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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Thu, 15 Nov 2007 03:48:50 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/15/t1195123535jujax97kt2nu1d2.htm/, Retrieved Sat, 04 May 2024 13:51:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5419, Retrieved Sat, 04 May 2024 13:51:48 +0000

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Estimated Impact

261

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

-       [Multiple Regression] [] [2007-11-15 10:48:50] [2cdb7403ed3391afb545b8c0d20da37e] [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=5419&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=5419&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5419&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
-25[t] = + 25.7095903042373 + 0.3341097741355`25 `[t] -1.35075440129733M1[t] -10.0278612159084M2[t] -17.6287970771281M3[t] -22.2951234107307M4[t] -25.6281164110000M5[t] -28.6242820943263M6[t] -32.5071367509352M7[t] -35.1119548161657M8[t] -39.2175493221984M9[t] -37.7690117474795M10[t] -7.89129973075869M11[t] -0.503834316673765t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
-25[t] =  +  25.7095903042373 +  0.3341097741355`25
`[t] -1.35075440129733M1[t] -10.0278612159084M2[t] -17.6287970771281M3[t] -22.2951234107307M4[t] -25.6281164110000M5[t] -28.6242820943263M6[t] -32.5071367509352M7[t] -35.1119548161657M8[t] -39.2175493221984M9[t] -37.7690117474795M10[t] -7.89129973075869M11[t] -0.503834316673765t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5419&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]-25[t] =  +  25.7095903042373 +  0.3341097741355`25
`[t] -1.35075440129733M1[t] -10.0278612159084M2[t] -17.6287970771281M3[t] -22.2951234107307M4[t] -25.6281164110000M5[t] -28.6242820943263M6[t] -32.5071367509352M7[t] -35.1119548161657M8[t] -39.2175493221984M9[t] -37.7690117474795M10[t] -7.89129973075869M11[t] -0.503834316673765t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5419&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5419&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
-25[t] = + 25.7095903042373 + 0.3341097741355`25 `[t] -1.35075440129733M1[t] -10.0278612159084M2[t] -17.6287970771281M3[t] -22.2951234107307M4[t] -25.6281164110000M5[t] -28.6242820943263M6[t] -32.5071367509352M7[t] -35.1119548161657M8[t] -39.2175493221984M9[t] -37.7690117474795M10[t] -7.89129973075869M11[t] -0.503834316673765t + 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)	25.7095903042373	9.160825	2.8065	0.006776	0.003388
`25 `	0.3341097741355	0.023379	14.2908	0	0
M1	-1.35075440129733	2.549443	-0.5298	0.598223	0.299111
M2	-10.0278612159084	2.651237	-3.7823	0.000365	0.000183
M3	-17.6287970771281	2.657874	-6.6327	0	0
M4	-22.2951234107307	2.650749	-8.4109	0	0
M5	-25.6281164110000	2.645881	-9.686	0	0
M6	-28.6242820943263	2.645331	-10.8207	0	0
M7	-32.5071367509352	2.649651	-12.2685	0	0
M8	-35.1119548161657	2.658738	-13.2062	0	0
M9	-39.2175493221984	2.668726	-14.6952	0	0
M10	-37.7690117474795	2.674232	-14.1233	0	0
M11	-7.89129973075869	2.638944	-2.9903	0.004061	0.00203
t	-0.503834316673765	0.041013	-12.2846	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) & 25.7095903042373 & 9.160825 & 2.8065 & 0.006776 & 0.003388 \tabularnewline
`25
` & 0.3341097741355 & 0.023379 & 14.2908 & 0 & 0 \tabularnewline
M1 & -1.35075440129733 & 2.549443 & -0.5298 & 0.598223 & 0.299111 \tabularnewline
M2 & -10.0278612159084 & 2.651237 & -3.7823 & 0.000365 & 0.000183 \tabularnewline
M3 & -17.6287970771281 & 2.657874 & -6.6327 & 0 & 0 \tabularnewline
M4 & -22.2951234107307 & 2.650749 & -8.4109 & 0 & 0 \tabularnewline
M5 & -25.6281164110000 & 2.645881 & -9.686 & 0 & 0 \tabularnewline
M6 & -28.6242820943263 & 2.645331 & -10.8207 & 0 & 0 \tabularnewline
M7 & -32.5071367509352 & 2.649651 & -12.2685 & 0 & 0 \tabularnewline
M8 & -35.1119548161657 & 2.658738 & -13.2062 & 0 & 0 \tabularnewline
M9 & -39.2175493221984 & 2.668726 & -14.6952 & 0 & 0 \tabularnewline
M10 & -37.7690117474795 & 2.674232 & -14.1233 & 0 & 0 \tabularnewline
M11 & -7.89129973075869 & 2.638944 & -2.9903 & 0.004061 & 0.00203 \tabularnewline
t & -0.503834316673765 & 0.041013 & -12.2846 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5419&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]25.7095903042373[/C][C]9.160825[/C][C]2.8065[/C][C]0.006776[/C][C]0.003388[/C][/ROW]
[ROW][C]`25
`[/C][C]0.3341097741355[/C][C]0.023379[/C][C]14.2908[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-1.35075440129733[/C][C]2.549443[/C][C]-0.5298[/C][C]0.598223[/C][C]0.299111[/C][/ROW]
[ROW][C]M2[/C][C]-10.0278612159084[/C][C]2.651237[/C][C]-3.7823[/C][C]0.000365[/C][C]0.000183[/C][/ROW]
[ROW][C]M3[/C][C]-17.6287970771281[/C][C]2.657874[/C][C]-6.6327[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M4[/C][C]-22.2951234107307[/C][C]2.650749[/C][C]-8.4109[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M5[/C][C]-25.6281164110000[/C][C]2.645881[/C][C]-9.686[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M6[/C][C]-28.6242820943263[/C][C]2.645331[/C][C]-10.8207[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M7[/C][C]-32.5071367509352[/C][C]2.649651[/C][C]-12.2685[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M8[/C][C]-35.1119548161657[/C][C]2.658738[/C][C]-13.2062[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M9[/C][C]-39.2175493221984[/C][C]2.668726[/C][C]-14.6952[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M10[/C][C]-37.7690117474795[/C][C]2.674232[/C][C]-14.1233[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]-7.89129973075869[/C][C]2.638944[/C][C]-2.9903[/C][C]0.004061[/C][C]0.00203[/C][/ROW]
[ROW][C]t[/C][C]-0.503834316673765[/C][C]0.041013[/C][C]-12.2846[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5419&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5419&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)	25.7095903042373	9.160825	2.8065	0.006776	0.003388
`25 `	0.3341097741355	0.023379	14.2908	0	0
M1	-1.35075440129733	2.549443	-0.5298	0.598223	0.299111
M2	-10.0278612159084	2.651237	-3.7823	0.000365	0.000183
M3	-17.6287970771281	2.657874	-6.6327	0	0
M4	-22.2951234107307	2.650749	-8.4109	0	0
M5	-25.6281164110000	2.645881	-9.686	0	0
M6	-28.6242820943263	2.645331	-10.8207	0	0
M7	-32.5071367509352	2.649651	-12.2685	0	0
M8	-35.1119548161657	2.658738	-13.2062	0	0
M9	-39.2175493221984	2.668726	-14.6952	0	0
M10	-37.7690117474795	2.674232	-14.1233	0	0
M11	-7.89129973075869	2.638944	-2.9903	0.004061	0.00203
t	-0.503834316673765	0.041013	-12.2846	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.971946355203395
R-squared	0.944679717393163
Adjusted R-squared	0.932490502581487
F-TEST (value)	77.5012773167527
F-TEST (DF numerator)	13
F-TEST (DF denominator)	59
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	4.57053009318048
Sum Squared Residuals	1232.49497462744

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.971946355203395 \tabularnewline
R-squared & 0.944679717393163 \tabularnewline
Adjusted R-squared & 0.932490502581487 \tabularnewline
F-TEST (value) & 77.5012773167527 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 59 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 4.57053009318048 \tabularnewline
Sum Squared Residuals & 1232.49497462744 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5419&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.971946355203395[/C][/ROW]
[ROW][C]R-squared[/C][C]0.944679717393163[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.932490502581487[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]77.5012773167527[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]59[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]4.57053009318048[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1232.49497462744[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5419&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5419&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	0.971946355203395
R-squared	0.944679717393163
Adjusted R-squared	0.932490502581487
F-TEST (value)	77.5012773167527
F-TEST (DF numerator)	13
F-TEST (DF denominator)	59
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	4.57053009318048
Sum Squared Residuals	1232.49497462744

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	140	148.477947338808	-8.47794733880753
2	132	138.628786659252	-6.62878665925186
3	117	124.844150321055	-7.84415032105496
4	114	120.676318993185	-6.67631899318502
5	113	118.844150321055	-5.84415032105493
6	110	115.678260095190	-5.67826009519042
7	107	110.957461347772	-3.95746134777218
8	103	106.178260095190	-3.17826009519043
9	98	101.234721498349	-3.23472149834853
10	98	102.179424756394	-4.17942475639371
11	137	139.237827261557	-2.23782726155721
12	148	145.957073127371	2.04292687262891
13	147	143.434264861129	3.56573513887098
14	139	135.589762826386	3.41023717361382
15	130	127.150882874357	2.84911712564274
16	128	123.651271094758	4.34872890524165
17	127	122.487321970899	4.51267802910073
18	123	119.655541519170	3.34445848082972
19	118	114.600632997617	3.39936700238348
20	114	112.828419712254	1.17158028774573
21	108	106.882551793006	1.11744820699416
22	111	109.163694147593	1.83630585240698
23	151	146.222096652757	4.77790334724349
24	159	154.277781615112	4.72221838488756
25	158	152.089083123006	5.91091687699415
26	148	142.23992244345	5.76007755655
27	138	131.462274072473	6.53772592752741
28	137	128.964991615280	8.03500838471982
29	136	127.801042491421	8.1989575085789
30	133	124.969262039692	8.03073796030791
31	126	121.250792614680	4.74920738531966
32	120	116.137481587963	3.86251841203691
33	114	111.193942991121	2.80605700887882
34	116	113.475085345708	2.52491465429166
35	153	147.526499883652	5.47350011634766
36	162	157.586843490821	4.41315650917874
37	161	156.734584095257	4.26541590474333
38	149	150.894740705327	-1.89474070532682
39	139	140.451202108485	-1.45120210848491
40	135	137.285700103021	-2.28570010302149
41	130	133.448872786078	-3.44887278607842
42	127	130.617092334349	-3.61709233434941
43	122	125.896293586931	-3.89629358693117
44	117	120.782982560214	-3.78298256021391
45	112	115.839443963372	-3.839443963372
46	113	117.118256995553	-4.11825699555265
47	149	151.837891081768	-2.83789108176766
48	157	159.225356495853	-2.22535649585258
49	157	157.036658003746	-0.0366580037459927
50	147	145.851058227648	1.14894177235185
51	137	135.741629404942	1.25837059505827
52	132	132.576127399478	-0.576127399478315
53	125	129.741629404942	-4.74162940494174
54	123	125.907519630806	-2.90751963080624
55	117	120.184391560981	-3.18439156098148
56	114	116.073409856671	-2.07340985667074
57	111	112.132200582235	-1.13220058223531
58	112	112.742794066145	-0.742794066144982
59	144	147.128318378224	-3.12831837822448
60	150	154.515783792309	-4.51578379230941
61	149	150.990646203661	-1.99064620366081
62	134	135.795729137937	-1.79572913793698
63	123	124.349861218689	-1.34986121868855
64	116	118.845590794277	-2.84559079427664
65	117	115.676983025605	1.32301697439545
66	111	110.172324380792	0.82767561920844
67	105	102.110427892018	2.8895721079817
68	102	97.9994461877075	4.00055381229244
69	95	90.7171391719171	4.28286082808286
70	93	88.3207446886073	4.6792553113927
71	124	126.047366742042	-2.04736674204180
72	130	134.437161478533	-4.43716147853323
73	124	127.236816374394	-3.23681637439413

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 140 & 148.477947338808 & -8.47794733880753 \tabularnewline
2 & 132 & 138.628786659252 & -6.62878665925186 \tabularnewline
3 & 117 & 124.844150321055 & -7.84415032105496 \tabularnewline
4 & 114 & 120.676318993185 & -6.67631899318502 \tabularnewline
5 & 113 & 118.844150321055 & -5.84415032105493 \tabularnewline
6 & 110 & 115.678260095190 & -5.67826009519042 \tabularnewline
7 & 107 & 110.957461347772 & -3.95746134777218 \tabularnewline
8 & 103 & 106.178260095190 & -3.17826009519043 \tabularnewline
9 & 98 & 101.234721498349 & -3.23472149834853 \tabularnewline
10 & 98 & 102.179424756394 & -4.17942475639371 \tabularnewline
11 & 137 & 139.237827261557 & -2.23782726155721 \tabularnewline
12 & 148 & 145.957073127371 & 2.04292687262891 \tabularnewline
13 & 147 & 143.434264861129 & 3.56573513887098 \tabularnewline
14 & 139 & 135.589762826386 & 3.41023717361382 \tabularnewline
15 & 130 & 127.150882874357 & 2.84911712564274 \tabularnewline
16 & 128 & 123.651271094758 & 4.34872890524165 \tabularnewline
17 & 127 & 122.487321970899 & 4.51267802910073 \tabularnewline
18 & 123 & 119.655541519170 & 3.34445848082972 \tabularnewline
19 & 118 & 114.600632997617 & 3.39936700238348 \tabularnewline
20 & 114 & 112.828419712254 & 1.17158028774573 \tabularnewline
21 & 108 & 106.882551793006 & 1.11744820699416 \tabularnewline
22 & 111 & 109.163694147593 & 1.83630585240698 \tabularnewline
23 & 151 & 146.222096652757 & 4.77790334724349 \tabularnewline
24 & 159 & 154.277781615112 & 4.72221838488756 \tabularnewline
25 & 158 & 152.089083123006 & 5.91091687699415 \tabularnewline
26 & 148 & 142.23992244345 & 5.76007755655 \tabularnewline
27 & 138 & 131.462274072473 & 6.53772592752741 \tabularnewline
28 & 137 & 128.964991615280 & 8.03500838471982 \tabularnewline
29 & 136 & 127.801042491421 & 8.1989575085789 \tabularnewline
30 & 133 & 124.969262039692 & 8.03073796030791 \tabularnewline
31 & 126 & 121.250792614680 & 4.74920738531966 \tabularnewline
32 & 120 & 116.137481587963 & 3.86251841203691 \tabularnewline
33 & 114 & 111.193942991121 & 2.80605700887882 \tabularnewline
34 & 116 & 113.475085345708 & 2.52491465429166 \tabularnewline
35 & 153 & 147.526499883652 & 5.47350011634766 \tabularnewline
36 & 162 & 157.586843490821 & 4.41315650917874 \tabularnewline
37 & 161 & 156.734584095257 & 4.26541590474333 \tabularnewline
38 & 149 & 150.894740705327 & -1.89474070532682 \tabularnewline
39 & 139 & 140.451202108485 & -1.45120210848491 \tabularnewline
40 & 135 & 137.285700103021 & -2.28570010302149 \tabularnewline
41 & 130 & 133.448872786078 & -3.44887278607842 \tabularnewline
42 & 127 & 130.617092334349 & -3.61709233434941 \tabularnewline
43 & 122 & 125.896293586931 & -3.89629358693117 \tabularnewline
44 & 117 & 120.782982560214 & -3.78298256021391 \tabularnewline
45 & 112 & 115.839443963372 & -3.839443963372 \tabularnewline
46 & 113 & 117.118256995553 & -4.11825699555265 \tabularnewline
47 & 149 & 151.837891081768 & -2.83789108176766 \tabularnewline
48 & 157 & 159.225356495853 & -2.22535649585258 \tabularnewline
49 & 157 & 157.036658003746 & -0.0366580037459927 \tabularnewline
50 & 147 & 145.851058227648 & 1.14894177235185 \tabularnewline
51 & 137 & 135.741629404942 & 1.25837059505827 \tabularnewline
52 & 132 & 132.576127399478 & -0.576127399478315 \tabularnewline
53 & 125 & 129.741629404942 & -4.74162940494174 \tabularnewline
54 & 123 & 125.907519630806 & -2.90751963080624 \tabularnewline
55 & 117 & 120.184391560981 & -3.18439156098148 \tabularnewline
56 & 114 & 116.073409856671 & -2.07340985667074 \tabularnewline
57 & 111 & 112.132200582235 & -1.13220058223531 \tabularnewline
58 & 112 & 112.742794066145 & -0.742794066144982 \tabularnewline
59 & 144 & 147.128318378224 & -3.12831837822448 \tabularnewline
60 & 150 & 154.515783792309 & -4.51578379230941 \tabularnewline
61 & 149 & 150.990646203661 & -1.99064620366081 \tabularnewline
62 & 134 & 135.795729137937 & -1.79572913793698 \tabularnewline
63 & 123 & 124.349861218689 & -1.34986121868855 \tabularnewline
64 & 116 & 118.845590794277 & -2.84559079427664 \tabularnewline
65 & 117 & 115.676983025605 & 1.32301697439545 \tabularnewline
66 & 111 & 110.172324380792 & 0.82767561920844 \tabularnewline
67 & 105 & 102.110427892018 & 2.8895721079817 \tabularnewline
68 & 102 & 97.9994461877075 & 4.00055381229244 \tabularnewline
69 & 95 & 90.7171391719171 & 4.28286082808286 \tabularnewline
70 & 93 & 88.3207446886073 & 4.6792553113927 \tabularnewline
71 & 124 & 126.047366742042 & -2.04736674204180 \tabularnewline
72 & 130 & 134.437161478533 & -4.43716147853323 \tabularnewline
73 & 124 & 127.236816374394 & -3.23681637439413 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5419&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]140[/C][C]148.477947338808[/C][C]-8.47794733880753[/C][/ROW]
[ROW][C]2[/C][C]132[/C][C]138.628786659252[/C][C]-6.62878665925186[/C][/ROW]
[ROW][C]3[/C][C]117[/C][C]124.844150321055[/C][C]-7.84415032105496[/C][/ROW]
[ROW][C]4[/C][C]114[/C][C]120.676318993185[/C][C]-6.67631899318502[/C][/ROW]
[ROW][C]5[/C][C]113[/C][C]118.844150321055[/C][C]-5.84415032105493[/C][/ROW]
[ROW][C]6[/C][C]110[/C][C]115.678260095190[/C][C]-5.67826009519042[/C][/ROW]
[ROW][C]7[/C][C]107[/C][C]110.957461347772[/C][C]-3.95746134777218[/C][/ROW]
[ROW][C]8[/C][C]103[/C][C]106.178260095190[/C][C]-3.17826009519043[/C][/ROW]
[ROW][C]9[/C][C]98[/C][C]101.234721498349[/C][C]-3.23472149834853[/C][/ROW]
[ROW][C]10[/C][C]98[/C][C]102.179424756394[/C][C]-4.17942475639371[/C][/ROW]
[ROW][C]11[/C][C]137[/C][C]139.237827261557[/C][C]-2.23782726155721[/C][/ROW]
[ROW][C]12[/C][C]148[/C][C]145.957073127371[/C][C]2.04292687262891[/C][/ROW]
[ROW][C]13[/C][C]147[/C][C]143.434264861129[/C][C]3.56573513887098[/C][/ROW]
[ROW][C]14[/C][C]139[/C][C]135.589762826386[/C][C]3.41023717361382[/C][/ROW]
[ROW][C]15[/C][C]130[/C][C]127.150882874357[/C][C]2.84911712564274[/C][/ROW]
[ROW][C]16[/C][C]128[/C][C]123.651271094758[/C][C]4.34872890524165[/C][/ROW]
[ROW][C]17[/C][C]127[/C][C]122.487321970899[/C][C]4.51267802910073[/C][/ROW]
[ROW][C]18[/C][C]123[/C][C]119.655541519170[/C][C]3.34445848082972[/C][/ROW]
[ROW][C]19[/C][C]118[/C][C]114.600632997617[/C][C]3.39936700238348[/C][/ROW]
[ROW][C]20[/C][C]114[/C][C]112.828419712254[/C][C]1.17158028774573[/C][/ROW]
[ROW][C]21[/C][C]108[/C][C]106.882551793006[/C][C]1.11744820699416[/C][/ROW]
[ROW][C]22[/C][C]111[/C][C]109.163694147593[/C][C]1.83630585240698[/C][/ROW]
[ROW][C]23[/C][C]151[/C][C]146.222096652757[/C][C]4.77790334724349[/C][/ROW]
[ROW][C]24[/C][C]159[/C][C]154.277781615112[/C][C]4.72221838488756[/C][/ROW]
[ROW][C]25[/C][C]158[/C][C]152.089083123006[/C][C]5.91091687699415[/C][/ROW]
[ROW][C]26[/C][C]148[/C][C]142.23992244345[/C][C]5.76007755655[/C][/ROW]
[ROW][C]27[/C][C]138[/C][C]131.462274072473[/C][C]6.53772592752741[/C][/ROW]
[ROW][C]28[/C][C]137[/C][C]128.964991615280[/C][C]8.03500838471982[/C][/ROW]
[ROW][C]29[/C][C]136[/C][C]127.801042491421[/C][C]8.1989575085789[/C][/ROW]
[ROW][C]30[/C][C]133[/C][C]124.969262039692[/C][C]8.03073796030791[/C][/ROW]
[ROW][C]31[/C][C]126[/C][C]121.250792614680[/C][C]4.74920738531966[/C][/ROW]
[ROW][C]32[/C][C]120[/C][C]116.137481587963[/C][C]3.86251841203691[/C][/ROW]
[ROW][C]33[/C][C]114[/C][C]111.193942991121[/C][C]2.80605700887882[/C][/ROW]
[ROW][C]34[/C][C]116[/C][C]113.475085345708[/C][C]2.52491465429166[/C][/ROW]
[ROW][C]35[/C][C]153[/C][C]147.526499883652[/C][C]5.47350011634766[/C][/ROW]
[ROW][C]36[/C][C]162[/C][C]157.586843490821[/C][C]4.41315650917874[/C][/ROW]
[ROW][C]37[/C][C]161[/C][C]156.734584095257[/C][C]4.26541590474333[/C][/ROW]
[ROW][C]38[/C][C]149[/C][C]150.894740705327[/C][C]-1.89474070532682[/C][/ROW]
[ROW][C]39[/C][C]139[/C][C]140.451202108485[/C][C]-1.45120210848491[/C][/ROW]
[ROW][C]40[/C][C]135[/C][C]137.285700103021[/C][C]-2.28570010302149[/C][/ROW]
[ROW][C]41[/C][C]130[/C][C]133.448872786078[/C][C]-3.44887278607842[/C][/ROW]
[ROW][C]42[/C][C]127[/C][C]130.617092334349[/C][C]-3.61709233434941[/C][/ROW]
[ROW][C]43[/C][C]122[/C][C]125.896293586931[/C][C]-3.89629358693117[/C][/ROW]
[ROW][C]44[/C][C]117[/C][C]120.782982560214[/C][C]-3.78298256021391[/C][/ROW]
[ROW][C]45[/C][C]112[/C][C]115.839443963372[/C][C]-3.839443963372[/C][/ROW]
[ROW][C]46[/C][C]113[/C][C]117.118256995553[/C][C]-4.11825699555265[/C][/ROW]
[ROW][C]47[/C][C]149[/C][C]151.837891081768[/C][C]-2.83789108176766[/C][/ROW]
[ROW][C]48[/C][C]157[/C][C]159.225356495853[/C][C]-2.22535649585258[/C][/ROW]
[ROW][C]49[/C][C]157[/C][C]157.036658003746[/C][C]-0.0366580037459927[/C][/ROW]
[ROW][C]50[/C][C]147[/C][C]145.851058227648[/C][C]1.14894177235185[/C][/ROW]
[ROW][C]51[/C][C]137[/C][C]135.741629404942[/C][C]1.25837059505827[/C][/ROW]
[ROW][C]52[/C][C]132[/C][C]132.576127399478[/C][C]-0.576127399478315[/C][/ROW]
[ROW][C]53[/C][C]125[/C][C]129.741629404942[/C][C]-4.74162940494174[/C][/ROW]
[ROW][C]54[/C][C]123[/C][C]125.907519630806[/C][C]-2.90751963080624[/C][/ROW]
[ROW][C]55[/C][C]117[/C][C]120.184391560981[/C][C]-3.18439156098148[/C][/ROW]
[ROW][C]56[/C][C]114[/C][C]116.073409856671[/C][C]-2.07340985667074[/C][/ROW]
[ROW][C]57[/C][C]111[/C][C]112.132200582235[/C][C]-1.13220058223531[/C][/ROW]
[ROW][C]58[/C][C]112[/C][C]112.742794066145[/C][C]-0.742794066144982[/C][/ROW]
[ROW][C]59[/C][C]144[/C][C]147.128318378224[/C][C]-3.12831837822448[/C][/ROW]
[ROW][C]60[/C][C]150[/C][C]154.515783792309[/C][C]-4.51578379230941[/C][/ROW]
[ROW][C]61[/C][C]149[/C][C]150.990646203661[/C][C]-1.99064620366081[/C][/ROW]
[ROW][C]62[/C][C]134[/C][C]135.795729137937[/C][C]-1.79572913793698[/C][/ROW]
[ROW][C]63[/C][C]123[/C][C]124.349861218689[/C][C]-1.34986121868855[/C][/ROW]
[ROW][C]64[/C][C]116[/C][C]118.845590794277[/C][C]-2.84559079427664[/C][/ROW]
[ROW][C]65[/C][C]117[/C][C]115.676983025605[/C][C]1.32301697439545[/C][/ROW]
[ROW][C]66[/C][C]111[/C][C]110.172324380792[/C][C]0.82767561920844[/C][/ROW]
[ROW][C]67[/C][C]105[/C][C]102.110427892018[/C][C]2.8895721079817[/C][/ROW]
[ROW][C]68[/C][C]102[/C][C]97.9994461877075[/C][C]4.00055381229244[/C][/ROW]
[ROW][C]69[/C][C]95[/C][C]90.7171391719171[/C][C]4.28286082808286[/C][/ROW]
[ROW][C]70[/C][C]93[/C][C]88.3207446886073[/C][C]4.6792553113927[/C][/ROW]
[ROW][C]71[/C][C]124[/C][C]126.047366742042[/C][C]-2.04736674204180[/C][/ROW]
[ROW][C]72[/C][C]130[/C][C]134.437161478533[/C][C]-4.43716147853323[/C][/ROW]
[ROW][C]73[/C][C]124[/C][C]127.236816374394[/C][C]-3.23681637439413[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5419&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5419&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	140	148.477947338808	-8.47794733880753
2	132	138.628786659252	-6.62878665925186
3	117	124.844150321055	-7.84415032105496
4	114	120.676318993185	-6.67631899318502
5	113	118.844150321055	-5.84415032105493
6	110	115.678260095190	-5.67826009519042
7	107	110.957461347772	-3.95746134777218
8	103	106.178260095190	-3.17826009519043
9	98	101.234721498349	-3.23472149834853
10	98	102.179424756394	-4.17942475639371
11	137	139.237827261557	-2.23782726155721
12	148	145.957073127371	2.04292687262891
13	147	143.434264861129	3.56573513887098
14	139	135.589762826386	3.41023717361382
15	130	127.150882874357	2.84911712564274
16	128	123.651271094758	4.34872890524165
17	127	122.487321970899	4.51267802910073
18	123	119.655541519170	3.34445848082972
19	118	114.600632997617	3.39936700238348
20	114	112.828419712254	1.17158028774573
21	108	106.882551793006	1.11744820699416
22	111	109.163694147593	1.83630585240698
23	151	146.222096652757	4.77790334724349
24	159	154.277781615112	4.72221838488756
25	158	152.089083123006	5.91091687699415
26	148	142.23992244345	5.76007755655
27	138	131.462274072473	6.53772592752741
28	137	128.964991615280	8.03500838471982
29	136	127.801042491421	8.1989575085789
30	133	124.969262039692	8.03073796030791
31	126	121.250792614680	4.74920738531966
32	120	116.137481587963	3.86251841203691
33	114	111.193942991121	2.80605700887882
34	116	113.475085345708	2.52491465429166
35	153	147.526499883652	5.47350011634766
36	162	157.586843490821	4.41315650917874
37	161	156.734584095257	4.26541590474333
38	149	150.894740705327	-1.89474070532682
39	139	140.451202108485	-1.45120210848491
40	135	137.285700103021	-2.28570010302149
41	130	133.448872786078	-3.44887278607842
42	127	130.617092334349	-3.61709233434941
43	122	125.896293586931	-3.89629358693117
44	117	120.782982560214	-3.78298256021391
45	112	115.839443963372	-3.839443963372
46	113	117.118256995553	-4.11825699555265
47	149	151.837891081768	-2.83789108176766
48	157	159.225356495853	-2.22535649585258
49	157	157.036658003746	-0.0366580037459927
50	147	145.851058227648	1.14894177235185
51	137	135.741629404942	1.25837059505827
52	132	132.576127399478	-0.576127399478315
53	125	129.741629404942	-4.74162940494174
54	123	125.907519630806	-2.90751963080624
55	117	120.184391560981	-3.18439156098148
56	114	116.073409856671	-2.07340985667074
57	111	112.132200582235	-1.13220058223531
58	112	112.742794066145	-0.742794066144982
59	144	147.128318378224	-3.12831837822448
60	150	154.515783792309	-4.51578379230941
61	149	150.990646203661	-1.99064620366081
62	134	135.795729137937	-1.79572913793698
63	123	124.349861218689	-1.34986121868855
64	116	118.845590794277	-2.84559079427664
65	117	115.676983025605	1.32301697439545
66	111	110.172324380792	0.82767561920844
67	105	102.110427892018	2.8895721079817
68	102	97.9994461877075	4.00055381229244
69	95	90.7171391719171	4.28286082808286
70	93	88.3207446886073	4.6792553113927
71	124	126.047366742042	-2.04736674204180
72	130	134.437161478533	-4.43716147853323
73	124	127.236816374394	-3.23681637439413

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Figure 2

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Figure 3

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Figure 4

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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 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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