146.222096652757	4.77790334724349
24	159	154.277781615112	4.72221838488756
25	158	152.089083123006	5.91091687699415
26	148	142.23992244345	5.76007755655
27	138	131.462274072473	6.53772592752741
28	137	128.964991615280	8.03500838471982
29	136	127.801042491421	8.1989575085789
30	133	124.969262039692	8.03073796030791
31	126	121.250792614680	4.74920738531966
32	120	116.137481587963	3.86251841203691
33	114	111.193942991121	2.80605700887882
34	116	113.475085345708	2.52491465429166
35	153	147.526499883652	5.47350011634766
36	162	157.586843490821	4.41315650917874
37	161	156.734584095257	4.26541590474333
38	149	150.894740705327	-1.89474070532682
39	139	140.451202108485	-1.45120210848491
40	135	137.285700103021	-2.28570010302149
41	130	133.448872786078	-3.44887278607842
42	127	130.617092334349	-3.61709233434941
43	122	125.896293586931	-3.89629358693117
44	117	120.782982560214	-3.78298256021391
45	112	115.839443963372	-3.839443963372
46	113	117.118256995553	-4.11825699555265
47	149	151.837891081768	-2.83789108176766
48	157	159.225356495853	-2.22535649585258
49	157	157.036658003746	-0.0366580037459927
50	147	145.851058227648	1.14894177235185
51	137	135.741629404942	1.25837059505827
52	132	132.576127399478	-0.576127399478315
53	125	129.741629404942	-4.74162940494174
54	123	125.907519630806	-2.90751963080624
55	117	120.184391560981	-3.18439156098148
56	114	116.073409856671	-2.07340985667074
57	111	112.132200582235	-1.13220058223531
58	112	112.742794066145	-0.742794066144982
59	144	147.128318378224	-3.12831837822448
60	150	154.515783792309	-4.51578379230941
61	149	150.990646203661	-1.99064620366081
62	134	135.795729137937	-1.79572913793698
63	123	124.349861218689	-1.34986121868855
64	116	118.845590794277	-2.84559079427664
65	117	115.676983025605	1.32301697439545
66	111	110.172324380792	0.82767561920844
67	105	102.110427892018	2.8895721079817
68	102	97.9994461877075	4.00055381229244
69	95	90.7171391719171	4.28286082808286
70	93	88.3207446886073	4.6792553113927
71	124	126.047366742042	-2.04736674204180
72	130	134.437161478533	-4.43716147853323
73	124	127.236816374394	-3.23681637439413

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

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

library(lattice)

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))

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')

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()

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('http://www.xycoon.com/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<br />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<br />Forecast', 1, TRUE)

a<-table.element(a, 'Residuals<br />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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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