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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 14 Dec 2007 02:59:07 -0700

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/2007/Dec/14/t11976255954sj2wpqg803vpfn.htm/, Retrieved Thu, 02 May 2024 20:41:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3783, Retrieved Thu, 02 May 2024 20:41:09 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

s0650921, s0650125

Estimated Impact

209

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Multiple Regression] [paper_regressie_m...] [2007-12-14 09:59:07] [1232d415564adb2a600743f77b12553a] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3783&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3783&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3783&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
graanprijs[t] = + 109.56 + 37.18ontkoppelde_bedrijfstoeslag[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
graanprijs[t] =  +  109.56 +  37.18ontkoppelde_bedrijfstoeslag[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3783&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]graanprijs[t] =  +  109.56 +  37.18ontkoppelde_bedrijfstoeslag[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3783&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3783&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
graanprijs[t] = + 109.56 + 37.18ontkoppelde_bedrijfstoeslag[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	109.56	2.929268	37.4018	0	0
ontkoppelde_bedrijfstoeslag	37.18	4.825995	7.7041	0	0

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 109.56 & 2.929268 & 37.4018 & 0 & 0 \tabularnewline
ontkoppelde_bedrijfstoeslag & 37.18 & 4.825995 & 7.7041 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3783&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]109.56[/C][C]2.929268[/C][C]37.4018[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]ontkoppelde_bedrijfstoeslag[/C][C]37.18[/C][C]4.825995[/C][C]7.7041[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3783&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3783&T=2

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	109.56	2.929268	37.4018	0	0
ontkoppelde_bedrijfstoeslag	37.18	4.825995	7.7041	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.624160879065545
R-squared	0.389576802955874
Adjusted R-squared	0.383013112665077
F-TEST (value)	59.3533188947229
F-TEST (DF numerator)	1
F-TEST (DF denominator)	93
p-value	1.40016886973626e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	22.6900120132469
Sum Squared Residuals	47879.808

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.624160879065545 \tabularnewline
R-squared & 0.389576802955874 \tabularnewline
Adjusted R-squared & 0.383013112665077 \tabularnewline
F-TEST (value) & 59.3533188947229 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 93 \tabularnewline
p-value & 1.40016886973626e-11 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 22.6900120132469 \tabularnewline
Sum Squared Residuals & 47879.808 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3783&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.624160879065545[/C][/ROW]
[ROW][C]R-squared[/C][C]0.389576802955874[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.383013112665077[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]59.3533188947229[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]93[/C][/ROW]
[ROW][C]p-value[/C][C]1.40016886973626e-11[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]22.6900120132469[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]47879.808[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3783&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3783&T=3

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Regression Statistics
Multiple R	0.624160879065545
R-squared	0.389576802955874
Adjusted R-squared	0.383013112665077
F-TEST (value)	59.3533188947229
F-TEST (DF numerator)	1
F-TEST (DF denominator)	93
p-value	1.40016886973626e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	22.6900120132469
Sum Squared Residuals	47879.808

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	102.7	109.560000000000	-6.8600000000002
2	103.2	109.56	-6.36000000000004
3	105.6	109.56	-3.96
4	103.9	109.56	-5.65999999999999
5	107.2	109.56	-2.35999999999999
6	100.7	109.56	-8.86
7	92.1	109.56	-17.46
8	90.3	109.56	-19.26
9	93.4	109.56	-16.16
10	98.5	109.56	-11.06
11	100.8	109.56	-8.76
12	102.3	109.56	-7.26
13	104.7	109.56	-4.86
14	101.1	109.56	-8.46
15	101.4	109.56	-8.16
16	99.5	109.56	-10.06
17	98.4	109.56	-11.16
18	96.3	109.56	-13.26
19	100.7	109.56	-8.86
20	101.2	109.56	-8.36
21	100.3	109.56	-9.26
22	97.8	109.56	-11.76
23	97.4	109.56	-12.16
24	98.6	109.56	-10.96
25	99.7	109.56	-9.86
26	99	109.56	-10.56
27	98.1	109.56	-11.46
28	97	109.56	-12.56
29	98.5	109.56	-11.06
30	103.8	109.56	-5.76
31	114.4	109.56	4.84000000000001
32	124.5	109.56	14.94
33	134.2	109.56	24.64
34	131.8	109.56	22.24
35	125.6	109.56	16.04
36	119.9	109.56	10.34
37	114.9	109.56	5.34000000000001
38	115.5	109.56	5.94
39	112.5	109.56	2.94
40	111.4	109.56	1.84000000000001
41	115.3	109.56	5.74
42	110.8	109.56	1.24
43	103.7	109.56	-5.86
44	111.1	109.56	1.54000000000000
45	113	109.56	3.44
46	111.2	109.56	1.64000000000000
47	117.6	109.56	8.04
48	121.7	109.56	12.14
49	127.3	109.56	17.74
50	129.8	109.56	20.24
51	137.1	109.56	27.54
52	141.4	109.56	31.84
53	137.4	109.56	27.84
54	130.7	109.56	21.14
55	117.2	109.56	7.64
56	110.8	109.56	1.24
57	111.4	109.56	1.84000000000001
58	108.2	109.56	-1.35999999999999
59	108.8	109.56	-0.76
60	110.2	109.56	0.640000000000005
61	109.5	146.74	-37.24
62	109.5	146.74	-37.24
63	116	146.74	-30.74
64	111.2	146.74	-35.54
65	112.1	146.74	-34.64
66	114	146.74	-32.74
67	119.1	146.74	-27.64
68	114.1	146.74	-32.64
69	115.1	146.74	-31.64
70	115.4	146.74	-31.34
71	110.8	146.74	-35.94
72	116	146.74	-30.74
73	119.2	146.74	-27.54
74	126.5	146.74	-20.24
75	127.8	146.74	-18.94
76	131.3	146.74	-15.44
77	140.3	146.74	-6.43999999999999
78	137.3	146.74	-9.44
79	143	146.74	-3.74
80	134.5	146.74	-12.24
81	139.9	146.74	-6.84
82	159.3	146.74	12.56
83	170.4	146.74	23.66
84	175	146.74	28.26
85	175.8	146.74	29.06
86	180.9	146.74	34.16
87	180.3	146.74	33.56
88	169.6	146.74	22.86
89	172.3	146.74	25.56
90	184.8	146.74	38.06
91	177.7	146.74	30.96
92	184.6	146.74	37.86
93	211.4	146.74	64.66
94	215.3	146.74	68.56
95	215.9	146.74	69.16

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 102.7 & 109.560000000000 & -6.8600000000002 \tabularnewline
2 & 103.2 & 109.56 & -6.36000000000004 \tabularnewline
3 & 105.6 & 109.56 & -3.96 \tabularnewline
4 & 103.9 & 109.56 & -5.65999999999999 \tabularnewline
5 & 107.2 & 109.56 & -2.35999999999999 \tabularnewline
6 & 100.7 & 109.56 & -8.86 \tabularnewline
7 & 92.1 & 109.56 & -17.46 \tabularnewline
8 & 90.3 & 109.56 & -19.26 \tabularnewline
9 & 93.4 & 109.56 & -16.16 \tabularnewline
10 & 98.5 & 109.56 & -11.06 \tabularnewline
11 & 100.8 & 109.56 & -8.76 \tabularnewline
12 & 102.3 & 109.56 & -7.26 \tabularnewline
13 & 104.7 & 109.56 & -4.86 \tabularnewline
14 & 101.1 & 109.56 & -8.46 \tabularnewline
15 & 101.4 & 109.56 & -8.16 \tabularnewline
16 & 99.5 & 109.56 & -10.06 \tabularnewline
17 & 98.4 & 109.56 & -11.16 \tabularnewline
18 & 96.3 & 109.56 & -13.26 \tabularnewline
19 & 100.7 & 109.56 & -8.86 \tabularnewline
20 & 101.2 & 109.56 & -8.36 \tabularnewline
21 & 100.3 & 109.56 & -9.26 \tabularnewline
22 & 97.8 & 109.56 & -11.76 \tabularnewline
23 & 97.4 & 109.56 & -12.16 \tabularnewline
24 & 98.6 & 109.56 & -10.96 \tabularnewline
25 & 99.7 & 109.56 & -9.86 \tabularnewline
26 & 99 & 109.56 & -10.56 \tabularnewline
27 & 98.1 & 109.56 & -11.46 \tabularnewline
28 & 97 & 109.56 & -12.56 \tabularnewline
29 & 98.5 & 109.56 & -11.06 \tabularnewline
30 & 103.8 & 109.56 & -5.76 \tabularnewline
31 & 114.4 & 109.56 & 4.84000000000001 \tabularnewline
32 & 124.5 & 109.56 & 14.94 \tabularnewline
33 & 134.2 & 109.56 & 24.64 \tabularnewline
34 & 131.8 & 109.56 & 22.24 \tabularnewline
35 & 125.6 & 109.56 & 16.04 \tabularnewline
36 & 119.9 & 109.56 & 10.34 \tabularnewline
37 & 114.9 & 109.56 & 5.34000000000001 \tabularnewline
38 & 115.5 & 109.56 & 5.94 \tabularnewline
39 & 112.5 & 109.56 & 2.94 \tabularnewline
40 & 111.4 & 109.56 & 1.84000000000001 \tabularnewline
41 & 115.3 & 109.56 & 5.74 \tabularnewline
42 & 110.8 & 109.56 & 1.24 \tabularnewline
43 & 103.7 & 109.56 & -5.86 \tabularnewline
44 & 111.1 & 109.56 & 1.54000000000000 \tabularnewline
45 & 113 & 109.56 & 3.44 \tabularnewline
46 & 111.2 & 109.56 & 1.64000000000000 \tabularnewline
47 & 117.6 & 109.56 & 8.04 \tabularnewline
48 & 121.7 & 109.56 & 12.14 \tabularnewline
49 & 127.3 & 109.56 & 17.74 \tabularnewline
50 & 129.8 & 109.56 & 20.24 \tabularnewline
51 & 137.1 & 109.56 & 27.54 \tabularnewline
52 & 141.4 & 109.56 & 31.84 \tabularnewline
53 & 137.4 & 109.56 & 27.84 \tabularnewline
54 & 130.7 & 109.56 & 21.14 \tabularnewline
55 & 117.2 & 109.56 & 7.64 \tabularnewline
56 & 110.8 & 109.56 & 1.24 \tabularnewline
57 & 111.4 & 109.56 & 1.84000000000001 \tabularnewline
58 & 108.2 & 109.56 & -1.35999999999999 \tabularnewline
59 & 108.8 & 109.56 & -0.76 \tabularnewline
60 & 110.2 & 109.56 & 0.640000000000005 \tabularnewline
61 & 109.5 & 146.74 & -37.24 \tabularnewline
62 & 109.5 & 146.74 & -37.24 \tabularnewline
63 & 116 & 146.74 & -30.74 \tabularnewline
64 & 111.2 & 146.74 & -35.54 \tabularnewline
65 & 112.1 & 146.74 & -34.64 \tabularnewline
66 & 114 & 146.74 & -32.74 \tabularnewline
67 & 119.1 & 146.74 & -27.64 \tabularnewline
68 & 114.1 & 146.74 & -32.64 \tabularnewline
69 & 115.1 & 146.74 & -31.64 \tabularnewline
70 & 115.4 & 146.74 & -31.34 \tabularnewline
71 & 110.8 & 146.74 & -35.94 \tabularnewline
72 & 116 & 146.74 & -30.74 \tabularnewline
73 & 119.2 & 146.74 & -27.54 \tabularnewline
74 & 126.5 & 146.74 & -20.24 \tabularnewline
75 & 127.8 & 146.74 & -18.94 \tabularnewline
76 & 131.3 & 146.74 & -15.44 \tabularnewline
77 & 140.3 & 146.74 & -6.43999999999999 \tabularnewline
78 & 137.3 & 146.74 & -9.44 \tabularnewline
79 & 143 & 146.74 & -3.74 \tabularnewline
80 & 134.5 & 146.74 & -12.24 \tabularnewline
81 & 139.9 & 146.74 & -6.84 \tabularnewline
82 & 159.3 & 146.74 & 12.56 \tabularnewline
83 & 170.4 & 146.74 & 23.66 \tabularnewline
84 & 175 & 146.74 & 28.26 \tabularnewline
85 & 175.8 & 146.74 & 29.06 \tabularnewline
86 & 180.9 & 146.74 & 34.16 \tabularnewline
87 & 180.3 & 146.74 & 33.56 \tabularnewline
88 & 169.6 & 146.74 & 22.86 \tabularnewline
89 & 172.3 & 146.74 & 25.56 \tabularnewline
90 & 184.8 & 146.74 & 38.06 \tabularnewline
91 & 177.7 & 146.74 & 30.96 \tabularnewline
92 & 184.6 & 146.74 & 37.86 \tabularnewline
93 & 211.4 & 146.74 & 64.66 \tabularnewline
94 & 215.3 & 146.74 & 68.56 \tabularnewline
95 & 215.9 & 146.74 & 69.16 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3783&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]102.7[/C][C]109.560000000000[/C][C]-6.8600000000002[/C][/ROW]
[ROW][C]2[/C][C]103.2[/C][C]109.56[/C][C]-6.36000000000004[/C][/ROW]
[ROW][C]3[/C][C]105.6[/C][C]109.56[/C][C]-3.96[/C][/ROW]
[ROW][C]4[/C][C]103.9[/C][C]109.56[/C][C]-5.65999999999999[/C][/ROW]
[ROW][C]5[/C][C]107.2[/C][C]109.56[/C][C]-2.35999999999999[/C][/ROW]
[ROW][C]6[/C][C]100.7[/C][C]109.56[/C][C]-8.86[/C][/ROW]
[ROW][C]7[/C][C]92.1[/C][C]109.56[/C][C]-17.46[/C][/ROW]
[ROW][C]8[/C][C]90.3[/C][C]109.56[/C][C]-19.26[/C][/ROW]
[ROW][C]9[/C][C]93.4[/C][C]109.56[/C][C]-16.16[/C][/ROW]
[ROW][C]10[/C][C]98.5[/C][C]109.56[/C][C]-11.06[/C][/ROW]
[ROW][C]11[/C][C]100.8[/C][C]109.56[/C][C]-8.76[/C][/ROW]
[ROW][C]12[/C][C]102.3[/C][C]109.56[/C][C]-7.26[/C][/ROW]
[ROW][C]13[/C][C]104.7[/C][C]109.56[/C][C]-4.86[/C][/ROW]
[ROW][C]14[/C][C]101.1[/C][C]109.56[/C][C]-8.46[/C][/ROW]
[ROW][C]15[/C][C]101.4[/C][C]109.56[/C][C]-8.16[/C][/ROW]
[ROW][C]16[/C][C]99.5[/C][C]109.56[/C][C]-10.06[/C][/ROW]
[ROW][C]17[/C][C]98.4[/C][C]109.56[/C][C]-11.16[/C][/ROW]
[ROW][C]18[/C][C]96.3[/C][C]109.56[/C][C]-13.26[/C][/ROW]
[ROW][C]19[/C][C]100.7[/C][C]109.56[/C][C]-8.86[/C][/ROW]
[ROW][C]20[/C][C]101.2[/C][C]109.56[/C][C]-8.36[/C][/ROW]
[ROW][C]21[/C][C]100.3[/C][C]109.56[/C][C]-9.26[/C][/ROW]
[ROW][C]22[/C][C]97.8[/C][C]109.56[/C][C]-11.76[/C][/ROW]
[ROW][C]23[/C][C]97.4[/C][C]109.56[/C][C]-12.16[/C][/ROW]
[ROW][C]24[/C][C]98.6[/C][C]109.56[/C][C]-10.96[/C][/ROW]
[ROW][C]25[/C][C]99.7[/C][C]109.56[/C][C]-9.86[/C][/ROW]
[ROW][C]26[/C][C]99[/C][C]109.56[/C][C]-10.56[/C][/ROW]
[ROW][C]27[/C][C]98.1[/C][C]109.56[/C][C]-11.46[/C][/ROW]
[ROW][C]28[/C][C]97[/C][C]109.56[/C][C]-12.56[/C][/ROW]
[ROW][C]29[/C][C]98.5[/C][C]109.56[/C][C]-11.06[/C][/ROW]
[ROW][C]30[/C][C]103.8[/C][C]109.56[/C][C]-5.76[/C][/ROW]
[ROW][C]31[/C][C]114.4[/C][C]109.56[/C][C]4.84000000000001[/C][/ROW]
[ROW][C]32[/C][C]124.5[/C][C]109.56[/C][C]14.94[/C][/ROW]
[ROW][C]33[/C][C]134.2[/C][C]109.56[/C][C]24.64[/C][/ROW]
[ROW][C]34[/C][C]131.8[/C][C]109.56[/C][C]22.24[/C][/ROW]
[ROW][C]35[/C][C]125.6[/C][C]109.56[/C][C]16.04[/C][/ROW]
[ROW][C]36[/C][C]119.9[/C][C]109.56[/C][C]10.34[/C][/ROW]
[ROW][C]37[/C][C]114.9[/C][C]109.56[/C][C]5.34000000000001[/C][/ROW]
[ROW][C]38[/C][C]115.5[/C][C]109.56[/C][C]5.94[/C][/ROW]
[ROW][C]39[/C][C]112.5[/C][C]109.56[/C][C]2.94[/C][/ROW]
[ROW][C]40[/C][C]111.4[/C][C]109.56[/C][C]1.84000000000001[/C][/ROW]
[ROW][C]41[/C][C]115.3[/C][C]109.56[/C][C]5.74[/C][/ROW]
[ROW][C]42[/C][C]110.8[/C][C]109.56[/C][C]1.24[/C][/ROW]
[ROW][C]43[/C][C]103.7[/C][C]109.56[/C][C]-5.86[/C][/ROW]
[ROW][C]44[/C][C]111.1[/C][C]109.56[/C][C]1.54000000000000[/C][/ROW]
[ROW][C]45[/C][C]113[/C][C]109.56[/C][C]3.44[/C][/ROW]
[ROW][C]46[/C][C]111.2[/C][C]109.56[/C][C]1.64000000000000[/C][/ROW]
[ROW][C]47[/C][C]117.6[/C][C]109.56[/C][C]8.04[/C][/ROW]
[ROW][C]48[/C][C]121.7[/C][C]109.56[/C][C]12.14[/C][/ROW]
[ROW][C]49[/C][C]127.3[/C][C]109.56[/C][C]17.74[/C][/ROW]
[ROW][C]50[/C][C]129.8[/C][C]109.56[/C][C]20.24[/C][/ROW]
[ROW][C]51[/C][C]137.1[/C][C]109.56[/C][C]27.54[/C][/ROW]
[ROW][C]52[/C][C]141.4[/C][C]109.56[/C][C]31.84[/C][/ROW]
[ROW][C]53[/C][C]137.4[/C][C]109.56[/C][C]27.84[/C][/ROW]
[ROW][C]54[/C][C]130.7[/C][C]109.56[/C][C]21.14[/C][/ROW]
[ROW][C]55[/C][C]117.2[/C][C]109.56[/C][C]7.64[/C][/ROW]
[ROW][C]56[/C][C]110.8[/C][C]109.56[/C][C]1.24[/C][/ROW]
[ROW][C]57[/C][C]111.4[/C][C]109.56[/C][C]1.84000000000001[/C][/ROW]
[ROW][C]58[/C][C]108.2[/C][C]109.56[/C][C]-1.35999999999999[/C][/ROW]
[ROW][C]59[/C][C]108.8[/C][C]109.56[/C][C]-0.76[/C][/ROW]
[ROW][C]60[/C][C]110.2[/C][C]109.56[/C][C]0.640000000000005[/C][/ROW]
[ROW][C]61[/C][C]109.5[/C][C]146.74[/C][C]-37.24[/C][/ROW]
[ROW][C]62[/C][C]109.5[/C][C]146.74[/C][C]-37.24[/C][/ROW]
[ROW][C]63[/C][C]116[/C][C]146.74[/C][C]-30.74[/C][/ROW]
[ROW][C]64[/C][C]111.2[/C][C]146.74[/C][C]-35.54[/C][/ROW]
[ROW][C]65[/C][C]112.1[/C][C]146.74[/C][C]-34.64[/C][/ROW]
[ROW][C]66[/C][C]114[/C][C]146.74[/C][C]-32.74[/C][/ROW]
[ROW][C]67[/C][C]119.1[/C][C]146.74[/C][C]-27.64[/C][/ROW]
[ROW][C]68[/C][C]114.1[/C][C]146.74[/C][C]-32.64[/C][/ROW]
[ROW][C]69[/C][C]115.1[/C][C]146.74[/C][C]-31.64[/C][/ROW]
[ROW][C]70[/C][C]115.4[/C][C]146.74[/C][C]-31.34[/C][/ROW]
[ROW][C]71[/C][C]110.8[/C][C]146.74[/C][C]-35.94[/C][/ROW]
[ROW][C]72[/C][C]116[/C][C]146.74[/C][C]-30.74[/C][/ROW]
[ROW][C]73[/C][C]119.2[/C][C]146.74[/C][C]-27.54[/C][/ROW]
[ROW][C]74[/C][C]126.5[/C][C]146.74[/C][C]-20.24[/C][/ROW]
[ROW][C]75[/C][C]127.8[/C][C]146.74[/C][C]-18.94[/C][/ROW]
[ROW][C]76[/C][C]131.3[/C][C]146.74[/C][C]-15.44[/C][/ROW]
[ROW][C]77[/C][C]140.3[/C][C]146.74[/C][C]-6.43999999999999[/C][/ROW]
[ROW][C]78[/C][C]137.3[/C][C]146.74[/C][C]-9.44[/C][/ROW]
[ROW][C]79[/C][C]143[/C][C]146.74[/C][C]-3.74[/C][/ROW]
[ROW][C]80[/C][C]134.5[/C][C]146.74[/C][C]-12.24[/C][/ROW]
[ROW][C]81[/C][C]139.9[/C][C]146.74[/C][C]-6.84[/C][/ROW]
[ROW][C]82[/C][C]159.3[/C][C]146.74[/C][C]12.56[/C][/ROW]
[ROW][C]83[/C][C]170.4[/C][C]146.74[/C][C]23.66[/C][/ROW]
[ROW][C]84[/C][C]175[/C][C]146.74[/C][C]28.26[/C][/ROW]
[ROW][C]85[/C][C]175.8[/C][C]146.74[/C][C]29.06[/C][/ROW]
[ROW][C]86[/C][C]180.9[/C][C]146.74[/C][C]34.16[/C][/ROW]
[ROW][C]87[/C][C]180.3[/C][C]146.74[/C][C]33.56[/C][/ROW]
[ROW][C]88[/C][C]169.6[/C][C]146.74[/C][C]22.86[/C][/ROW]
[ROW][C]89[/C][C]172.3[/C][C]146.74[/C][C]25.56[/C][/ROW]
[ROW][C]90[/C][C]184.8[/C][C]146.74[/C][C]38.06[/C][/ROW]
[ROW][C]91[/C][C]177.7[/C][C]146.74[/C][C]30.96[/C][/ROW]
[ROW][C]92[/C][C]184.6[/C][C]146.74[/C][C]37.86[/C][/ROW]
[ROW][C]93[/C][C]211.4[/C][C]146.74[/C][C]64.66[/C][/ROW]
[ROW][C]94[/C][C]215.3[/C][C]146.74[/C][C]68.56[/C][/ROW]
[ROW][C]95[/C][C]215.9[/C][C]146.74[/C][C]69.16[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3783&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3783&T=4

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	102.7	109.560000000000	-6.8600000000002
2	103.2	109.56	-6.36000000000004
3	105.6	109.56	-3.96
4	103.9	109.56	-5.65999999999999
5	107.2	109.56	-2.35999999999999
6	100.7	109.56	-8.86
7	92.1	109.56	-17.46
8	90.3	109.56	-19.26
9	93.4	109.56	-16.16
10	98.5	109.56	-11.06
11	100.8	109.56	-8.76
12	102.3	109.56	-7.26
13	104.7	109.56	-4.86
14	101.1	109.56	-8.46
15	101.4	109.56	-8.16
16	99.5	109.56	-10.06
17	98.4	109.56	-11.16
18	96.3	109.56	-13.26
19	100.7	109.56	-8.86
20	101.2	109.56	-8.36
21	100.3	109.56	-9.26
22	97.8	109.56	-11.76
23	97.4	109.56	-12.16
24	98.6	109.56	-10.96
25	99.7	109.56	-9.86
26	99	109.56	-10.56
27	98.1	109.56	-11.46
28	97	109.56	-12.56
29	98.5	109.56	-11.06
30	103.8	109.56	-5.76
31	114.4	109.56	4.84000000000001
32	124.5	109.56	14.94
33	134.2	109.56	24.64
34	131.8	109.56	22.24
35	125.6	109.56	16.04
36	119.9	109.56	10.34
37	114.9	109.56	5.34000000000001
38	115.5	109.56	5.94
39	112.5	109.56	2.94
40	111.4	109.56	1.84000000000001
41	115.3	109.56	5.74
42	110.8	109.56	1.24
43	103.7	109.56	-5.86
44	111.1	109.56	1.54000000000000
45	113	109.56	3.44
46	111.2	109.56	1.64000000000000
47	117.6	109.56	8.04
48	121.7	109.56	12.14
49	127.3	109.56	17.74
50	129.8	109.56	20.24
51	137.1	109.56	27.54
52	141.4	109.56	31.84
53	137.4	109.56	27.84
54	130.7	109.56	21.14
55	117.2	109.56	7.64
56	110.8	109.56	1.24
57	111.4	109.56	1.84000000000001
58	108.2	109.56	-1.35999999999999
59	108.8	109.56	-0.76
60	110.2	109.56	0.640000000000005
61	109.5	146.74	-37.24
62	109.5	146.74	-37.24
63	116	146.74	-30.74
64	111.2	146.74	-35.54
65	112.1	146.74	-34.64
66	114	146.74	-32.74
67	119.1	146.74	-27.64
68	114.1	146.74	-32.64
69	115.1	146.74	-31.64
70	115.4	146.74	-31.34
71	110.8	146.74	-35.94
72	116	146.74	-30.74
73	119.2	146.74	-27.54
74	126.5	146.74	-20.24
75	127.8	146.74	-18.94
76	131.3	146.74	-15.44
77	140.3	146.74	-6.43999999999999
78	137.3	146.74	-9.44
79	143	146.74	-3.74
80	134.5	146.74	-12.24
81	139.9	146.74	-6.84
82	159.3	146.74	12.56
83	170.4	146.74	23.66
84	175	146.74	28.26
85	175.8	146.74	29.06
86	180.9	146.74	34.16
87	180.3	146.74	33.56
88	169.6	146.74	22.86
89	172.3	146.74	25.56
90	184.8	146.74	38.06
91	177.7	146.74	30.96
92	184.6	146.74	37.86
93	211.4	146.74	64.66
94	215.3	146.74	68.56
95	215.9	146.74	69.16

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

library(lattice)
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code