FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Module--
Title produced by softwareSimple Linear Regression
Date of computationWed, 05 Nov 2014 18:55:35 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/05/t141521375173ambgikgb3mn9d.htm/, Retrieved Tue, 21 Apr 2026 01:14:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=252224, Retrieved Tue, 21 Apr 2026 01:14:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact387

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Blocked Bootstrap Plot - Central Tendency] [] [2014-11-02 13:37:17] [cc401d1001c65f55a3dfc6f2420e9570]
- RMPD  [Simple Linear Regression] [] [2014-11-02 15:26:26] [cc401d1001c65f55a3dfc6f2420e9570]
- RM        [Simple Linear Regression] [] [2014-11-05 18:55:35] [4ce2356216df8db4950cd852fec912aa] [Current]
-  MPD        [Simple Linear Regression] [] [2014-12-09 12:47:37] [36c866d94170840abc594fd3e7d5794f]
-   PD          [Simple Linear Regression] [] [2014-12-14 12:39:34] [36c866d94170840abc594fd3e7d5794f]
-   PD          [Simple Linear Regression] [] [2014-12-14 12:50:11] [36c866d94170840abc594fd3e7d5794f]
-    D            [Simple Linear Regression] [] [2014-12-14 12:55:18] [36c866d94170840abc594fd3e7d5794f]
-    D              [Simple Linear Regression] [] [2014-12-14 12:59:02] [36c866d94170840abc594fd3e7d5794f]
-    D                [Simple Linear Regression] [] [2014-12-14 13:02:17] [36c866d94170840abc594fd3e7d5794f]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
87.28	255
87.28	280.2
87.09	299.9
86.92	339.2
87.59	374.2
90.72	393.5
90.69	389.2
90.3	381.7
89.55	375.2
88.94	369
88.41	357.4
87.82	352.1
87.07	346.5
86.82	342.9
86.4	340.3
86.02	328.3
85.66	322.9
85.32	314.3
85	308.9
84.67	294
83.94	285.6
82.83	281.2
81.95	280.3
81.19	278.8
80.48	274.5
78.86	270.4
69.47	263.4
68.77	259.9
70.06	258
73.95	262.7
75.8	284.7
77.79	311.3
81.57	322.1
83.07	327
84.34	331.3
85.1	333.3
85.25	321.4
84.26	327
83.63	320
86.44	314.7
85.3	316.7
84.1	314.4
83.36	321.3
82.48	318.2
81.58	307.2
80.47	301.3
79.34	287.5
82.13	277.7
81.69	274.4
80.7	258.8
79.88	253.3
79.16	251
78.38	248.4
77.42	249.5
76.47	246.1
75.46	244.5
74.48	243.6
78.27	244
80.7	240.8
79.91	249.8
78.75	248
77.78	259.4
81.14	260.5
81.08	260.8
80.03	261.3
78.91	259.5
78.01	256.6
76.9	257.9
75.97	256.5
81.93	254.2
80.27	253.3
78.67	253.8
77.42	255.5
76.16	257.1
74.7	257.3
76.39	253.2
76.04	252.8
74.65	252
73.29	250.7
71.79	252.2
74.39	250
74.91	251
74.54	253.4
73.08	251.2
72.75	255.6
71.32	261.1
70.38	258.9
70.35	259.9
70.01	261.2
69.36	264.7
67.77	267.1
69.26	266.4
69.8	267.7
68.38	268.6
67.62	267.5
68.39	268.5
66.95	268.5
65.21	270.5
66.64	270.9
63.45	270.1
60.66	269.3
62.34	269.8
60.32	270.1
58.64	264.9
60.46	263.7
58.59	264.8
61.87	263.7
61.85	255.9
67.44	276.2
77.06	360.1
91.74	380.5
93.15	373.7
94.15	369.8
93.11	366.6
91.51	359.3
89.96	345.8
88.16	326.2
86.98	324.5
88.03	328.1
86.24	327.5
84.65	324.4
83.23	316.5
81.7	310.9
80.25	301.5
78.8	291.7
77.51	290.4
76.2	287.4
75.04	277.7
74	281.6
75.49	288
77.14	276
76.15	272.9
76.27	283
78.19	283.3
76.49	276.8
77.31	284.5
76.65	282.7
74.99	281.2
73.51	287.4
72.07	283.1
70.59	284
71.96	285.5
76.29	289.2
74.86	292.5
74.93	296.4
71.9	305.2
71.01	303.9
77.47	311.5
75.78	316.3
76.6	316.7
76.07	322.5
74.57	317.1
73.02	309.8
72.65	303.8
73.16	290.3
71.53	293.7
69.78	291.7
67.98	296.5
69.96	289.1
72.16	288.5
70.47	293.8
68.86	297.7
67.37	305.4
65.87	302.7
72.16	302.5
71.34	303
69.93	294.5
68.44	294.1
67.16	294.5
66.01	297.1
67.25	289.4
70.91	292.4
69.75	287.9
68.59	286.6
67.48	280.5
66.31	272.4
64.81	269.2
66.58	270.6
65.97	267.3
64.7	262.5
64.7	266.8
60.94	268.8
59.08	263.1
58.42	261.2
57.77	266
57.11	262.5
53.31	265.2
49.96	261.3
49.4	253.7
48.84	249.2
48.3	239.1
47.74	236.4
47.24	235.2
46.76	245.2
46.29	246.2
48.9	247.7
49.23	251.4
48.53	253.3
48.03	254.8
54.34	250
53.79	249.3
53.24	241.5
52.96	243.3
52.17	248
51.7	253
58.55	252.9
78.2	251.5
77.03	251.6
76.19	253.5
77.15	259.8
75.87	334.1
95.47	448
109.67	445.8
112.28	445
112.01	448.2
107.93	438.2
105.96	439.8
105.06	423.4
102.98	410.8
102.2	408.4
105.23	406.7
101.85	405.9
99.89	402.7
96.23	405.1
94.76	399.6
91.51	386.5
91.63	381.4
91.54	375.2
85.23	357.7
87.83	359
87.38	355
84.44	352.7
85.19	344.4
84.03	343.8
86.73	338
102.52	339
104.45	333.3
106.98	334.4
107.02	328.3
99.26	330.7
94.45	330
113.44	331.6
157.33	351.2
147.38	389.4
171.89	410.9
171.95	442.8
132.71	462.8
126.02	466.9
121.18	461.7
115.45	439.2
110.48	430.3
117.85	416.1
117.63	402.5
124.65	397.3
109.59	403.3
111.27	395.9
99.78	387.8
98.21	378.6
99.2	377.1
97.97	370.4
89.55	362
87.91	350.3
93.34	348.2
94.42	344.6
93.2	343.5
90.29	342.8
91.46	347.6
89.98	346.6
88.35	349.5
88.41	342.1
82.44	342
79.89	342.8
75.69	339.3
75.66	348.2
84.5	333.7
96.73	334.7
87.48	354
82.39	367.7
83.48	363.3
79.31	358.4
78.16	353.1
72.77	343.1
72.45	344.6
68.46	344.4
67.62	333.9
68.76	331.7
70.07	324.3
68.55	321.2
65.3	322.4
58.96	321.7
59.17	320.5
62.37	312.8
66.28	309.7
55.62	315.6
55.23	309.7
55.85	304.6
56.75	302.5
50.89	301.5
53.88	298.8
52.95	291.3
55.08	293.6
53.61	294.6
58.78	285.9
61.85	297.6
55.91	301.1
53.32	293.8
46.41	297.7
44.57	292.9
50	292.1
50	287.2
53.36	288.2
46.23	283.8
50.45	299.9
49.07	292.4
45.85	293.3
48.45	300.8
49.96	293.7
46.53	293.1
50.51	294.4
47.58	292.1
48.05	291.9
46.84	282.5
47.67	277.9
49.16	287.5
55.54	289.2
55.82	285.6
58.22	293.2
56.19	290.8
57.77	283.1
63.19	275
54.76	287.8
55.74	287.8
62.54	287.4
61.39	284
69.6	277.8
79.23	277.6
80	304.9
93.68	294
107.63	300.9
100.18	324
97.3	332.9
90.45	341.6
80.64	333.4
80.58	348.2
75.82	344.7
85.59	344.7
89.35	329.3
89.42	323.5
104.73	323.2
95.32	317.4
89.27	330.1
90.44	329.2
86.97	334.9
79.98	315.8
81.22	315.4
87.35	319.6
83.64	317.3
82.22	313.8
94.4	315.8
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 time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=252224&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=252224&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=252224&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 time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)165.557.74121.3870
X1.8420.09718.9840
- - -
Residual Std. Err. 34.651 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) & 165.55 & 7.741 & 21.387 & 0 \tabularnewline
X & 1.842 & 0.097 & 18.984 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 34.651  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=252224&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]165.55[/C][C]7.741[/C][C]21.387[/C][C]0[/C][/ROW]
[C]X[/C][C]1.842[/C][C]0.097[/C][C]18.984[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]34.651  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=252224&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=252224&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)165.557.74121.3870
X1.8420.09718.9840
- - -
Residual Std. Err. 34.651 on 358 df
Multiple R-sq. 0.502
Adjusted R-sq. 0.5






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
X_t1432728.838432728.838360.4070
Residuals358429839.4221200.669 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
X_t & 1 & 432728.838 & 432728.838 & 360.407 & 0 \tabularnewline
Residuals & 358 & 429839.422 & 1200.669 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=252224&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]X_t[/C][C]1[/C][C]432728.838[/C][C]432728.838[/C][C]360.407[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]358[/C][C]429839.422[/C][C]1200.669[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=252224&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=252224&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)
X_t1432728.838432728.838360.4070
Residuals358429839.4221200.669


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 2 ; par2 = 1 ; par3 = TRUE ;
Parameters (R input):
par1 = 2 ; par2 = 1 ; par3 = TRUE ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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()