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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: Tue, 07 Dec 2010 10:51:05 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn.htm/, Retrieved Tue, 07 Dec 2010 12:05:51 +0100

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/2010/Dec/07/t1291719951y0x12p36et417kn.htm/},
    year = {2010},
}
@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 = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

9911 8915 9452 9112 8472 8230 8384 8625 8221 8649 8625 10443 10357 8586 8892 8329 8101 7922 8120 7838 7735 8406 8209 9451 10041 9411 10405 8467 8464 8102 7627 7513 7510 8291 8064 9383 9706 8579 9474 8318 8213 8059 9111 7708 7680 8014 8007 8718 9486 9113 9025 8476 7952 7759 7835 7600 7651 8319 8812 8630

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

[t] = + 9653.025 + 474.970138888886M1[t] -495.318055555555M2[t] + 42.5937500000002M3[t] -857.494444444444M4[t] -1148.38263888889M5[t] -1365.27083333333M6[t] -1155.15902777778M7[t] -1504.64722222222M8[t] -1592.93541666667M9[t] -1007.42361111111M10[t] -990.711805555556M11[t] -9.11180555555554t + 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)	9653.025	201.513676	47.9026	0	0
M1	474.970138888886	245.152664	1.9374	0.058713	0.029357
M2	-495.318055555555	244.786387	-2.0235	0.048732	0.024366
M3	42.5937500000002	244.45452	0.1742	0.862425	0.431213
M4	-857.494444444444	244.157205	-3.5121	0.000994	0.000497
M5	-1148.38263888889	243.894567	-4.7085	2.2e-05	1.1e-05
M6	-1365.27083333333	243.666718	-5.603	1e-06	1e-06
M7	-1155.15902777778	243.473756	-4.7445	2e-05	1e-05
M8	-1504.64722222222	243.315765	-6.1839	0	0
M9	-1592.93541666667	243.192811	-6.5501	0	0
M10	-1007.42361111111	243.104949	-4.144	0.000141	7.1e-05
M11	-990.711805555556	243.052217	-4.0761	0.000175	8.8e-05
t	-9.11180555555554	2.923252	-3.117	0.003114	0.001557

Multiple Linear Regression - Regression Statistics
Multiple R	0.890871803322973
R-squared	0.793652569955925
Adjusted R-squared	0.740968119731906
F-TEST (value)	15.0642659566768
F-TEST (DF numerator)	12
F-TEST (DF denominator)	47
p-value	2.80897527460411e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	384.271501749398
Sum Squared Residuals	6940235.59166667

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	9911	10118.8833333333	-207.883333333343
2	8915	9139.48333333333	-224.483333333332
3	9452	9668.28333333333	-216.283333333333
4	9112	8759.08333333333	352.916666666667
5	8472	8459.08333333333	12.9166666666675
6	8230	8233.08333333333	-3.08333333333285
7	8384	8434.08333333333	-50.0833333333328
8	8625	8075.48333333333	549.516666666668
9	8221	7978.08333333333	242.916666666666
10	8649	8554.48333333333	94.5166666666667
11	8625	8562.08333333333	62.9166666666671
12	10443	9543.68333333333	899.316666666667
13	10357	10009.5416666667	347.458333333336
14	8586	9030.14166666667	-444.141666666667
15	8892	9558.94166666667	-666.941666666667
16	8329	8649.74166666667	-320.741666666667
17	8101	8349.74166666667	-248.741666666667
18	7922	8123.74166666667	-201.741666666667
19	8120	8324.74166666667	-204.741666666666
20	7838	7966.14166666667	-128.141666666667
21	7735	7868.74166666667	-133.741666666666
22	8406	8445.14166666667	-39.1416666666664
23	8209	8452.74166666667	-243.741666666666
24	9451	9434.34166666667	16.6583333333334
25	10041	9900.2	140.800000000003
26	9411	8920.8	490.2
27	10405	9449.6	955.4
28	8467	8540.4	-73.4
29	8464	8240.4	223.6
30	8102	8014.4	87.6
31	7627	8215.4	-588.4
32	7513	7856.8	-343.8
33	7510	7759.4	-249.4
34	8291	8335.8	-44.7999999999999
35	8064	8343.4	-279.4
36	9383	9325	58
37	9706	9790.85833333333	-84.858333333331
38	8579	8811.45833333333	-232.458333333334
39	9474	9340.25833333333	133.741666666666
40	8318	8431.05833333333	-113.058333333334
41	8213	8131.05833333333	81.9416666666664
42	8059	7905.05833333333	153.941666666666
43	9111	8106.05833333333	1004.94166666667
44	7708	7747.45833333333	-39.4583333333336
45	7680	7650.05833333333	29.9416666666666
46	8014	8226.45833333333	-212.458333333333
47	8007	8234.05833333333	-227.058333333334
48	8718	9215.65833333333	-497.658333333334
49	9486	9681.51666666666	-195.516666666665
50	9113	8702.11666666667	410.883333333333
51	9025	9230.91666666667	-205.916666666667
52	8476	8321.71666666667	154.283333333333
53	7952	8021.71666666667	-69.7166666666672
54	7759	7795.71666666667	-36.7166666666671
55	7835	7996.71666666667	-161.716666666667
56	7600	7638.11666666667	-38.116666666667
57	7651	7540.71666666667	110.283333333333
58	8319	8117.11666666667	201.883333333333
59	8812	8124.71666666667	687.283333333333
60	8630	9106.31666666667	-476.316666666667

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/1daue1291719058.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/1daue1291719058.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/2o2uh1291719058.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/2o2uh1291719058.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/3o2uh1291719058.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/3o2uh1291719058.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/4o2uh1291719058.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/4o2uh1291719058.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/5hbb21291719058.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/5hbb21291719058.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/6hbb21291719058.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/6hbb21291719058.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/79ksm1291719058.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/79ksm1291719058.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/89ksm1291719058.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/89ksm1291719058.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/9kbs71291719058.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291719951y0x12p36et417kn/9kbs71291719058.ps (open in new window)

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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