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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: Wed, 14 Nov 2007 15:56:56 -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/14/t1195080804tmyvg82nc4k51iy.htm/, Retrieved Wed, 14 Nov 2007 23:53:25 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

128 0 123 0 118 0 112 0 105 0 102 0 131 0 149 0 145 0 132 0 122 0 119 0 116 0 111 0 104 0 100 0 93 0 91 0 119 0 139 0 134 0 124 0 113 0 109 0 109 0 106 0 101 0 98 0 93 0 91 0 122 0 139 0 140 1 132 1 117 1 114 1 113 1 110 1 107 1 103 1 98 1 98 1 137 1 148 1 147 1 139 1 130 1 128 1 127 1 123 1 118 1 114 1 108 1 111 1 151 1 159 1 158 1 148 1 138 1 137 1 136 1 133 1 126 1 120 1 114 1 116 1 153 1 162 1 161 1 149 0 139 0 135 0 130 0 127 0 122 0 117 0 112 0 113 0 149 0 157 0 157 0 147 0 137 0 132 0 125 0 123 0 117 0 114 0 111 0 112 0 144 0 150 0 149 0 134 0 123 0 116 0 117 0 111 0 105 0 102 0 95 0 93 0 124 0 130 0 124 0 115 0

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	9 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 121.086956521739 + 7.9400705052879x[t] + 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)	121.086956521739	2.112778	57.3117	0	0
x	7.9400705052879	3.576069	2.2203	0.028566	0.014283

Multiple Linear Regression - Regression Statistics
Multiple R	0.212737912240693
R-squared	0.0452574193045288
Adjusted R-squared	0.036077202182457
F-TEST (value)	4.92988550300376
F-TEST (DF numerator)	1
F-TEST (DF denominator)	104
p-value	0.0285657456080748
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	17.5500523870143
Sum Squared Residuals	32032.4512338425

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	128	121.086956521739	6.91304347826062
2	123	121.086956521739	1.91304347826087
3	118	121.086956521739	-3.08695652173913
4	112	121.086956521739	-9.08695652173913
5	105	121.086956521739	-16.0869565217391
6	102	121.086956521739	-19.0869565217391
7	131	121.086956521739	9.91304347826087
8	149	121.086956521739	27.9130434782609
9	145	121.086956521739	23.9130434782609
10	132	121.086956521739	10.9130434782609
11	122	121.086956521739	0.913043478260873
12	119	121.086956521739	-2.08695652173913
13	116	121.086956521739	-5.08695652173913
14	111	121.086956521739	-10.0869565217391
15	104	121.086956521739	-17.0869565217391
16	100	121.086956521739	-21.0869565217391
17	93	121.086956521739	-28.0869565217391
18	91	121.086956521739	-30.0869565217391
19	119	121.086956521739	-2.08695652173913
20	139	121.086956521739	17.9130434782609
21	134	121.086956521739	12.9130434782609
22	124	121.086956521739	2.91304347826087
23	113	121.086956521739	-8.08695652173913
24	109	121.086956521739	-12.0869565217391
25	109	121.086956521739	-12.0869565217391
26	106	121.086956521739	-15.0869565217391
27	101	121.086956521739	-20.0869565217391
28	98	121.086956521739	-23.0869565217391
29	93	121.086956521739	-28.0869565217391
30	91	121.086956521739	-30.0869565217391
31	122	121.086956521739	0.913043478260873
32	139	121.086956521739	17.9130434782609
33	140	129.027027027027	10.9729729729730
34	132	129.027027027027	2.97297297297297
35	117	129.027027027027	-12.0270270270270
36	114	129.027027027027	-15.0270270270270
37	113	129.027027027027	-16.0270270270270
38	110	129.027027027027	-19.0270270270270
39	107	129.027027027027	-22.0270270270270
40	103	129.027027027027	-26.0270270270270
41	98	129.027027027027	-31.027027027027
42	98	129.027027027027	-31.027027027027
43	137	129.027027027027	7.97297297297297
44	148	129.027027027027	18.9729729729730
45	147	129.027027027027	17.9729729729730
46	139	129.027027027027	9.97297297297297
47	130	129.027027027027	0.972972972972972
48	128	129.027027027027	-1.02702702702703
49	127	129.027027027027	-2.02702702702703
50	123	129.027027027027	-6.02702702702703
51	118	129.027027027027	-11.0270270270270
52	114	129.027027027027	-15.0270270270270
53	108	129.027027027027	-21.0270270270270
54	111	129.027027027027	-18.0270270270270
55	151	129.027027027027	21.9729729729730
56	159	129.027027027027	29.972972972973
57	158	129.027027027027	28.972972972973
58	148	129.027027027027	18.9729729729730
59	138	129.027027027027	8.97297297297297
60	137	129.027027027027	7.97297297297297
61	136	129.027027027027	6.97297297297297
62	133	129.027027027027	3.97297297297297
63	126	129.027027027027	-3.02702702702703
64	120	129.027027027027	-9.02702702702703
65	114	129.027027027027	-15.0270270270270
66	116	129.027027027027	-13.0270270270270
67	153	129.027027027027	23.9729729729730
68	162	129.027027027027	32.972972972973
69	161	129.027027027027	31.972972972973
70	149	121.086956521739	27.9130434782609
71	139	121.086956521739	17.9130434782609
72	135	121.086956521739	13.9130434782609
73	130	121.086956521739	8.91304347826087
74	127	121.086956521739	5.91304347826087
75	122	121.086956521739	0.913043478260873
76	117	121.086956521739	-4.08695652173913
77	112	121.086956521739	-9.08695652173913
78	113	121.086956521739	-8.08695652173913
79	149	121.086956521739	27.9130434782609
80	157	121.086956521739	35.9130434782609
81	157	121.086956521739	35.9130434782609
82	147	121.086956521739	25.9130434782609
83	137	121.086956521739	15.9130434782609
84	132	121.086956521739	10.9130434782609
85	125	121.086956521739	3.91304347826087
86	123	121.086956521739	1.91304347826087
87	117	121.086956521739	-4.08695652173913
88	114	121.086956521739	-7.08695652173913
89	111	121.086956521739	-10.0869565217391
90	112	121.086956521739	-9.08695652173913
91	144	121.086956521739	22.9130434782609
92	150	121.086956521739	28.9130434782609
93	149	121.086956521739	27.9130434782609
94	134	121.086956521739	12.9130434782609
95	123	121.086956521739	1.91304347826087
96	116	121.086956521739	-5.08695652173913
97	117	121.086956521739	-4.08695652173913
98	111	121.086956521739	-10.0869565217391
99	105	121.086956521739	-16.0869565217391
100	102	121.086956521739	-19.0869565217391
101	95	121.086956521739	-26.0869565217391
102	93	121.086956521739	-28.0869565217391
103	124	121.086956521739	2.91304347826087
104	130	121.086956521739	8.91304347826087
105	124	121.086956521739	2.91304347826087
106	115	121.086956521739	-6.08695652173913

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195080804tmyvg82nc4k51iy/1t8v51195081003.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195080804tmyvg82nc4k51iy/3enxn1195081003.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195080804tmyvg82nc4k51iy/3enxn1195081003.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195080804tmyvg82nc4k51iy/4iwt91195081003.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195080804tmyvg82nc4k51iy/4iwt91195081003.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195080804tmyvg82nc4k51iy/5yjtn1195081003.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195080804tmyvg82nc4k51iy/5yjtn1195081003.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195080804tmyvg82nc4k51iy/6cfry1195081003.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195080804tmyvg82nc4k51iy/6cfry1195081003.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195080804tmyvg82nc4k51iy/70rha1195081003.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195080804tmyvg82nc4k51iy/70rha1195081003.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195080804tmyvg82nc4k51iy/8aieu1195081003.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195080804tmyvg82nc4k51iy/8aieu1195081003.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195080804tmyvg82nc4k51iy/9pd3s1195081003.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195080804tmyvg82nc4k51iy/9pd3s1195081003.ps (open in new window)

Parameters:

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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