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Multiple regression Totaal

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

Title produced by software: Multiple Regression

Date of computation: Sun, 16 Dec 2007 18:17:47 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/17/t1197853280v2r6rud4yo683jj.htm/, Retrieved Mon, 17 Dec 2007 02:01:20 +0100

User-defined keywords:

Multiple regression Totaal 2

Dataseries X:

» Textbox « » Textfile « » CSV «

153.4 0 159.5 0 157.4 0 169.1 0 172.6 0 161.7 0 159.2 0 157.4 0 153.9 0 144.8 0 142.2 0 140.1 0 143.4 0 153.3 0 166.9 0 170.6 0 182.8 0 170.3 0 156.6 0 155.2 0 154.7 0 151.6 0 152.1 0 153.2 0 149.5 0 149.7 0 144.3 0 140 0 137.8 0 132.2 0 128.9 0 123.1 0 120.4 0 122.8 0 126 0 124.5 0 120.6 0 114.7 0 111.7 0 109.1 0 108 0 107.7 0 99.9 0 103.7 0 103.4 0 103.4 0 104.7 0 105.8 0 105.3 0 103 0 103.8 0 103.4 0 105.8 0 101.4 0 97 0 94.3 0 96.6 0 97.1 0 95.7 0 96.9 0 97.4 0 95.3 0 93.6 0 91.5 0 93.1 0 91.7 0 94.3 0 93.9 0 90.9 0 88.3 0 91.3 1 91.7 1 92.4 1 92 1 95.6 1 95.8 1 96.4 1 99 1 107 1 109.7 1 116.2 1 115.9 1 113.8 1 112.6 1 113.7 1 115.9 1 110.3 1 111.3 1 113.4 1 108.2 1 104.8 1 106 1 110.9 1 115 1 118.4 1 121.4 1 128.8 1 131.7 1 141.7 1 142.9 1 139.4 1 134.7 1 125 1 113.6 1 111.5 1 108.5 1 112.3 1 116.6 1 115.5 1 120.1 1 132.9 1 128.1 1 129.3 1 132.5 1 131 1 124.9 1 120.8 1 122 1 122.1 1 127.4 1 135.2 1 137.3 1 135 1 136 1 138.4 1 134.7 1 138.4 1 133.9 1 133.6 1 141.2 1 151.8 1 155.4 1 156.6 1 161.6 1 160.7 1 156 1 159.5 1 168.7 1 169.9 1 169.9 1 185.9 1

Text written by user:

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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

Totaal[t] = + 127.441258741259 + 11.4961538461539`9/11`[t] + 3.38801476301479M1[t] + 5.40446775446775M2[t] + 7.21258741258741M3[t] + 7.36237373737374M4[t] + 9.41216006216006M5[t] + 6.76194638694639M6[t] + 4.35339937839938M7[t] + 2.31151903651904M8[t] + 3.56963869463870M9[t] -2.45295260295260M10[t] -1.53993783993784M11[t] -0.158119658119658t + 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)	127.441258741259	8.647778	14.7369	0	0
`9/11`	11.4961538461539	8.511764	1.3506	0.179219	0.08961
M1	3.38801476301479	10.472919	0.3235	0.746847	0.373423
M2	5.40446775446775	10.47157	0.5161	0.606676	0.303338
M3	7.21258741258741	10.471266	0.6888	0.492207	0.246103
M4	7.36237373737374	10.472007	0.7031	0.48331	0.241655
M5	9.41216006216006	10.473794	0.8986	0.370546	0.185273
M6	6.76194638694639	10.476625	0.6454	0.519812	0.259906
M7	4.35339937839938	10.4805	0.4154	0.678564	0.339282
M8	2.31151903651904	10.485418	0.2205	0.825874	0.412937
M9	3.56963869463870	10.491376	0.3402	0.734234	0.367117
M10	-2.45295260295260	10.711542	-0.229	0.819237	0.409618
M11	-1.53993783993784	10.695166	-0.144	0.885741	0.44287
t	-0.158119658119658	0.104627	-1.5113	0.133203	0.066601

Multiple Linear Regression - Regression Statistics
Multiple R	0.196747891442341
R-squared	0.0387097327870072
Adjusted R-squared	-0.0596900583450315
F-TEST (value)	0.39339242839514
F-TEST (DF numerator)	13
F-TEST (DF denominator)	127
p-value	0.969820277163018
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	25.0811877331051
Sum Squared Residuals	79891.3792191142

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	153.4	130.671153846154	22.7288461538465
2	159.5	132.529487179487	26.9705128205128
3	157.4	134.179487179487	23.2205128205128
4	169.1	134.171153846154	34.9288461538461
5	172.6	136.062820512821	36.5371794871795
6	161.7	133.254487179487	28.4455128205128
7	159.2	130.687820512821	28.5121794871795
8	157.4	128.487820512821	28.9121794871795
9	153.9	129.587820512821	24.3121794871795
10	144.8	123.407109557110	21.3928904428904
11	142.2	124.162004662005	18.0379953379953
12	140.1	125.543822843823	14.5561771561771
13	143.4	128.773717948718	14.6262820512820
14	153.3	130.632051282051	22.6679487179487
15	166.9	132.282051282051	34.6179487179487
16	170.6	132.273717948718	38.3262820512820
17	182.8	134.165384615385	48.6346153846154
18	170.3	131.357051282051	38.9429487179487
19	156.6	128.790384615385	27.8096153846154
20	155.2	126.590384615385	28.6096153846154
21	154.7	127.690384615385	27.0096153846154
22	151.6	121.509673659674	30.0903263403263
23	152.1	122.264568764569	29.8354312354312
24	153.2	123.646386946387	29.5536130536130
25	149.5	126.876282051282	22.6237179487179
26	149.7	128.734615384615	20.9653846153846
27	144.3	130.384615384615	13.9153846153846
28	140	130.376282051282	9.62371794871795
29	137.8	132.267948717949	5.53205128205129
30	132.2	129.459615384615	2.74038461538460
31	128.9	126.892948717949	2.00705128205129
32	123.1	124.692948717949	-1.59294871794872
33	120.4	125.792948717949	-5.39294871794872
34	122.8	119.612237762238	3.18776223776224
35	126	120.367132867133	5.63286713286713
36	124.5	121.748951048951	2.75104895104895
37	120.6	124.978846153846	-4.37884615384619
38	114.7	126.837179487179	-12.1371794871795
39	111.7	128.487179487180	-16.7871794871795
40	109.1	128.478846153846	-19.3788461538462
41	108	130.370512820513	-22.3705128205128
42	107.7	127.562179487179	-19.8621794871795
43	99.9	124.995512820513	-25.0955128205128
44	103.7	122.795512820513	-19.0955128205128
45	103.4	123.895512820513	-20.4955128205128
46	103.4	117.714801864802	-14.3148018648019
47	104.7	118.469696969697	-13.7696969696970
48	105.8	119.851515151515	-14.0515151515152
49	105.3	123.081410256410	-17.7814102564103
50	103	124.939743589744	-21.9397435897436
51	103.8	126.589743589744	-22.7897435897436
52	103.4	126.581410256410	-23.1814102564102
53	105.8	128.473076923077	-22.6730769230769
54	101.4	125.664743589744	-24.2647435897436
55	97	123.098076923077	-26.0980769230769
56	94.3	120.898076923077	-26.5980769230769
57	96.6	121.998076923077	-25.3980769230769
58	97.1	115.817365967366	-18.7173659673660
59	95.7	116.572261072261	-20.8722610722611
60	96.9	117.954079254079	-21.0540792540792
61	97.4	121.183974358974	-23.7839743589744
62	95.3	123.042307692308	-27.7423076923077
63	93.6	124.692307692308	-31.0923076923077
64	91.5	124.683974358974	-33.1839743589743
65	93.1	126.575641025641	-33.475641025641
66	91.7	123.767307692308	-32.0673076923077
67	94.3	121.200641025641	-26.9006410256410
68	93.9	119.000641025641	-25.100641025641
69	90.9	120.100641025641	-29.200641025641
70	88.3	113.91993006993	-25.6199300699300
71	91.3	126.170979020979	-34.870979020979
72	91.7	127.552797202797	-35.8527972027972
73	92.4	130.782692307692	-38.3826923076923
74	92	132.641025641026	-40.6410256410256
75	95.6	134.291025641026	-38.6910256410256
76	95.8	134.282692307692	-38.4826923076923
77	96.4	136.174358974359	-39.774358974359
78	99	133.366025641026	-34.3660256410257
79	107	130.799358974359	-23.799358974359
80	109.7	128.599358974359	-18.899358974359
81	116.2	129.699358974359	-13.4993589743590
82	115.9	123.518648018648	-7.61864801864801
83	113.8	124.273543123543	-10.4735431235431
84	112.6	125.655361305361	-13.0553613053613
85	113.7	128.885256410256	-15.1852564102564
86	115.9	130.743589743590	-14.8435897435897
87	110.3	132.393589743590	-22.0935897435897
88	111.3	132.385256410256	-21.0852564102564
89	113.4	134.276923076923	-20.8769230769231
90	108.2	131.468589743590	-23.2685897435897
91	104.8	128.901923076923	-24.1019230769231
92	106	126.701923076923	-20.7019230769231
93	110.9	127.801923076923	-16.9019230769231
94	115	121.621212121212	-6.62121212121212
95	118.4	122.376107226107	-3.97610722610722
96	121.4	123.757925407925	-2.35792540792540
97	128.8	126.987820512821	1.81217948717946
98	131.7	128.846153846154	2.85384615384614
99	141.7	130.496153846154	11.2038461538461
100	142.9	130.487820512821	12.4121794871795
101	139.4	132.379487179487	7.02051282051282
102	134.7	129.571153846154	5.12884615384614
103	125	127.004487179487	-2.00448717948718
104	113.6	124.804487179487	-11.2044871794872
105	111.5	125.904487179487	-14.4044871794872
106	108.5	119.723776223776	-11.2237762237762
107	112.3	120.478671328671	-8.17867132867133
108	116.6	121.860489510490	-5.26048951048951
109	115.5	125.090384615385	-9.59038461538465
110	120.1	126.948717948718	-6.84871794871795
111	132.9	128.598717948718	4.30128205128206
112	128.1	128.590384615385	-0.490384615384618
113	129.3	130.482051282051	-1.18205128205127
114	132.5	127.673717948718	4.82628205128205
115	131	125.107051282051	5.89294871794872
116	124.9	122.907051282051	1.99294871794872
117	120.8	124.007051282051	-3.20705128205128
118	122	117.826340326340	4.17365967365968
119	122.1	118.581235431235	3.51876456876457
120	127.4	119.963053613054	7.4369463869464
121	135.2	123.192948717949	12.0070512820513
122	137.3	125.051282051282	12.2487179487180
123	135	126.701282051282	8.29871794871796
124	136	126.692948717949	9.3070512820513
125	138.4	128.584615384615	9.81538461538462
126	134.7	125.776282051282	8.92371794871794
127	138.4	123.209615384615	15.1903846153846
128	133.9	121.009615384615	12.8903846153846
129	133.6	122.109615384615	11.4903846153846
130	141.2	115.928904428904	25.2710955710956
131	151.8	116.683799533800	35.1162004662005
132	155.4	118.065617715618	37.3343822843823
133	156.6	121.295512820513	35.3044871794872
134	161.6	123.153846153846	38.4461538461539
135	160.7	124.803846153846	35.8961538461538
136	156	124.795512820513	31.2044871794872
137	159.5	126.687179487179	32.8128205128205
138	168.7	123.878846153846	44.8211538461538
139	169.9	121.312179487179	48.5878205128205
140	169.9	119.112179487179	50.7878205128205
141	185.9	120.212179487179	65.6878205128205

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197853280v2r6rud4yo683jj/1zn4m1197854257.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197853280v2r6rud4yo683jj/7eou01197854257.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197853280v2r6rud4yo683jj/7eou01197854257.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197853280v2r6rud4yo683jj/8ea4p1197854257.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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