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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 computationSat, 28 Nov 2015 22:02:30 +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/2015/Nov/28/t14487483766t8e4f2rlaahg9a.htm/, Retrieved Tue, 14 May 2024 01:07:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284387, Retrieved Tue, 14 May 2024 01:07:06 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
1	221
2	219
3	214
4	210
5	207
6	206
7	217
8	231
9	234
10	233
11	228
12	226
13	227
14	225
15	219
16	215
17	210
18	206
19	215
20	228
21	229
22	222
23	215
24	212
25	211
26	208
27	205
28	201
29	198
30	198
31	210
32	224
33	226
34	222
35	216
36	215
37	215
38	214
39	211
40	207
41	203
42	200
43	209
44	223
45	225
46	216
47	206
48	203
49	203
50	201
51	197
52	192
53	187
54	184
55	194
56	203
57	197
58	191
59	182
60	175
61	163
62	155
63	151
64	156
65	154
66	153
67	167
68	177
69	171
70	169
71	160
72	151
73	139
74	130
75	126
76	130
77	127
78	122
79	129
80	135
81	142
82	156
83	157
84	165
85	170
86	169
87	162
88	148
89	143
90	146
91	175
92	181
93	178
94	166
95	161
96	164
97	173
98	174
99	167
100	156
101	148
102	150
103	174
104	181
105	183
106	178
107	176
108	184
109	193
110	192
111	182
112	163
113	157
114	167
115	205
116	219
117	214
118	198
119	183
120	184
121	192
122	196
123	194
124	185
125	181
126	184
127	206
128	210
129	208
130	197
131	189
132	190
133	191
134	190
135	187
136	184
137	183
138	184
139	203
140	208
141	205
142	195
143	189
144	188
145	190
146	190
147	190
148	193
149	185
150	173
151	176
152	170
153	163
154	170
155	171
156	173
157	171
158	162
159	152
160	142
161	136
162	146
163	179
164	191
165	181
166	170
167	161
168	168
169	180
170	182
171	176
172	164
173	154
174	160
175	189
176	196
177	186
178	171
179	169
180	181
181	198
182	202
183	196
184	183
185	173
186	175
187	198
188	203
189	197
190	191
191	182
192	172
193	158
194	147
195	143
196	146
197	147
198	152
199	177
200	184
201	174
202	162
203	157
204	155
205	159
206	158
207	156
208	157
209	156
210	158
211	173
212	179
213	172
214	169
215	168
216	172
217	180
218	182
219	182
220	181
221	178
222	178
223	196
224	199
225	192
226	187
227	184
228	184
229	188
230	183
231	176
232	168
233	163
234	166
235	189
236	195
237	192
238	189
239	187
240	187
241	190
242	187
243	179
244	168
245	160
246	161
247	177
248	182
249	176




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 6 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284387&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284387&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284387&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)198.9752.76571.9720
X-0.1310.019-6.820
- - -
Residual Std. Err. 21.747 on 247 df
Multiple R-sq. 0.158
95% CI Multiple R-sq. [0.07, 0.256]
Adjusted R-sq. 0.155

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 198.975 & 2.765 & 71.972 & 0 \tabularnewline
X & -0.131 & 0.019 & -6.82 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 21.747  on  247 df \tabularnewline
Multiple R-sq.  & 0.158 \tabularnewline
95% CI Multiple R-sq.  & [0.07, 0.256] \tabularnewline
Adjusted R-sq.  & 0.155 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284387&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]198.975[/C][C]2.765[/C][C]71.972[/C][C]0[/C][/ROW]
[C]X[/C][C]-0.131[/C][C]0.019[/C][C]-6.82[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]21.747  on  247 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.158[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0.07, 0.256][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.155[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284387&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284387&T=1

As an alternative you can also use a QR Code:  

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

Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)198.9752.76571.9720
X-0.1310.019-6.820
- - -
Residual Std. Err. 21.747 on 247 df
Multiple R-sq. 0.158
95% CI Multiple R-sq. [0.07, 0.256]
Adjusted R-sq. 0.155







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Tijd121996.61221996.61246.5110
Residuals247116813.396472.929

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Tijd & 1 & 21996.612 & 21996.612 & 46.511 & 0 \tabularnewline
Residuals & 247 & 116813.396 & 472.929 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284387&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]Tijd[/C][C]1[/C][C]21996.612[/C][C]21996.612[/C][C]46.511[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]247[/C][C]116813.396[/C][C]472.929[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284387&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284387&T=2

As an alternative you can also use a QR Code:  

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

ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Tijd121996.61221996.61246.5110
Residuals247116813.396472.929



Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = TRUE ;
Parameters (R input):
par1 = 2 ; par2 = 1 ; par3 = TRUE ;
R code (references can be found in the software module):
par3 <- 'TRUE'
par2 <- '1'
par1 <- '2'
library(boot)
cat1 <- as.numeric(par1)
cat2<- as.numeric(par2)
intercept<-as.logical(par3)
x <- t(x)
rsq <- function(formula, data, indices) {
d <- data[indices,] # allows boot to select sample
fit <- lm(formula, data=d)
return(summary(fit)$r.square)
}
xdf<-data.frame(t(y))
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
xdf <- data.frame(xdf[[cat1]], xdf[[cat2]])
names(xdf)<-c('Y', 'X')
if(intercept == FALSE) (lmxdf<-lm(Y~ X - 1, data = xdf) ) else (lmxdf<-lm(Y~ X, data = xdf) )
(results <- boot(data=xdf, statistic=rsq, R=1000, formula=Y~X))
sumlmxdf<-summary(lmxdf)
(aov.xdf<-aov(lmxdf) )
(anova.xdf<-anova(lmxdf) )
load(file='createtable')
a<-table.start()
nc <- ncol(sumlmxdf$'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, '95% CI Multiple R-sq. ',1,TRUE)
a<-table.element(a, paste('[',round(boot.ci(results,type='bca')$bca[1,4], digits=3),', ', round(boot.ci(results,type='bca')$bca[1,5], digits=3), ']',sep='') ,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(lmxdf, which=4)
dev.off()