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q3

*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 07:01:17 -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/t12274489798yyp99k6a19nwc6.htm/, Retrieved Sun, 23 Nov 2008 14:03:07 +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/t12274489798yyp99k6a19nwc6.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 «

2236.0 0 2084.9 0 2409.5 0 2199.3 0 2203.5 0 2254.1 0 1975.8 0 1742.2 0 2520.6 0 2438.1 0 2126.3 0 2267.5 0 2201.1 0 2128.5 0 2596.0 0 2458.2 0 2210.5 0 2621.2 0 2231.4 0 2103.6 0 2685.8 0 2539.3 0 2462.4 0 2693.3 0 2307.7 0 2385.9 0 2737.6 0 2653.9 0 2545.4 0 2848.8 0 2359.5 1 2488.3 1 2861.1 1 2717.9 1 2844.0 1 2749.0 1 2652.9 1 2660.2 1 3187.1 1 2774.1 1 3158.2 1 3244.6 1 2665.5 1 2820.8 1 2983.4 1 3077.4 1 3024.8 1 2731.8 1 3046.2 1 2834.8 1 3292.8 1 2946.1 1 3196.9 1 3284.2 1 3003.0 1 2979.0 1 3137.4 1 3647.7 1 3283.0 1 2947.3 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	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 1993.795 + 80.9416666666657x[t] + 21.3444444444422M1[t] -66.2261111111109M2[t] + 341.863333333333M3[t] + 85.9327777777775M4[t] + 124.862222222223M5[t] + 294.891666666667M6[t] -142.487222222222M7[t] -180.397777777778M8[t] + 212.831666666667M9[t] + 241.601111111111M10[t] + 87.9705555555556M11[t] + 17.6505555555556t + 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)	1993.795	73.110383	27.271	0	0
x	80.9416666666657	70.350499	1.1505	0.255864	0.127932
M1	21.3444444444422	85.319621	0.2502	0.80357	0.401785
M2	-66.2261111111109	85.101814	-0.7782	0.440437	0.220218
M3	341.863333333333	84.932022	4.0251	0.000211	0.000105
M4	85.9327777777775	84.810535	1.0132	0.316249	0.158125
M5	124.862222222223	84.737558	1.4735	0.147422	0.073711
M6	294.891666666667	84.713219	3.4811	0.001105	0.000553
M7	-142.487222222222	85.029088	-1.6757	0.100573	0.050287
M8	-180.397777777778	84.810535	-2.1271	0.038809	0.019404
M9	212.831666666667	84.640159	2.5145	0.015479	0.007739
M10	241.601111111111	84.518252	2.8586	0.006374	0.003187
M11	87.9705555555556	84.445023	1.0417	0.302972	0.151486
t	17.6505555555556	2.030844	8.6912	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.954836582345761
R-squared	0.911712898985734
Adjusted R-squared	0.88676219652518
F-TEST (value)	36.5405703677936
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	133.480687225976
Sum Squared Residuals	819586.317666662

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	2236	2032.79000000001	203.209999999991
2	2084.9	1962.87	122.030000000001
3	2409.5	2388.61	20.8900000000003
4	2199.3	2150.33	48.9700000000005
5	2203.5	2206.91	-3.40999999999902
6	2254.1	2394.59	-140.489999999999
7	1975.8	1974.86166666667	0.938333333333311
8	1742.2	1954.60166666667	-212.401666666666
9	2520.6	2365.48166666667	155.118333333333
10	2438.1	2411.90166666667	26.1983333333336
11	2126.3	2275.92166666667	-149.621666666666
12	2267.5	2205.60166666667	61.8983333333335
13	2201.1	2244.59666666666	-43.4966666666642
14	2128.5	2174.67666666667	-46.1766666666671
15	2596	2600.41666666667	-4.41666666666652
16	2458.2	2362.13666666667	96.0633333333332
17	2210.5	2418.71666666667	-208.216666666667
18	2621.2	2606.39666666667	14.8033333333331
19	2231.4	2186.66833333333	44.7316666666669
20	2103.6	2166.40833333333	-62.8083333333334
21	2685.8	2577.28833333333	108.511666666667
22	2539.3	2623.70833333333	-84.4083333333333
23	2462.4	2487.72833333333	-25.3283333333333
24	2693.3	2417.40833333333	275.891666666667
25	2307.7	2456.40333333333	-148.703333333331
26	2385.9	2386.48333333333	-0.583333333333599
27	2737.6	2812.22333333333	-74.6233333333336
28	2653.9	2573.94333333333	79.9566666666666
29	2545.4	2630.52333333333	-85.1233333333336
30	2848.8	2818.20333333333	30.5966666666667
31	2359.5	2479.41666666667	-119.916666666666
32	2488.3	2459.15666666667	29.1433333333337
33	2861.1	2870.03666666667	-8.93666666666656
34	2717.9	2916.45666666667	-198.556666666666
35	2844	2780.47666666667	63.5233333333334
36	2749	2710.15666666667	38.8433333333335
37	2652.9	2749.15166666666	-96.2516666666642
38	2660.2	2679.23166666667	-19.0316666666670
39	3187.1	3104.97166666667	82.1283333333332
40	2774.1	2866.69166666667	-92.5916666666667
41	3158.2	2923.27166666667	234.928333333333
42	3244.6	3110.95166666667	133.648333333333
43	2665.5	2691.22333333333	-25.7233333333333
44	2820.8	2670.96333333333	149.836666666667
45	2983.4	3081.84333333333	-98.4433333333334
46	3077.4	3128.26333333333	-50.8633333333334
47	3024.8	2992.28333333333	32.5166666666667
48	2731.8	2921.96333333333	-190.163333333333
49	3046.2	2960.95833333333	85.2416666666686
50	2834.8	2891.03833333333	-56.2383333333337
51	3292.8	3316.77833333333	-23.9783333333335
52	2946.1	3078.49833333333	-132.398333333334
53	3196.9	3135.07833333333	61.8216666666662
54	3284.2	3322.75833333333	-38.558333333334
55	3003	2903.03	99.9699999999996
56	2979	2882.77	96.2299999999994
57	3137.4	3293.65	-156.250000000000
58	3647.7	3340.07	307.629999999999
59	3283	3204.09	78.9099999999995
60	2947.3	3133.77	-186.470000000000

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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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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