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*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Mon, 24 Nov 2008 14:13:33 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/24/t1227561276yqrukevi4v39ilz.htm/, Retrieved Mon, 24 Nov 2008 21:14:37 +0000

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Nov/24/t1227561276yqrukevi4v39ilz.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

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

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

106.7 0 110.2 0 125.9 0 100.1 0 106.4 0 114.8 0 81.3 0 87 0 104.2 0 108 0 105 0 94.5 0 92 0 95.9 0 108.8 0 103.4 0 102.1 0 110.1 0 83.2 0 82.7 0 106.8 0 113.7 0 102.5 0 96.6 0 92.1 0 95.6 0 102.3 0 98.6 0 98.2 0 104.5 0 84 0 73.8 0 103.9 0 106 0 97.2 0 102.6 0 89 0 93.8 0 116.7 1 106.8 1 98.5 1 118.7 1 90 1 91.9 1 113.3 1 113.1 1 104.1 1 108.7 1 96.7 1 101 1 116.9 1 105.8 1 99 1 129.4 1 83 1 88.9 1 115.9 1 104.2 1 113.4 1 112.2 1 100.8 1 107.3 1 126.6 1 102.9 1 117.9 1 128.8 1 87.5 1 93.8 1 122.7 1 126.2 1 124.6 1 116.7 1 115.2 1 111.1 1 129.9 1 113.3 1 118.5 1 133.5 1 102.1 1 102.4 1

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 computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 97.545 + 5.53874999999999x[t] -5.30886408730161M1[t] -2.22558531746032M2[t] + 12.8950148809524M3[t] -0.964563492063495M4[t] + 0.30442956349206M5[t] + 14.3591369047619M6[t] -18.4290128968254M7[t] -17.2028769841270M8[t] + 6.26683035714286M9[t] + 6.88344246031746M10[t] + 2.70005456349206M11[t] + 0.116721230158730t + 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)	97.545	3.117271	31.2918	0	0
x	5.53874999999999	2.969448	1.8652	0.066593	0.033297
M1	-5.30886408730161	3.660279	-1.4504	0.151683	0.075842
M2	-2.22558531746032	3.658449	-0.6083	0.545049	0.272525
M3	12.8950148809524	3.677018	3.5069	0.000821	0.00041
M4	-0.964563492063495	3.671017	-0.2628	0.793561	0.39678
M5	0.30442956349206	3.666127	0.083	0.934072	0.467036
M6	14.3591369047619	3.662351	3.9207	0.000213	0.000106
M7	-18.4290128968254	3.659693	-5.0357	4e-06	2e-06
M8	-17.2028769841270	3.658156	-4.7026	1.4e-05	7e-06
M9	6.26683035714286	3.799089	1.6496	0.103785	0.051892
M10	6.88344246031746	3.796386	1.8132	0.074355	0.037177
M11	2.70005456349206	3.794763	0.7115	0.479269	0.239634
t	0.116721230158730	0.064078	1.8215	0.073057	0.036529

Multiple Linear Regression - Regression Statistics
Multiple R	0.881461940737189
R-squared	0.776975152968171
Adjusted R-squared	0.733046016431599
F-TEST (value)	17.6870117244694
F-TEST (DF numerator)	13
F-TEST (DF denominator)	66
p-value	1.11022302462516e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.57178533306779
Sum Squared Residuals	2850.43192261904

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	106.7	92.3528571428573	14.3471428571427
2	110.2	95.5528571428571	14.6471428571429
3	125.9	110.790178571429	15.1098214285714
4	100.1	97.0473214285714	3.05267857142857
5	106.4	98.4330357142857	7.96696428571428
6	114.8	112.604464285714	2.19553571428571
7	81.3	79.9330357142857	1.36696428571429
8	87	81.2758928571429	5.72410714285714
9	104.2	104.862321428571	-0.662321428571411
10	108	105.595654761905	2.40434523809524
11	105	101.528988095238	3.47101190476191
12	94.5	98.9456547619048	-4.44565476190476
13	92	93.7535119047619	-1.75351190476188
14	95.9	96.9535119047619	-1.05351190476189
15	108.8	112.190833333333	-3.39083333333333
16	103.4	98.4479761904762	4.95202380952382
17	102.1	99.8336904761905	2.26630952380952
18	110.1	114.005119047619	-3.90511904761905
19	83.2	81.3336904761905	1.86630952380953
20	82.7	82.6765476190476	0.0234523809523847
21	106.8	106.262976190476	0.537023809523803
22	113.7	106.996309523810	6.70369047619048
23	102.5	102.929642857143	-0.429642857142855
24	96.6	100.346309523810	-3.74630952380953
25	92.1	95.1541666666666	-3.05416666666665
26	95.6	98.3541666666667	-2.75416666666667
27	102.3	113.591488095238	-11.2914880952381
28	98.6	99.848630952381	-1.24863095238096
29	98.2	101.234345238095	-3.03434523809523
30	104.5	115.405773809524	-10.9057738095238
31	84	82.7343452380952	1.26565476190476
32	73.8	84.0772023809524	-10.2772023809524
33	103.9	107.663630952381	-3.76363095238095
34	106	108.396964285714	-2.39696428571429
35	97.2	104.330297619048	-7.13029761904762
36	102.6	101.746964285714	0.853035714285705
37	89	96.5548214285714	-7.55482142857141
38	93.8	99.7548214285714	-5.95482142857143
39	116.7	120.530892857143	-3.83089285714285
40	106.8	106.788035714286	0.0119642857142872
41	98.5	108.17375	-9.67375
42	118.7	122.345178571429	-3.64517857142857
43	90	89.67375	0.326250000000006
44	91.9	91.0166071428571	0.883392857142866
45	113.3	114.603035714286	-1.30303571428572
46	113.1	115.336369047619	-2.23636904761905
47	104.1	111.269702380952	-7.16970238095238
48	108.7	108.686369047619	0.0136309523809534
49	96.7	103.494226190476	-6.79422619047616
50	101	106.694226190476	-5.69422619047619
51	116.9	121.931547619048	-5.03154761904762
52	105.8	108.188690476190	-2.38869047619048
53	99	109.574404761905	-10.5744047619048
54	129.4	123.745833333333	5.65416666666667
55	83	91.0744047619048	-8.07440476190476
56	88.9	92.4172619047619	-3.5172619047619
57	115.9	116.003690476190	-0.103690476190477
58	104.2	116.737023809524	-12.5370238095238
59	113.4	112.670357142857	0.729642857142862
60	112.2	110.087023809524	2.11297619047619
61	100.8	104.894880952381	-4.09488095238094
62	107.3	108.094880952381	-0.794880952380958
63	126.6	123.332202380952	3.26779761904761
64	102.9	109.589345238095	-6.68934523809524
65	117.9	110.975059523810	6.92494047619048
66	128.8	125.146488095238	3.65351190476191
67	87.5	92.4750595238095	-4.97505952380952
68	93.8	93.8179166666667	-0.0179166666666755
69	122.7	117.404345238095	5.29565476190476
70	126.2	118.137678571429	8.06232142857143
71	124.6	114.071011904762	10.5289880952381
72	116.7	111.487678571429	5.21232142857143
73	115.2	106.295535714286	8.90446428571431
74	111.1	109.495535714286	1.60446428571427
75	129.9	124.732857142857	5.16714285714286
76	113.3	110.99	2.30999999999999
77	118.5	112.375714285714	6.12428571428571
78	133.5	126.547142857143	6.95285714285714
79	102.1	93.8757142857143	8.2242857142857
80	102.4	95.2185714285714	7.18142857142857

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227561276yqrukevi4v39ilz/1gs8i1227561205.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227561276yqrukevi4v39ilz/3w4ma1227561205.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227561276yqrukevi4v39ilz/7n2em1227561205.ps (open in new window)

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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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