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*The author of this computation has been verified*

R Software Module

rwasp_grangercausality.wasp

Title produced by software

Bivariate Granger Causality

Date of computation

Wed, 05 Nov 2025 05:57:12 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2025/Nov/05/t1762319148iuwknl699evb5of.htm/, Retrieved Mon, 20 Apr 2026 21:18:39 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 20 Apr 2026 21:18:39 +0200

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Original text written by user:

(Weekly Test Volume) X (Weekly Percent Test Positivity) /100 is equal to (Weekly Positive Test Results) (Weekly Positive Test Results) is a far better predictor of COVID Deaths than (Weekly Percent Test Positivity). This supports the hypothesis that test sample collection forces virus, formerly trapped safely on the nasophryngeal mucus, into contact with bloodstream and epithelial cells in which it can rapidly reproduce, leading to death.

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Dataseries Y:

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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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

3 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

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	Big Analytics Cloud Computing Center

Granger Causality Test: Y = f(X)
Model	Res.DF	Diff. DF	F	p-value
Complete model	279
Reduced model	280	-1	444.076253317656	1.22814865610815e-59

\begin{tabular}{lllllllll}
\hline
Granger Causality Test: Y = f(X) \tabularnewline
Model & Res.DF & Diff. DF & F & p-value \tabularnewline
Complete model & 279 &  &  &  \tabularnewline
Reduced model & 280 & -1 & 444.076253317656 & 1.22814865610815e-59 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Granger Causality Test: Y = f(X)[/C][/ROW]
[ROW][C]Model[/C][C]Res.DF[/C][C]Diff. DF[/C][C]F[/C][C]p-value[/C][/ROW]
[ROW][C]Complete model[/C][C]279[/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Reduced model[/C][C]280[/C][C]-1[/C][C]444.076253317656[/C][C]1.22814865610815e-59[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Granger Causality Test: Y = f(X)
Model	Res.DF	Diff. DF	F	p-value
Complete model	279
Reduced model	280	-1	444.076253317656	1.22814865610815e-59

Granger Causality Test: X = f(Y)
Model	Res.DF	Diff. DF	F	p-value
Complete model	279
Reduced model	280	-1	22.3240747463552	3.65513677540534e-06

\begin{tabular}{lllllllll}
\hline
Granger Causality Test: X = f(Y) \tabularnewline
Model & Res.DF & Diff. DF & F & p-value \tabularnewline
Complete model & 279 &  &  &  \tabularnewline
Reduced model & 280 & -1 & 22.3240747463552 & 3.65513677540534e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Granger Causality Test: X = f(Y)[/C][/ROW]
[ROW][C]Model[/C][C]Res.DF[/C][C]Diff. DF[/C][C]F[/C][C]p-value[/C][/ROW]
[ROW][C]Complete model[/C][C]279[/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Reduced model[/C][C]280[/C][C]-1[/C][C]22.3240747463552[/C][C]3.65513677540534e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Granger Causality Test: X = f(Y)
Model	Res.DF	Diff. DF	F	p-value
Complete model	279
Reduced model	280	-1	22.3240747463552	3.65513677540534e-06

Figure 1

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Figure 2

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Figure 3

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Parameters (Session):

Parameters (R input):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 1 ; par5 = 1 ; par6 = 0 ; par7 = 0 ; par8 = 1 ;

R code (references can be found in the software module):

library(lmtest)
par1 &lt;- as.numeric(par1)
par2 &lt;- as.numeric(par2)
par3 &lt;- as.numeric(par3)
par4 &lt;- as.numeric(par4)
par5 &lt;- as.numeric(par5)
par6 &lt;- as.numeric(par6)
par7 &lt;- as.numeric(par7)
par8 &lt;- as.numeric(par8)
ox &lt;- x
oy &lt;- y
if (par1 == 0) {
x &lt;- log(x)
} else {
x &lt;- (x ^ par1 - 1) / par1
}
if (par5 == 0) {
y &lt;- log(y)
} else {
y &lt;- (y ^ par5 - 1) / par5
}
if (par2 &gt; 0) x &lt;- diff(x,lag=1,difference=par2)
if (par6 &gt; 0) y &lt;- diff(y,lag=1,difference=par6)
if (par3 &gt; 0) x &lt;- diff(x,lag=par4,difference=par3)
if (par7 &gt; 0) y &lt;- diff(y,lag=par4,difference=par7)
print(x)
print(y)
(gyx &lt;- grangertest(y ~ x, order=par8))
(gxy &lt;- grangertest(x ~ y, order=par8))
bitmap(file='test1.png')
op &lt;- par(mfrow=c(2,1))
(r &lt;- ccf(ox,oy,main='Cross Correlation Function (raw data)',ylab='CCF',xlab='Lag (k)'))
(r &lt;- ccf(x,y,main='Cross Correlation Function (transformed and differenced)',ylab='CCF',xlab='Lag (k)'))
par(op)
dev.off()
bitmap(file='test2.png')
op &lt;- par(mfrow=c(2,1))
acf(ox,lag.max=round(length(x)/2),main='ACF of x (raw)')
acf(x,lag.max=round(length(x)/2),main='ACF of x (transformed and differenced)')
par(op)
dev.off()
bitmap(file='test3.png')
op &lt;- par(mfrow=c(2,1))
acf(oy,lag.max=round(length(y)/2),main='ACF of y (raw)')
acf(y,lag.max=round(length(y)/2),main='ACF of y (transformed and differenced)')
par(op)
dev.off()
load(file='createtable')
a&lt;-table.start()
a&lt;-table.row.start(a)
a&lt;-table.element(a,'Granger Causality Test: Y = f(X)',5,TRUE)
a&lt;-table.row.end(a)
a&lt;-table.row.start(a)
a&lt;-table.element(a,'Model',header=TRUE)
a&lt;-table.element(a,'Res.DF',header=TRUE)
a&lt;-table.element(a,'Diff. DF',header=TRUE)
a&lt;-table.element(a,'F',header=TRUE)
a&lt;-table.element(a,'p-value',header=TRUE)
a&lt;-table.row.end(a)
a&lt;-table.row.start(a)
a&lt;-table.element(a,'Complete model',header=TRUE)
a&lt;-table.element(a,gyx$Res.Df[1])
a&lt;-table.element(a,'')
a&lt;-table.element(a,'')
a&lt;-table.element(a,'')
a&lt;-table.row.end(a)
a&lt;-table.row.start(a)
a&lt;-table.element(a,'Reduced model',header=TRUE)
a&lt;-table.element(a,gyx$Res.Df[2])
a&lt;-table.element(a,gyx$Df[2])
a&lt;-table.element(a,gyx$F[2])
a&lt;-table.element(a,gyx$Pr[2])
a&lt;-table.row.end(a)
a&lt;-table.end(a)
table.save(a,file='mytable1.tab')
a&lt;-table.start()
a&lt;-table.row.start(a)
a&lt;-table.element(a,'Granger Causality Test: X = f(Y)',5,TRUE)
a&lt;-table.row.end(a)
a&lt;-table.row.start(a)
a&lt;-table.element(a,'Model',header=TRUE)
a&lt;-table.element(a,'Res.DF',header=TRUE)
a&lt;-table.element(a,'Diff. DF',header=TRUE)
a&lt;-table.element(a,'F',header=TRUE)
a&lt;-table.element(a,'p-value',header=TRUE)
a&lt;-table.row.end(a)
a&lt;-table.row.start(a)
a&lt;-table.element(a,'Complete model',header=TRUE)
a&lt;-table.element(a,gxy$Res.Df[1])
a&lt;-table.element(a,'')
a&lt;-table.element(a,'')
a&lt;-table.element(a,'')
a&lt;-table.row.end(a)
a&lt;-table.row.start(a)
a&lt;-table.element(a,'Reduced model',header=TRUE)
a&lt;-table.element(a,gxy$Res.Df[2])
a&lt;-table.element(a,gxy$Df[2])
a&lt;-table.element(a,gxy$F[2])
a&lt;-table.element(a,gxy$Pr[2])
a&lt;-table.row.end(a)
a&lt;-table.end(a)
table.save(a,file='mytable2.tab')

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Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code