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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: Mon, 24 Nov 2008 15:54:13 -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/t1227567515fz04sc8vwpszszw.htm/, Retrieved Mon, 24 Nov 2008 22:58:44 +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/t1227567515fz04sc8vwpszszw.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 «

94.5 0 114.2 0 104.9 0 106.2 0 99.9 0 97.6 0 103.6 0 192.4 0 113.4 0 106.5 0 104.1 0 98.8 0 92.2 0 120.8 0 97.1 0 89.7 0 105 0 86.2 0 95.1 0 155 0 116.5 0 92.6 0 96 0 82.9 0 81.7 0 106.5 0 96.2 0 84.9 0 93 0 80.9 0 73.9 0 157.4 0 98.2 0 88.3 0 92.6 0 78.4 0 79.2 0 105.5 0 80.6 0 80.9 0 84.6 0 71.2 0 71.4 0 148 0 83.7 0 83.3 0 92.3 0 74.8 0 82.1 0 100 0 71.7 0 79.1 0 86.8 0 64.2 0 75.4 0 139.3 1 77.3 1 112.4 1 98.6 1 77.3 1 73.5 1 100.1 1 76.5 1 77.7 1 80.4 1 72.2 1 65.4 1 181.2 1 96.3 1 106.4 1 90.9 1 75.3 1 71.2 1 96.1 1 80.6 1 77.7 1 83 1 67.5 1 88.5 1 167.6 1 96.4 1 91 1 90.3 1 92.3 1 84.5 1 100.9 1 90 1 84.2 1 97.4 1 78.2 1 90 1 182.4 1 100.2 1 95.1 1 105 1 86.9 1 80.7 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] = + 85.3925591715976 -4.11011834319527x[t] -1.38806213017746M1[t] + 21.6612352071007M2[t] + 3.34873520710063M3[t] + 1.19873520710063M4[t] + 7.41123520710061M5[t] -6.60126479289932M6[t] -0.9387647928994M7[t] + 82.075M8[t] + 14.4125000000000M9[t] + 13.6125000000000M10[t] + 12.8875000000000M11[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)	85.3925591715976	3.998819	21.3544	0	0
x	-4.11011834319527	2.241008	-1.834	0.070188	0.035094
M1	-1.38806213017746	5.277151	-0.263	0.79317	0.396585
M2	21.6612352071007	5.435855	3.9849	0.000143	7.2e-05
M3	3.34873520710063	5.435855	0.616	0.53953	0.269765
M4	1.19873520710063	5.435855	0.2205	0.825998	0.412999
M5	7.41123520710061	5.435855	1.3634	0.1764	0.0882
M6	-6.60126479289932	5.435855	-1.2144	0.228001	0.114
M7	-0.9387647928994	5.435855	-0.1727	0.863304	0.431652
M8	82.075	5.428632	15.1189	0	0
M9	14.4125000000000	5.428632	2.6549	0.009489	0.004744
M10	13.6125000000000	5.428632	2.5075	0.014083	0.007041
M11	12.8875000000000	5.428632	2.374	0.019878	0.009939

Multiple Linear Regression - Regression Statistics
Multiple R	0.911507110576896
R-squared	0.83084521263224
Adjusted R-squared	0.806680243008275
F-TEST (value)	34.382216305716
F-TEST (DF numerator)	12
F-TEST (DF denominator)	84
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	10.8572646005278
Sum Squared Residuals	9901.93634689348

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	94.5	84.00449704142	10.4955029585801
2	114.2	107.053794378698	7.1462056213018
3	104.9	88.7412943786983	16.1587056213018
4	106.2	86.5912943786983	19.6087056213017
5	99.9	92.8037943786983	7.09620562130174
6	97.6	78.7912943786983	18.8087056213017
7	103.6	84.4537943786982	19.1462056213018
8	192.4	167.467559171598	24.9324408284022
9	113.4	99.8050591715976	13.5949408284024
10	106.5	99.0050591715976	7.4949408284024
11	104.1	98.2800591715976	5.81994082840237
12	98.8	85.3925591715976	13.4074408284024
13	92.2	84.0044970414202	8.19550295857985
14	120.8	107.053794378698	13.7462056213018
15	97.1	88.7412943786982	8.35870562130177
16	89.7	86.5912943786982	3.10870562130178
17	105	92.8037943786982	12.1962056213018
18	86.2	78.7912943786982	7.40870562130178
19	95.1	84.4537943786982	10.6462056213018
20	155	167.467559171598	-12.4675591715976
21	116.5	99.8050591715976	16.6949408284024
22	92.6	99.0050591715976	-6.40505917159765
23	96	98.2800591715976	-2.28005917159763
24	82.9	85.3925591715976	-2.4925591715976
25	81.7	84.0044970414201	-2.30449704142013
26	106.5	107.053794378698	-0.553794378698241
27	96.2	88.7412943786982	7.45870562130178
28	84.9	86.5912943786982	-1.69129437869822
29	93	92.8037943786982	0.196205621301774
30	80.9	78.7912943786982	2.10870562130179
31	73.9	84.4537943786982	-10.5537943786982
32	157.4	167.467559171598	-10.0675591715976
33	98.2	99.8050591715976	-1.60505917159764
34	88.3	99.0050591715976	-10.7050591715976
35	92.6	98.2800591715976	-5.68005917159764
36	78.4	85.3925591715976	-6.9925591715976
37	79.2	84.0044970414201	-4.80449704142013
38	105.5	107.053794378698	-1.55379437869824
39	80.6	88.7412943786982	-8.14129437869823
40	80.9	86.5912943786982	-5.69129437869822
41	84.6	92.8037943786982	-8.20379437869824
42	71.2	78.7912943786982	-7.59129437869822
43	71.4	84.4537943786982	-13.0537943786982
44	148	167.467559171598	-19.4675591715976
45	83.7	99.8050591715976	-16.1050591715976
46	83.3	99.0050591715976	-15.7050591715976
47	92.3	98.2800591715976	-5.98005917159764
48	74.8	85.3925591715976	-10.5925591715976
49	82.1	84.0044970414201	-1.90449704142014
50	100	107.053794378698	-7.05379437869824
51	71.7	88.7412943786982	-17.0412943786982
52	79.1	86.5912943786982	-7.49129437869823
53	86.8	92.8037943786982	-6.00379437869823
54	64.2	78.7912943786982	-14.5912943786982
55	75.4	84.4537943786982	-9.05379437869822
56	139.3	163.357440828402	-24.0574408284023
57	77.3	95.6949408284024	-18.3949408284024
58	112.4	94.8949408284024	17.5050591715976
59	98.6	94.1699408284024	4.43005917159762
60	77.3	81.2824408284023	-3.98244082840235
61	73.5	79.8943786982249	-6.39437869822487
62	100.1	102.943676035503	-2.84367603550298
63	76.5	84.631176035503	-8.13117603550296
64	77.7	82.481176035503	-4.78117603550296
65	80.4	88.693676035503	-8.29367603550296
66	72.2	74.681176035503	-2.48117603550295
67	65.4	80.343676035503	-14.9436760355030
68	181.2	163.357440828402	17.8425591715976
69	96.3	95.6949408284024	0.605059171597625
70	106.4	94.8949408284024	11.5050591715976
71	90.9	94.1699408284024	-3.26994082840237
72	75.3	81.2824408284023	-5.98244082840235
73	71.2	79.8943786982249	-8.69437869822487
74	96.1	102.943676035503	-6.84367603550298
75	80.6	84.631176035503	-4.03117603550297
76	77.7	82.481176035503	-4.78117603550296
77	83	88.693676035503	-5.69367603550296
78	67.5	74.681176035503	-7.18117603550295
79	88.5	80.343676035503	8.15632396449704
80	167.6	163.357440828402	4.24255917159766
81	96.4	95.6949408284024	0.705059171597633
82	91	94.8949408284024	-3.89494082840238
83	90.3	94.1699408284024	-3.86994082840237
84	92.3	81.2824408284023	11.0175591715977
85	84.5	79.8943786982249	4.60562130177512
86	100.9	102.943676035503	-2.04367603550296
87	90	84.631176035503	5.36882396449704
88	84.2	82.481176035503	1.71882396449704
89	97.4	88.693676035503	8.70632396449704
90	78.2	74.681176035503	3.51882396449705
91	90	80.343676035503	9.65632396449704
92	182.4	163.357440828402	19.0425591715977
93	100.2	95.6949408284024	4.50505917159763
94	95.1	94.8949408284024	0.205059171597615
95	105	94.1699408284024	10.8300591715976
96	86.9	81.2824408284023	5.61755917159766
97	80.7	79.8943786982249	0.805621301775132

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227567515fz04sc8vwpszszw/1lh5n1227567249.png (open in new window)

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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