::Free Statistics and Forecasting Software::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the multiple regression model based on the Ordinary Least Squares method.

Click here to edit the underlying code of this R Module.

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!

Send output to:
Browser Blue - Charts White Browser Black/White CSV MS Excel MS Word
Data X:
99.2 96.7 101.0 99.0 98.1 100.1 100.0 100.0 100.0 111.6 104.9 90.6 122.2 104.9 86.5 117.6 109.5 89.7 121.1 110.8 90.6 136.0 112.3 82.8 154.2 109.3 70.1 153.6 105.3 65.4 158.5 101.7 61.3 140.6 95.4 62.5 136.2 96.4 63.6 168.0 97.6 52.6 154.3 102.4 59.7 149.0 101.6 59.5 165.5 103.8 61.3
Names of X columns:
Cons Inc Price
Sample Range: (leave blank to include all observations)
From:
To:
Column Number of Endogenous Series (?)
Fixed Seasonal Effects
Do not include Seasonal DummiesInclude Monthly DummiesInclude Quarterly Dummies
Type of Equation
No Linear TrendLinear TrendFirst Differences
Chart options
Width:
Height:

Click here to edit the underlying code of this R Module.

---

Source code of R module
1	library(lattice)
2	library(lmtest)
3	n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
4	par1 <- as.numeric(par1)
5	x <- t(y)
6	k <- length(x[1,])
7	n <- length(x[,1])
8	x1 <- cbind(x[,par1], x[,1:k!=par1])
9	mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
10	colnames(x1) <- mycolnames #colnames(x)[par1]
11	x <- x1
12	if (par3 == "First Differences"){
13	x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste("(1-B)",colnames(x),sep="")))
14	for (i in 1:n-1) {
15	for (j in 1:k) {
16	x2[i,j] <- x[i+1,j] - x[i,j]
17	}
18	}
19	x <- x2
20	}
21	if (par2 == "Include Monthly Dummies"){
22	x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste("M", seq(1:11), sep ="")))
23	for (i in 1:11){
24	x2[seq(i,n,12),i] <- 1
25	}
26	x <- cbind(x, x2)
27	}
28	if (par2 == "Include Quarterly Dummies"){
29	x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste("Q", seq(1:3), sep ="")))
30	for (i in 1:3){
31	x2[seq(i,n,4),i] <- 1
32	}
33	x <- cbind(x, x2)
34	}
35	k <- length(x[1,])
36	if (par3 == "Linear Trend"){
37	x <- cbind(x, c(1:n))
38	colnames(x)[k+1] <- "t"
39	}
40	x
41	k <- length(x[1,])
42	df <- as.data.frame(x)
43	(mylm <- lm(df))
44	(mysum <- summary(mylm))
45	if (n > n25) {
46	kp3 <- k + 3
47	nmkm3 <- n - k - 3
48	gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
49	numgqtests <- 0
50	numsignificant1 <- 0
51	numsignificant5 <- 0
52	numsignificant10 <- 0
53	for (mypoint in kp3:nmkm3) {
54	j <- 0
55	numgqtests <- numgqtests + 1
56	for (myalt in c("greater", "two.sided", "less")) {
57	j <- j + 1
58	gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
59	}
60	if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
61	if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
62	if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
63	}
64	gqarr
65	}
66	bitmap(file="test0.png")
67	plot(x[,1], type="l", main="Actuals and Interpolation", ylab="value of Actuals and Interpolation (dots)", xlab="time or index")
68	points(x[,1]-mysum$resid)
69	grid()
70	dev.off()
71	bitmap(file="test1.png")
72	plot(mysum$resid, type="b", pch=19, main="Residuals", ylab="value of Residuals", xlab="time or index")
73	grid()
74	dev.off()
75	bitmap(file="test2.png")
76	hist(mysum$resid, main="Residual Histogram", xlab="values of Residuals")
77	grid()
78	dev.off()
79	bitmap(file="test3.png")
80	densityplot(~mysum$resid,col="black",main="Residual Density Plot", xlab="values of Residuals")
81	dev.off()
82	bitmap(file="test4.png")
83	qqnorm(mysum$resid, main="Residual Normal Q-Q Plot")
84	qqline(mysum$resid)
85	grid()
86	dev.off()
87	(myerror <- as.ts(mysum$resid))
88	bitmap(file='test5.png')
89	dum <- cbind(lag(myerror,k=1),myerror)
90	dum
91	dum1 <- dum[2:length(myerror),]
92	dum1
93	z <- as.data.frame(dum1)
94	z
95	plot(z,main=paste("Residual Lag plot, lowess, and regression line"), ylab="values of Residuals", xlab="lagged values of Residuals")
96	lines(lowess(z))
97	abline(lm(z))
98	grid()
99	dev.off()
100	bitmap(file="test6.png")
101	acf(mysum$resid, lag.max=length(mysum$resid)/2, main="Residual Autocorrelation Function")
102	grid()
103	dev.off()
104	bitmap(file="test7.png")
105	pacf(mysum$resid, lag.max=length(mysum$resid)/2, main="Residual Partial Autocorrelation Function")
106	grid()
107	dev.off()
108	bitmap(file="test8.png")
109	opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
110	plot(mylm, las = 1, sub="Residual Diagnostics")
111	par(opar)
112	dev.off()
113	if (n > n25) {
114	bitmap(file="test9.png")
115	plot(kp3:nmkm3,gqarr[,2], main="Goldfeld-Quandt test",ylab="2-sided p-value",xlab="breakpoint")
116	grid()
117	dev.off()
118	}
119	load(file="createtable")
120	a<-table.start()
121	a<-table.row.start(a)
122	a<-table.element(a, "Multiple Linear Regression - Estimated Regression Equation", 1, TRUE)
123	a<-table.row.end(a)
124	myeq <- colnames(x)[1]
125	myeq <- paste(myeq, "[t] = ", sep="")
126	for (i in 1:k){
127	if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, "+", "")
128	myeq <- paste(myeq, mysum$coefficients[i,1], sep=" ")
129	if (rownames(mysum$coefficients)[i] != "(Intercept)") {
130	myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep="")
131	if (rownames(mysum$coefficients)[i] != "t") myeq <- paste(myeq, "[t]", sep="")
132	}
133	}
134	myeq <- paste(myeq, " + e[t]")
135	a<-table.row.start(a)
136	a<-table.element(a, myeq)
137	a<-table.row.end(a)
138	a<-table.end(a)
139	table.save(a,file="mytable1.tab")
140	a<-table.start()
141	a<-table.row.start(a)
142	a<-table.element(a,hyperlink("http://www.xycoon.com/ols1.htm","Multiple Linear Regression - Ordinary Least Squares",""), 6, TRUE)
143	a<-table.row.end(a)
144	a<-table.row.start(a)
145	a<-table.element(a,"Variable",header=TRUE)
146	a<-table.element(a,"Parameter",header=TRUE)
147	a<-table.element(a,"S.D.",header=TRUE)
148	a<-table.element(a,"T-STAT H0: parameter = 0",header=TRUE)
149	a<-table.element(a,"2-tail p-value",header=TRUE)
150	a<-table.element(a,"1-tail p-value",header=TRUE)
151	a<-table.row.end(a)
152	for (i in 1:k){
153	a<-table.row.start(a)
154	a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
155	a<-table.element(a,mysum$coefficients[i,1])
156	a<-table.element(a, round(mysum$coefficients[i,2],6))
157	a<-table.element(a, round(mysum$coefficients[i,3],4))
158	a<-table.element(a, round(mysum$coefficients[i,4],6))
159	a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
160	a<-table.row.end(a)
161	}
162	a<-table.end(a)
163	table.save(a,file="mytable2.tab")
164	a<-table.start()
165	a<-table.row.start(a)
166	a<-table.element(a, "Multiple Linear Regression - Regression Statistics", 2, TRUE)
167	a<-table.row.end(a)
168	a<-table.row.start(a)
169	a<-table.element(a, "Multiple R",1,TRUE)
170	a<-table.element(a, sqrt(mysum$r.squared))
171	a<-table.row.end(a)
172	a<-table.row.start(a)
173	a<-table.element(a, "R-squared",1,TRUE)
174	a<-table.element(a, mysum$r.squared)
175	a<-table.row.end(a)
176	a<-table.row.start(a)
177	a<-table.element(a, "Adjusted R-squared",1,TRUE)
178	a<-table.element(a, mysum$adj.r.squared)
179	a<-table.row.end(a)
180	a<-table.row.start(a)
181	a<-table.element(a, "F-TEST (value)",1,TRUE)
182	a<-table.element(a, mysum$fstatistic[1])
183	a<-table.row.end(a)
184	a<-table.row.start(a)
185	a<-table.element(a, "F-TEST (DF numerator)",1,TRUE)
186	a<-table.element(a, mysum$fstatistic[2])
187	a<-table.row.end(a)
188	a<-table.row.start(a)
189	a<-table.element(a, "F-TEST (DF denominator)",1,TRUE)
190	a<-table.element(a, mysum$fstatistic[3])
191	a<-table.row.end(a)
192	a<-table.row.start(a)
193	a<-table.element(a, "p-value",1,TRUE)
194	a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
195	a<-table.row.end(a)
196	a<-table.row.start(a)
197	a<-table.element(a, "Multiple Linear Regression - Residual Statistics", 2, TRUE)
198	a<-table.row.end(a)
199	a<-table.row.start(a)
200	a<-table.element(a, "Residual Standard Deviation",1,TRUE)
201	a<-table.element(a, mysum$sigma)
202	a<-table.row.end(a)
203	a<-table.row.start(a)
204	a<-table.element(a, "Sum Squared Residuals",1,TRUE)
205	a<-table.element(a, sum(myerror*myerror))
206	a<-table.row.end(a)
207	a<-table.end(a)
208	table.save(a,file="mytable3.tab")
209	a<-table.start()
210	a<-table.row.start(a)
211	a<-table.element(a, "Multiple Linear Regression - Actuals, Interpolation, and Residuals", 4, TRUE)
212	a<-table.row.end(a)
213	a<-table.row.start(a)
214	a<-table.element(a, "Time or Index", 1, TRUE)
215	a<-table.element(a, "Actuals", 1, TRUE)
216	a<-table.element(a, "Interpolation Forecast", 1, TRUE)
217	a<-table.element(a, "Residuals Prediction Error", 1, TRUE)
218	a<-table.row.end(a)
219	for (i in 1:n) {
220	a<-table.row.start(a)
221	a<-table.element(a,i, 1, TRUE)
222	a<-table.element(a,x[i])
223	a<-table.element(a,x[i]-mysum$resid[i])
224	a<-table.element(a,mysum$resid[i])
225	a<-table.row.end(a)
226	}
227	a<-table.end(a)
228	table.save(a,file="mytable4.tab")
229	if (n > n25) {
230	a<-table.start()
231	a<-table.row.start(a)
232	a<-table.element(a,"Goldfeld-Quandt test for Heteroskedasticity",4,TRUE)
233	a<-table.row.end(a)
234	a<-table.row.start(a)
235	a<-table.element(a,"p-values",header=TRUE)
236	a<-table.element(a,"Alternative Hypothesis",3,header=TRUE)
237	a<-table.row.end(a)
238	a<-table.row.start(a)
239	a<-table.element(a,"breakpoint index",header=TRUE)
240	a<-table.element(a,"greater",header=TRUE)
241	a<-table.element(a,"2-sided",header=TRUE)
242	a<-table.element(a,"less",header=TRUE)
243	a<-table.row.end(a)
244	for (mypoint in kp3:nmkm3) {
245	a<-table.row.start(a)
246	a<-table.element(a,mypoint,header=TRUE)
247	a<-table.element(a,gqarr[mypoint-kp3+1,1])
248	a<-table.element(a,gqarr[mypoint-kp3+1,2])
249	a<-table.element(a,gqarr[mypoint-kp3+1,3])
250	a<-table.row.end(a)
251	}
252	a<-table.end(a)
253	table.save(a,file="mytable5.tab")
254	a<-table.start()
255	a<-table.row.start(a)
256	a<-table.element(a,"Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity",4,TRUE)
257	a<-table.row.end(a)
258	a<-table.row.start(a)
259	a<-table.element(a,"Description",header=TRUE)
260	a<-table.element(a,"# significant tests",header=TRUE)
261	a<-table.element(a,"% significant tests",header=TRUE)
262	a<-table.element(a,"OK/NOK",header=TRUE)
263	a<-table.row.end(a)
264	a<-table.row.start(a)
265	a<-table.element(a,"1% type I error level",header=TRUE)
266	a<-table.element(a,numsignificant1)
267	a<-table.element(a,numsignificant1/numgqtests)
268	if (numsignificant1/numgqtests < 0.01) dum <- "OK" else dum <- "NOK"
269	a<-table.element(a,dum)
270	a<-table.row.end(a)
271	a<-table.row.start(a)
272	a<-table.element(a,"5% type I error level",header=TRUE)
273	a<-table.element(a,numsignificant5)
274	a<-table.element(a,numsignificant5/numgqtests)
275	if (numsignificant5/numgqtests < 0.05) dum <- "OK" else dum <- "NOK"
276	a<-table.element(a,dum)
277	a<-table.row.end(a)
278	a<-table.row.start(a)
279	a<-table.element(a,"10% type I error level",header=TRUE)
280	a<-table.element(a,numsignificant10)
281	a<-table.element(a,numsignificant10/numgqtests)
282	if (numsignificant10/numgqtests < 0.1) dum <- "OK" else dum <- "NOK"
283	a<-table.element(a,dum)
284	a<-table.row.end(a)
285	a<-table.end(a)
286	table.save(a,file="mytable6.tab")
287	}

Cite this software as:

Wessa P., (2008), Multiple Regression (v1.0.26) in Free Statistics Software (v1.1.23-r5), Office for Research Development and Education, URL http://www.wessa.net/rwasp_multipleregression.wasp/

The R code is based on :

Chambers, J. M. (1992), Linear models. (Chapter 4 of Statistical Models in S), eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

Borghers, E, and P. Wessa, Statistics - Econometrics - Forecasting, Office for Research Development and Education, http://www.xycoon.com/

To cite Wessa.net in publications use:
Wessa, P. (2010), Free Statistics Software, Office for Research Development and Education,
version 1.1.23-r5, URL http://www.wessa.net/

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Software Version : 1.1.23-r5
Algorithms & Software : Prof. dr. P. Wessa
Facilities : Resa R&D - Office for Research, Development, and Education
Server : www.wessa.net

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