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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_Simple Regression Y ~ X.wasp
Title produced by softwareSimple Linear Regression
Date of computationMon, 10 Dec 2012 13:48:23 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/10/t1355165320owr3buy4470g094.htm/, Retrieved Fri, 19 Apr 2024 17:46:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=198282, Retrieved Fri, 19 Apr 2024 17:46:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact36

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Simple Linear Regression] [] [2012-12-10 18:48:23] [108821faace101f0b67e40eaa0fe63e0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
	
1977	1	87.28	255
1977	2	87.28	280.2
1977	3	87.09	299.9
1977	4	86.92	339.2
1977	5	87.59	374.2
1977	6	90.72	393.5
1977	7	90.69	389.2
1977	8	90.3	381.7
1977	9	89.55	375.2
1977	10	88.94	369
1977	11	88.41	357.4
1977	12	87.82	352.1
1978	1	87.07	346.5
1978	2	86.82	342.9
1978	3	86.4	340.3
1978	4	86.02	328.3
1978	5	85.66	322.9
1978	6	85.32	314.3
1978	7	85	308.9
1978	8	84.67	294
1978	9	83.94	285.6
1978	10	82.83	281.2
1978	11	81.95	280.3
1978	12	81.19	278.8
1979	1	80.48	274.5
1979	2	78.86	270.4
1979	3	69.47	263.4
1979	4	68.77	259.9
1979	5	70.06	258
1979	6	73.95	262.7
1979	7	75.8	284.7
1979	8	77.79	311.3
1979	9	81.57	322.1
1979	10	83.07	327
1979	11	84.34	331.3
1979	12	85.1	333.3
1980	1	85.25	321.4
1980	2	84.26	327
1980	3	83.63	320
1980	4	86.44	314.7
1980	5	85.3	316.7
1980	6	84.1	314.4
1980	7	83.36	321.3
1980	8	82.48	318.2
1980	9	81.58	307.2
1980	10	80.47	301.3
1980	11	79.34	287.5
1980	12	82.13	277.7
1981	1	81.69	274.4
1981	2	80.7	258.8
1981	3	79.88	253.3
1981	4	79.16	251
1981	5	78.38	248.4
1981	6	77.42	249.5
1981	7	76.47	246.1
1981	8	75.46	244.5
1981	9	74.48	243.6
1981	10	78.27	244
1981	11	80.7	240.8
1981	12	79.91	249.8
1982	1	78.75	248
1982	2	77.78	259.4
1982	3	81.14	260.5
1982	4	81.08	260.8
1982	5	80.03	261.3
1982	6	78.91	259.5
1982	7	78.01	256.6
1982	8	76.9	257.9
1982	9	75.97	256.5
1982	10	81.93	254.2
1982	11	80.27	253.3
1982	12	78.67	253.8
1983	1	77.42	255.5
1983	2	76.16	257.1
1983	3	74.7	257.3
1983	4	76.39	253.2
1983	5	76.04	252.8
1983	6	74.65	252
1983	7	73.29	250.7
1983	8	71.79	252.2
1983	9	74.39	250
1983	10	74.91	251
1983	11	74.54	253.4
1983	12	73.08	251.2
1984	1	72.75	255.6
1984	2	71.32	261.1
1984	3	70.38	258.9
1984	4	70.35	259.9
1984	5	70.01	261.2
1984	6	69.36	264.7
1984	7	67.77	267.1
1984	8	69.26	266.4
1984	9	69.8	267.7
1984	10	68.38	268.6
1984	11	67.62	267.5
1984	12	68.39	268.5
1985	1	66.95	268.5
1985	2	65.21	270.5
1985	3	66.64	270.9
1985	4	63.45	270.1
1985	5	60.66	269.3
1985	6	62.34	269.8
1985	7	60.32	270.1
1985	8	58.64	264.9
1985	9	60.46	263.7
1985	10	58.59	264.8
1985	11	61.87	263.7
1985	12	61.85	255.9
1986	1	67.44	276.2
1986	2	77.06	360.1
1986	3	91.74	380.5
1986	4	93.15	373.7
1986	5	94.15	369.8
1986	6	93.11	366.6
1986	7	91.51	359.3
1986	8	89.96	345.8
1986	9	88.16	326.2
1986	10	86.98	324.5
1986	11	88.03	328.1
1986	12	86.24	327.5
1987	1	84.65	324.4
1987	2	83.23	316.5
1987	3	81.7	310.9
1987	4	80.25	301.5
1987	5	78.8	291.7
1987	6	77.51	290.4
1987	7	76.2	287.4
1987	8	75.04	277.7
1987	9	74	281.6
1987	10	75.49	288
1987	11	77.14	276
1987	12	76.15	272.9
1988	1	76.27	283
1988	2	78.19	283.3
1988	3	76.49	276.8
1988	4	77.31	284.5
1988	5	76.65	282.7
1988	6	74.99	281.2
1988	7	73.51	287.4
1988	8	72.07	283.1
1988	9	70.59	284
1988	10	71.96	285.5
1988	11	76.29	289.2
1988	12	74.86	292.5
1989	1	74.93	296.4
1989	2	71.9	305.2
1989	3	71.01	303.9
1989	4	77.47	311.5
1989	5	75.78	316.3
1989	6	76.6	316.7
1989	7	76.07	322.5
1989	8	74.57	317.1
1989	9	73.02	309.8
1989	10	72.65	303.8
1989	11	73.16	290.3
1989	12	71.53	293.7
1990	1	69.78	291.7
1990	2	67.98	296.5
1990	3	69.96	289.1
1990	4	72.16	288.5
1990	5	70.47	293.8
1990	6	68.86	297.7
1990	7	67.37	305.4
1990	8	65.87	302.7
1990	9	72.16	302.5
1990	10	71.34	303
1990	11	69.93	294.5
1990	12	68.44	294.1
1991	1	67.16	294.5
1991	2	66.01	297.1
1991	3	67.25	289.4
1991	4	70.91	292.4
1991	5	69.75	287.9
1991	6	68.59	286.6
1991	7	67.48	280.5
1991	8	66.31	272.4
1991	9	64.81	269.2
1991	10	66.58	270.6
1991	11	65.97	267.3
1991	12	64.7	262.5
1992	1	64.7	266.8
1992	2	60.94	268.8
1992	3	59.08	263.1
1992	4	58.42	261.2
1992	5	57.77	266
1992	6	57.11	262.5
1992	7	53.31	265.2
1992	8	49.96	261.3
1992	9	49.4	253.7
1992	10	48.84	249.2
1992	11	48.3	239.1
1992	12	47.74	236.4
1993	1	47.24	235.2
1993	2	46.76	245.2
1993	3	46.29	246.2
1993	4	48.9	247.7
1993	5	49.23	251.4
1993	6	48.53	253.3
1993	7	48.03	254.8
1993	8	54.34	250
1993	9	53.79	249.3
1993	10	53.24	241.5
1993	11	52.96	243.3
1993	12	52.17	248
1994	1	51.7	253
1994	2	58.55	252.9
1994	3	78.2	251.5
1994	4	77.03	251.6
1994	5	76.19	253.5
1994	6	77.15	259.8
1994	7	75.87	334.1
1994	8	95.47	448
1994	9	109.67	445.8
1994	10	112.28	445
1994	11	112.01	448.2
1994	12	107.93	438.2
1995	1	105.96	439.8
1995	2	105.06	423.4
1995	3	102.98	410.8
1995	4	102.2	408.4
1995	5	105.23	406.7
1995	6	101.85	405.9
1995	7	99.89	402.7
1995	8	96.23	405.1
1995	9	94.76	399.6
1995	10	91.51	386.5
1995	11	91.63	381.4
1995	12	91.54	375.2
1996	1	85.23	357.7
1996	2	87.83	359
1996	3	87.38	355
1996	4	84.44	352.7
1996	5	85.19	344.4
1996	6	84.03	343.8
1996	7	86.73	338
1996	8	102.52	339
1996	9	104.45	333.3
1996	10	106.98	334.4
1996	11	107.02	328.3
1996	12	99.26	330.7
1997	1	94.45	330
1997	2	113.44	331.6
1997	3	157.33	351.2
1997	4	147.38	389.4
1997	5	171.89	410.9
1997	6	171.95	442.8
1997	7	132.71	462.8
1997	8	126.02	466.9
1997	9	121.18	461.7
1997	10	115.45	439.2
1997	11	110.48	430.3
1997	12	117.85	416.1
1998	1	117.63	402.5
1998	2	124.65	397.3
1998	3	109.59	403.3
1998	4	111.27	395.9
1998	5	99.78	387.8
1998	6	98.21	378.6
1998	7	99.2	377.1
1998	8	97.97	370.4
1998	9	89.55	362
1998	10	87.91	350.3
1998	11	93.34	348.2
1998	12	94.42	344.6
1999	1	93.2	343.5
1999	2	90.29	342.8
1999	3	91.46	347.6
1999	4	89.98	346.6
1999	5	88.35	349.5
1999	6	88.41	342.1
1999	7	82.44	342
1999	8	79.89	342.8
1999	9	75.69	339.3
1999	10	75.66	348.2
1999	11	84.5	333.7
1999	12	96.73	334.7
2000	1	87.48	354
2000	2	82.39	367.7
2000	3	83.48	363.3
2000	4	79.31	358.4
2000	5	78.16	353.1
2000	6	72.77	343.1
2000	7	72.45	344.6
2000	8	68.46	344.4
2000	9	67.62	333.9
2000	10	68.76	331.7
2000	11	70.07	324.3
2000	12	68.55	321.2
2001	1	65.3	322.4
2001	2	58.96	321.7
2001	3	59.17	320.5
2001	4	62.37	312.8
2001	5	66.28	309.7
2001	6	55.62	315.6
2001	7	55.23	309.7
2001	8	55.85	304.6
2001	9	56.75	302.5
2001	10	50.89	301.5
2001	11	53.88	298.8
2001	12	52.95	291.3
2002	1	55.08	293.6
2002	2	53.61	294.6
2002	3	58.78	285.9
2002	4	61.85	297.6
2002	5	55.91	301.1
2002	6	53.32	293.8
2002	7	46.41	297.7
2002	8	44.57	292.9
2002	9	50	292.1
2002	10	50	287.2
2002	11	53.36	288.2
2002	12	46.23	283.8
2003	1	50.45	299.9
2003	2	49.07	292.4
2003	3	45.85	293.3
2003	4	48.45	300.8
2003	5	49.96	293.7
2003	6	46.53	293.1
2003	7	50.51	294.4
2003	8	47.58	292.1
2003	9	48.05	291.9
2003	10	46.84	282.5
2003	11	47.67	277.9
2003	12	49.16	287.5
2004	1	55.54	289.2
2004	2	55.82	285.6
2004	3	58.22	293.2
2004	4	56.19	290.8
2004	5	57.77	283.1
2004	6	63.19	275
2004	7	54.76	287.8
2004	8	55.74	287.8
2004	9	62.54	287.4
2004	10	61.39	284
2004	11	69.6	277.8
2004	12	79.23	277.6
2005	1	80	304.9
2005	2	93.68	294
2005	3	107.63	300.9
2005	4	100.18	324
2005	5	97.3	332.9
2005	6	90.45	341.6
2005	7	80.64	333.4
2005	8	80.58	348.2
2005	9	75.82	344.7
2005	10	85.59	344.7
2005	11	89.35	329.3
2005	12	89.42	323.5
2006	1	104.73	323.2
2006	2	95.32	317.4
2006	3	89.27	330.1
2006	4	90.44	329.2
2006	5	86.97	334.9
2006	6	79.98	315.8
2006	7	81.22	315.4
2006	8	87.35	319.6
2006	9	83.64	317.3
2006	10	82.22	313.8
2006	11	94.4	315.8
2006	12	102.18	311.3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198282&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198282&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198282&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ yule.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)-6.4574.48-1.4410.15
X0.2720.01418.9840
- - -
Residual Std. Err. 13.326 on 358 df
Multiple R-sq. 0.502
Adjusted R-sq. 0.5

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & -6.457 & 4.48 & -1.441 & 0.15 \tabularnewline
X & 0.272 & 0.014 & 18.984 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 13.326  on  358 df \tabularnewline
Multiple R-sq.  & 0.502 \tabularnewline
Adjusted R-sq.  & 0.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198282&T=1

[TABLE]
[ROW][C]Linear Regression Model[/C][/ROW]
[ROW][C]Y ~ X[/C][/ROW]
[ROW][C]coefficients:[/C][C] [/C][/ROW]
[ROW][C] [/C][C]Estimate[/C][C]Std. Error[/C][C]t value[/C][C]Pr(>|t|)[/C][/ROW]
[C](Intercept)[/C][C]-6.457[/C][C]4.48[/C][C]-1.441[/C][C]0.15[/C][/ROW]
[C]X[/C][C]0.272[/C][C]0.014[/C][C]18.984[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]13.326  on  358 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.502[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198282&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198282&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)-6.4574.48-1.4410.15
X0.2720.01418.9840
- - -
Residual Std. Err. 13.326 on 358 df
Multiple R-sq. 0.502
Adjusted R-sq. 0.5






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
USA164004.18564004.185360.4070
Residuals35863576.816177.589 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
USA & 1 & 64004.185 & 64004.185 & 360.407 & 0 \tabularnewline
Residuals & 358 & 63576.816 & 177.589 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198282&T=2

[TABLE]
[ROW][C]ANOVA Statistics[/C][/ROW]
[ROW][C] [/C][C]Df[/C][C]Sum Sq[/C][C]Mean Sq[/C][C]F value[/C][C]Pr(>F)[/C][/ROW]
[ROW][C]USA[/C][C]1[/C][C]64004.185[/C][C]64004.185[/C][C]360.407[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]358[/C][C]63576.816[/C][C]177.589[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198282&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198282&T=2

As an alternative you can also use a QR Code:  
QR Code


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

ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
USA164004.18564004.185360.4070
Residuals35863576.816177.589


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 3 ; par2 = 4 ; par3 = TRUE ;
Parameters (R input):
par1 = 3 ; par2 = 4 ; par3 = TRUE ;
R code (references can be found in the software module):
cat1 <- as.numeric(par1)
cat2<- as.numeric(par2)
intercept<-as.logical(par3)
x <- t(x)
xdf<-data.frame(t(y))
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
xdf <- data.frame(xdf[[cat1]], xdf[[cat2]])
names(xdf)<-c('Y', 'X')
if(intercept == FALSE) (lmxdf<-lm(Y~ X - 1, data = xdf) ) else (lmxdf<-lm(Y~ X, data = xdf) )
sumlmxdf<-summary(lmxdf)
(aov.xdf<-aov(lmxdf) )
(anova.xdf<-anova(lmxdf) )
load(file='createtable')
a<-table.start()
nc <- ncol(sumlmxdf$'coefficients')
nr <- nrow(sumlmxdf$'coefficients')
a<-table.row.start(a)
a<-table.element(a,'Linear Regression Model', nc+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, lmxdf$call['formula'],nc+1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'coefficients:',1,TRUE)
a<-table.element(a, ' ',nc,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ',1,TRUE)
for(i in 1 : nc){
a<-table.element(a, dimnames(sumlmxdf$'coefficients')[[2]][i],1,TRUE)
}#end header
a<-table.row.end(a)
for(i in 1: nr){
a<-table.element(a,dimnames(sumlmxdf$'coefficients')[[1]][i] ,1,TRUE)
for(j in 1 : nc){
a<-table.element(a, round(sumlmxdf$coefficients[i, j], digits=3), 1 ,FALSE)
}
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, '- - - ',1,TRUE)
a<-table.element(a, ' ',nc,FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Std. Err. ',1,TRUE)
a<-table.element(a, paste(round(sumlmxdf$'sigma', digits=3), ' on ', sumlmxdf$'df'[2], 'df') ,nc, FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R-sq. ',1,TRUE)
a<-table.element(a, round(sumlmxdf$'r.squared', digits=3) ,nc, FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-sq. ',1,TRUE)
a<-table.element(a, round(sumlmxdf$'adj.r.squared', digits=3) ,nc, FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Statistics', 5+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ',1,TRUE)
a<-table.element(a, 'Df',1,TRUE)
a<-table.element(a, 'Sum Sq',1,TRUE)
a<-table.element(a, 'Mean Sq',1,TRUE)
a<-table.element(a, 'F value',1,TRUE)
a<-table.element(a, 'Pr(>F)',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, V2,1,TRUE)
a<-table.element(a, anova.xdf$Df[1])
a<-table.element(a, round(anova.xdf$'Sum Sq'[1], digits=3))
a<-table.element(a, round(anova.xdf$'Mean Sq'[1], digits=3))
a<-table.element(a, round(anova.xdf$'F value'[1], digits=3))
a<-table.element(a, round(anova.xdf$'Pr(>F)'[1], digits=3))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residuals',1,TRUE)
a<-table.element(a, anova.xdf$Df[2])
a<-table.element(a, round(anova.xdf$'Sum Sq'[2], digits=3))
a<-table.element(a, round(anova.xdf$'Mean Sq'[2], digits=3))
a<-table.element(a, ' ')
a<-table.element(a, ' ')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
bitmap(file='regressionplot.png')
plot(Y~ X, data=xdf, xlab=V2, ylab=V1, main='Regression Solution')
if(intercept == TRUE) abline(coef(lmxdf), col='red')
if(intercept == FALSE) abline(0.0, coef(lmxdf), col='red')
dev.off()
library(car)
bitmap(file='residualsQQplot.png')
qq.plot(resid(lmxdf), main='QQplot of Residuals of Fit')
dev.off()
bitmap(file='residualsplot.png')
plot(xdf$X, resid(lmxdf), main='Scatterplot of Residuals of Model Fit')
dev.off()
bitmap(file='cooksDistanceLmplot.png')
plot.lm(lmxdf, which=4)
dev.off()