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q3a

*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: Sun, 23 Nov 2008 06:50:37 -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/23/t1227448262ku64jdn4nd8xylf.htm/, Retrieved Sun, 23 Nov 2008 13:51:10 +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/23/t1227448262ku64jdn4nd8xylf.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 «

3258.1 0 3140.1 0 3627.4 0 3279.4 0 3204.0 0 3515.6 0 3146.6 0 2271.7 0 3627.9 0 3553.4 0 3018.3 0 3355.4 0 3242.0 0 3311.1 0 4125.2 0 3423.0 0 3120.3 0 3863.0 0 3240.8 0 2837.4 0 3945.0 0 3684.1 0 3659.6 0 3769.6 0 3592.7 0 3754.0 0 4507.8 0 3853.2 0 3817.2 0 3958.4 0 3428.9 1 3125.7 1 3977.0 1 3983.3 1 4299.6 1 4306.9 1 4259.5 1 3986.0 1 4755.6 1 3925.6 1 4206.5 1 4323.4 1 3816.1 1 3410.7 1 4227.4 1 4296.9 1 4351.7 1 3800.0 1 4277.0 1 4100.2 1 4672.5 1 4189.9 1 4231.9 1 4654.9 1 4298.5 1 3635.9 1 4505.1 1 4910.1 1 4908.7 1 4101.4 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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 3490.07666666667 + 675.486666666667x[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)	3490.07666666667	77.707369	44.9131	0	0
x	675.486666666667	109.894815	6.1467	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.628056578228752
R-squared	0.394455065456408
Adjusted R-squared	0.384014635550484
F-TEST (value)	37.7814964528032
F-TEST (DF numerator)	1
F-TEST (DF denominator)	58
p-value	7.80014348666924e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	425.62078927652
Sum Squared Residuals	10506877.2633333

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	3258.1	3490.07666666667	-231.976666666671
2	3140.1	3490.07666666667	-349.976666666666
3	3627.4	3490.07666666667	137.323333333334
4	3279.4	3490.07666666667	-210.676666666666
5	3204	3490.07666666667	-286.076666666666
6	3515.6	3490.07666666667	25.5233333333334
7	3146.6	3490.07666666667	-343.476666666667
8	2271.7	3490.07666666667	-1218.37666666667
9	3627.9	3490.07666666667	137.823333333334
10	3553.4	3490.07666666667	63.3233333333336
11	3018.3	3490.07666666667	-471.776666666666
12	3355.4	3490.07666666667	-134.676666666666
13	3242	3490.07666666667	-248.076666666666
14	3311.1	3490.07666666667	-178.976666666667
15	4125.2	3490.07666666667	635.123333333333
16	3423	3490.07666666667	-67.0766666666665
17	3120.3	3490.07666666667	-369.776666666666
18	3863	3490.07666666667	372.923333333334
19	3240.8	3490.07666666667	-249.276666666666
20	2837.4	3490.07666666667	-652.676666666666
21	3945	3490.07666666667	454.923333333334
22	3684.1	3490.07666666667	194.023333333333
23	3659.6	3490.07666666667	169.523333333333
24	3769.6	3490.07666666667	279.523333333333
25	3592.7	3490.07666666667	102.623333333333
26	3754	3490.07666666667	263.923333333334
27	4507.8	3490.07666666667	1017.72333333333
28	3853.2	3490.07666666667	363.123333333333
29	3817.2	3490.07666666667	327.123333333333
30	3958.4	3490.07666666667	468.323333333334
31	3428.9	4165.56333333333	-736.663333333333
32	3125.7	4165.56333333333	-1039.86333333333
33	3977	4165.56333333333	-188.563333333333
34	3983.3	4165.56333333333	-182.263333333333
35	4299.6	4165.56333333333	134.036666666667
36	4306.9	4165.56333333333	141.336666666666
37	4259.5	4165.56333333333	93.9366666666667
38	3986	4165.56333333333	-179.563333333333
39	4755.6	4165.56333333333	590.036666666667
40	3925.6	4165.56333333333	-239.963333333333
41	4206.5	4165.56333333333	40.9366666666667
42	4323.4	4165.56333333333	157.836666666666
43	3816.1	4165.56333333333	-349.463333333333
44	3410.7	4165.56333333333	-754.863333333333
45	4227.4	4165.56333333333	61.8366666666664
46	4296.9	4165.56333333333	131.336666666666
47	4351.7	4165.56333333333	186.136666666667
48	3800	4165.56333333333	-365.563333333333
49	4277	4165.56333333333	111.436666666667
50	4100.2	4165.56333333333	-65.3633333333335
51	4672.5	4165.56333333333	506.936666666667
52	4189.9	4165.56333333333	24.3366666666664
53	4231.9	4165.56333333333	66.3366666666664
54	4654.9	4165.56333333333	489.336666666666
55	4298.5	4165.56333333333	132.936666666667
56	3635.9	4165.56333333333	-529.663333333333
57	4505.1	4165.56333333333	339.536666666667
58	4910.1	4165.56333333333	744.536666666667
59	4908.7	4165.56333333333	743.136666666667
60	4101.4	4165.56333333333	-64.1633333333336

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

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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