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Multiple regression Oliezaden

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

Title produced by software: Multiple Regression

Date of computation: Sun, 16 Dec 2007 18:26:06 -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/Dec/17/t1197853779ebekkg9dql9rw4p.htm/, Retrieved Mon, 17 Dec 2007 02:09:49 +0100

User-defined keywords:

Multiple regression Oliezaden

Dataseries X:

» Textbox « » Textfile « » CSV «

145.3 0 143.6 0 142.8 0 155.9 0 156.2 0 149.8 0 152.7 0 155.5 0 159.3 0 143 0 141.4 0 142.8 0 146.4 0 152.3 0 164.3 0 168 0 171.3 0 162.7 0 150.2 0 142.5 0 138.2 0 138 0 145.1 0 138.4 0 131.8 0 130.8 0 126.3 0 123 0 124 0 120.8 0 122.1 0 106.5 0 104.3 0 108.7 0 113.8 0 112.5 0 106.1 0 98.4 0 96 0 99.3 0 97.5 0 95.3 0 88 0 94.7 0 99.4 0 98.9 0 96.4 0 95.3 0 99.5 0 101.6 0 103.9 0 106.6 0 108.3 0 102 0 93.8 0 91.6 0 97.7 0 94.8 0 98 0 103.8 0 97.8 0 91.2 0 89.3 0 87.5 0 90.4 0 94.2 0 102.2 0 101.3 0 96 0 90.8 0 93.2 1 90.9 1 91.1 1 90.2 1 94.3 1 96 1 99 1 103.3 1 113.1 1 112.8 1 112.1 1 107.4 1 111 1 110.5 1 110.8 1 112.4 1 111.5 1 116.2 1 122.5 1 121.3 1 113.9 1 110.7 1 120.8 1 141.1 1 147.4 1 148 1 158.1 1 165 1 187 1 190.3 1 182.4 1 168.8 1 151.2 1 120.1 1 112.5 1 106.2 1 107.1 1 108.5 1 106.5 1 108.3 1 125.6 1 124 1 127.2 1 136.9 1 135.8 1 124.3 1 115.4 1 113.6 1 114.4 1 118.4 1 117 1 116.5 1 115.4 1 113.6 1 117.4 1 116.9 1 116.4 1 111.1 1 110.2 1 118.9 1 131.8 1 130.6 1 138.3 1 148.4 1 148.7 1 144.3 1 152.5 1 162.9 1 167.2 1 166.5 1 185.6 1

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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Oliezaden[t] = + 123.555477855478 + 26.046688034188`9/11`[t] + 2.39271318958814M1[t] + 3.49838286713286M2[t] + 7.63738587801083M3[t] + 9.54305555555553M4[t] + 11.8153918997669M5[t] + 10.9377282439782M6[t] + 8.85173125485623M7[t] + 3.37406759906758M8[t] + 4.80473727661226M9[t] -1.65861013986017M10[t] -0.28142725330227M11[t] -0.272336344211344t + 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)	123.555477855478	8.58204	14.397	0	0
`9/11`	26.046688034188	8.447059	3.0835	0.00251	0.001255
M1	2.39271318958814	10.393306	0.2302	0.818294	0.409147
M2	3.49838286713286	10.391967	0.3366	0.736942	0.368471
M3	7.63738587801083	10.391666	0.735	0.463723	0.231862
M4	9.54305555555553	10.392402	0.9183	0.360217	0.180108
M5	11.8153918997669	10.394175	1.1367	0.257791	0.128895
M6	10.9377282439782	10.396984	1.052	0.294793	0.147396
M7	8.85173125485623	10.40083	0.8511	0.396338	0.198169
M8	3.37406759906758	10.40571	0.3243	0.746281	0.373141
M9	4.80473727661226	10.411624	0.4615	0.645245	0.322622
M10	-1.65861013986017	10.630116	-0.156	0.876258	0.438129
M11	-0.28142725330227	10.613864	-0.0265	0.978888	0.489444
t	-0.272336344211344	0.103831	-2.6229	0.009786	0.004893

Multiple Linear Regression - Regression Statistics
Multiple R	0.31196528410929
R-squared	0.09732233848939
Adjusted R-squared	0.00492226290168984
F-TEST (value)	1.05327119994635
F-TEST (DF numerator)	13
F-TEST (DF denominator)	127
p-value	0.405799651168767
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	24.8905270527959
Sum Squared Residuals	78681.3687946775

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	145.3	125.675854700855	19.6241452991452
2	143.6	126.509188034188	17.0908119658120
3	142.8	130.375854700855	12.4241452991453
4	155.9	132.009188034188	23.8908119658119
5	156.2	134.009188034188	22.1908119658120
6	149.8	132.859188034188	16.940811965812
7	152.7	130.500854700855	22.1991452991454
8	155.5	124.750854700855	30.7491452991453
9	159.3	125.909188034188	33.390811965812
10	143	119.173504273504	23.8264957264957
11	141.4	120.278350815851	21.1216491841492
12	142.8	120.287441724942	22.5125582750583
13	146.4	122.407818570319	23.9921814296815
14	152.3	123.241151903652	29.0588480963481
15	164.3	127.107818570319	37.1921814296815
16	168	128.741151903652	39.2588480963481
17	171.3	130.741151903652	40.5588480963482
18	162.7	129.591151903652	33.1088480963481
19	150.2	127.232818570319	22.9671814296814
20	142.5	121.482818570319	21.0171814296814
21	138.2	122.641151903652	15.5588480963481
22	138	115.905468142968	22.0945318570319
23	145.1	117.010314685315	28.0896853146853
24	138.4	117.019405594406	21.3805944055944
25	131.8	119.139782439782	12.6602175602176
26	130.8	119.973115773116	10.8268842268842
27	126.3	123.839782439782	2.46021756021757
28	123	125.473115773116	-2.47311577311576
29	124	127.473115773116	-3.47311577311576
30	120.8	126.323115773116	-5.52311577311577
31	122.1	123.964782439782	-1.86478243978243
32	106.5	118.214782439782	-11.7147824397824
33	104.3	119.373115773116	-15.0731157731158
34	108.7	112.637432012432	-3.93743201243199
35	113.8	113.742278554779	0.0577214452214472
36	112.5	113.751369463869	-1.25136946386948
37	106.1	115.871746309246	-9.7717463092463
38	98.4	116.705079642580	-18.3050796425796
39	96	120.571746309246	-24.5717463092463
40	99.3	122.205079642580	-22.9050796425796
41	97.5	124.205079642580	-26.7050796425796
42	95.3	123.055079642580	-27.7550796425797
43	88	120.696746309246	-32.6967463092463
44	94.7	114.946746309246	-20.2467463092463
45	99.4	116.105079642580	-16.7050796425796
46	98.9	109.369395881896	-10.4693958818959
47	96.4	110.474242424242	-14.0742424242424
48	95.3	110.483333333333	-15.1833333333334
49	99.5	112.603710178710	-13.1037101787102
50	101.6	113.437043512044	-11.8370435120435
51	103.9	117.303710178710	-13.4037101787102
52	106.6	118.937043512044	-12.3370435120435
53	108.3	120.937043512044	-12.6370435120435
54	102	119.787043512044	-17.7870435120435
55	93.8	117.428710178710	-23.6287101787102
56	91.6	111.678710178710	-20.0787101787102
57	97.7	112.837043512044	-15.1370435120435
58	94.8	106.101359751360	-11.3013597513598
59	98	107.206206293706	-9.2062062937063
60	103.8	107.215297202797	-3.41529720279724
61	97.8	109.335674048174	-11.5356740481740
62	91.2	110.169007381507	-18.9690073815074
63	89.3	114.035674048174	-24.7356740481741
64	87.5	115.669007381507	-28.1690073815074
65	90.4	117.669007381507	-27.2690073815074
66	94.2	116.519007381507	-22.3190073815074
67	102.2	114.160674048174	-11.9606740481740
68	101.3	108.410674048174	-7.11067404817406
69	96	109.569007381507	-13.5690073815074
70	90.8	102.833323620824	-12.0333236208236
71	93.2	129.984858197358	-36.7848581973582
72	90.9	129.993949106449	-39.0939491064491
73	91.1	132.114325951826	-41.0143259518259
74	90.2	132.947659285159	-42.7476592851593
75	94.3	136.814325951826	-42.5143259518259
76	96	138.447659285159	-42.4476592851593
77	99	140.447659285159	-41.4476592851593
78	103.3	139.297659285159	-35.9976592851593
79	113.1	136.939325951826	-23.8393259518259
80	112.8	131.189325951826	-18.3893259518259
81	112.1	132.347659285159	-20.2476592851593
82	107.4	125.611975524476	-18.2119755244755
83	111	126.716822066822	-15.7168220668221
84	110.5	126.725912975913	-16.225912975913
85	110.8	128.846289821290	-18.0462898212898
86	112.4	129.679623154623	-17.2796231546231
87	111.5	133.546289821290	-22.0462898212898
88	116.2	135.179623154623	-18.9796231546231
89	122.5	137.179623154623	-14.6796231546231
90	121.3	136.029623154623	-14.7296231546232
91	113.9	133.671289821290	-19.7712898212898
92	110.7	127.921289821290	-17.2212898212898
93	120.8	129.079623154623	-8.27962315462315
94	141.1	122.343939393939	18.7560606060606
95	147.4	123.448785936286	23.9512140637141
96	148	123.457876845377	24.5421231546231
97	158.1	125.578253690754	32.5217463092463
98	165	126.411587024087	38.588412975913
99	187	130.278253690754	56.7217463092463
100	190.3	131.911587024087	58.388412975913
101	182.4	133.911587024087	48.488412975913
102	168.8	132.761587024087	36.038412975913
103	151.2	130.403253690754	20.7967463092463
104	120.1	124.653253690754	-4.55325369075369
105	112.5	125.811587024087	-13.3115870240870
106	106.2	119.075903263403	-12.8759032634033
107	107.1	120.180749805750	-13.0807498057498
108	108.5	120.189840714841	-11.6898407148407
109	106.5	122.310217560218	-15.8102175602175
110	108.3	123.143550893551	-14.8435508935509
111	125.6	127.010217560218	-1.41021756021756
112	124	128.643550893551	-4.6435508935509
113	127.2	130.643550893551	-3.44355089355088
114	136.9	129.493550893551	7.4064491064491
115	135.8	127.135217560218	8.66478243978246
116	124.3	121.385217560218	2.91478243978244
117	115.4	122.543550893551	-7.14355089355089
118	113.6	115.807867132867	-2.20786713286713
119	114.4	116.912713675214	-2.51271367521367
120	118.4	116.921804584305	1.47819541569540
121	117	119.042181429681	-2.04218142968141
122	116.5	119.875514763015	-3.37551476301476
123	115.4	123.742181429681	-8.34218142968142
124	113.6	125.375514763015	-11.7755147630148
125	117.4	127.375514763015	-9.97551476301475
126	116.9	126.225514763015	-9.32551476301476
127	116.4	123.867181429681	-7.46718142968142
128	111.1	118.117181429681	-7.01718142968144
129	110.2	119.275514763015	-9.07551476301477
130	118.9	112.539831002331	6.360168997669
131	131.8	113.644677544678	18.1553224553225
132	130.6	113.653768453768	16.9462315462315
133	138.3	115.774145299145	22.5258547008547
134	148.4	116.607478632479	31.7925213675214
135	148.7	120.474145299145	28.2258547008547
136	144.3	122.107478632479	22.1925213675214
137	152.5	124.107478632479	28.3925213675214
138	162.9	122.957478632479	39.9425213675213
139	167.2	120.599145299145	46.6008547008547
140	166.5	114.849145299145	51.6508547008547
141	185.6	116.007478632479	69.5925213675214

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

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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