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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 13 Sep 2021 03:20:59 +0200

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/2021/Sep/13/t1631496242gpdo36ktmhpk2mv.htm/, Retrieved Mon, 06 May 2024 06:00:44 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 06 May 2024 06:00:44 +0200

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Paste this QR Code to cite your computation.

Original text written by user:

Pius Thoams

IsPrivate?

This computation is private

User-defined keywords

A2151,

Estimated Impact

Dataseries X:

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Histogram

Boxplots

19.28	594	44.5
19.54	616	44.3
20.26	617	44.2
20.6	658	42.3
19.94	625	42.6
19.32	605	42.4
19.2	585	42.9
19.6	600	44.0
18.53	548	43.5
20.93	683	44.8
20.91	650	43.9
19.31	570	43.6
19.32	585	42.1
20.19	638	43.0
18.7	564	42.0
18.92	590	43.8
19.8	629	45.2
20.27	626	45
18.92	578	44.7
19.55	581	43.4
20.35	647	44.4
19	601	42.9
20.6	658	42.3
20.47	617	43.3
19.24	589	41.5
13.5	373	39.0
19.95	645	42.2
19.47	588	43.95
20.96	654	41.2
20.73	672	45.3
19.72	611	43.4

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

3 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	Big Analytics Cloud Computing Center

Multiple Linear Regression - Estimated Regression Equation
DE[t] = + 33.3249 + 0.491587`Solids,`[t] + 0.00123242`Osmo,`[t] -0.0262518t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
DE[t] =  +  33.3249 +  0.491587`Solids,`[t] +  0.00123242`Osmo,`[t] -0.0262518t  + e[t] \tabularnewline
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]DE[t] =  +  33.3249 +  0.491587`Solids,`[t] +  0.00123242`Osmo,`[t] -0.0262518t  + e[t][/C][/ROW]
[ROW][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
DE[t] = + 33.3249 + 0.491587`Solids,`[t] + 0.00123242`Osmo,`[t] -0.0262518t + 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)	+33.33	4.257	+7.8270e+00	2.042e-08	1.021e-08
`Solids,`	+0.4916	0.6357	+7.7330e-01	0.446	0.223
`Osmo,`	+0.001232	0.01534	+8.0320e-02	0.9366	0.4683
t	-0.02625	0.0237	-1.1080e+00	0.2777	0.1388

\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) & +33.33 &  4.257 & +7.8270e+00 &  2.042e-08 &  1.021e-08 \tabularnewline
`Solids,` & +0.4916 &  0.6357 & +7.7330e-01 &  0.446 &  0.223 \tabularnewline
`Osmo,` & +0.001232 &  0.01534 & +8.0320e-02 &  0.9366 &  0.4683 \tabularnewline
t & -0.02625 &  0.0237 & -1.1080e+00 &  0.2777 &  0.1388 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]+33.33[/C][C] 4.257[/C][C]+7.8270e+00[/C][C] 2.042e-08[/C][C] 1.021e-08[/C][/ROW]
[ROW][C]`Solids,`[/C][C]+0.4916[/C][C] 0.6357[/C][C]+7.7330e-01[/C][C] 0.446[/C][C] 0.223[/C][/ROW]
[ROW][C]`Osmo,`[/C][C]+0.001232[/C][C] 0.01534[/C][C]+8.0320e-02[/C][C] 0.9366[/C][C] 0.4683[/C][/ROW]
[ROW][C]t[/C][C]-0.02625[/C][C] 0.0237[/C][C]-1.1080e+00[/C][C] 0.2777[/C][C] 0.1388[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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)	+33.33	4.257	+7.8270e+00	2.042e-08	1.021e-08
`Solids,`	+0.4916	0.6357	+7.7330e-01	0.446	0.223
`Osmo,`	+0.001232	0.01534	+8.0320e-02	0.9366	0.4683
t	-0.02625	0.0237	-1.1080e+00	0.2777	0.1388

Multiple Linear Regression - Regression Statistics
Multiple R	0.5711
R-squared	0.3262
Adjusted R-squared	0.2513
F-TEST (value)	4.357
F-TEST (DF numerator)	3
F-TEST (DF denominator)	27
p-value	0.01258
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.172
Sum Squared Residuals	37.07

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R &  0.5711 \tabularnewline
R-squared &  0.3262 \tabularnewline
Adjusted R-squared &  0.2513 \tabularnewline
F-TEST (value) &  4.357 \tabularnewline
F-TEST (DF numerator) & 3 \tabularnewline
F-TEST (DF denominator) & 27 \tabularnewline
p-value &  0.01258 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation &  1.172 \tabularnewline
Sum Squared Residuals &  37.07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C] 0.5711[/C][/ROW]
[ROW][C]R-squared[/C][C] 0.3262[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C] 0.2513[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C] 4.357[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]3[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]27[/C][/ROW]
[ROW][C]p-value[/C][C] 0.01258[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C] 1.172[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C] 37.07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.5711
R-squared	0.3262
Adjusted R-squared	0.2513
F-TEST (value)	4.357
F-TEST (DF numerator)	3
F-TEST (DF denominator)	27
p-value	0.01258
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.172
Sum Squared Residuals	37.07

Menu of Residual Diagnostics
Description	Link
Histogram	Compute
Central Tendency	Compute
QQ Plot	Compute
Kernel Density Plot	Compute
Skewness/Kurtosis Test	Compute
Skewness-Kurtosis Plot	Compute
Harrell-Davis Plot	Compute
Bootstrap Plot -- Central Tendency	Compute
Blocked Bootstrap Plot -- Central Tendency	Compute
(Partial) Autocorrelation Plot	Compute
Spectral Analysis	Compute
Tukey lambda PPCC Plot	Compute
Box-Cox Normality Plot	Compute
Summary Statistics	Compute

\begin{tabular}{lllllllll}
\hline
Menu of Residual Diagnostics \tabularnewline
Description & Link \tabularnewline
Histogram & Compute \tabularnewline
Central Tendency & Compute \tabularnewline
QQ Plot & Compute \tabularnewline
Kernel Density Plot & Compute \tabularnewline
Skewness/Kurtosis Test & Compute \tabularnewline
Skewness-Kurtosis Plot & Compute \tabularnewline
Harrell-Davis Plot & Compute \tabularnewline
Bootstrap Plot -- Central Tendency & Compute \tabularnewline
Blocked Bootstrap Plot -- Central Tendency & Compute \tabularnewline
(Partial) Autocorrelation Plot & Compute \tabularnewline
Spectral Analysis & Compute \tabularnewline
Tukey lambda PPCC Plot & Compute \tabularnewline
Box-Cox Normality Plot & Compute \tabularnewline
Summary Statistics & Compute \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=4

[TABLE]
[ROW][C]Menu of Residual Diagnostics[/C][/ROW]
[ROW][C]Description[/C][C]Link[/C][/ROW]
[ROW][C]Histogram[/C][C]Compute[/C][/ROW]
[ROW][C]Central Tendency[/C][C]Compute[/C][/ROW]
[ROW][C]QQ Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Kernel Density Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Skewness/Kurtosis Test[/C][C]Compute[/C][/ROW]
[ROW][C]Skewness-Kurtosis Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Harrell-Davis Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Bootstrap Plot -- Central Tendency[/C][C]Compute[/C][/ROW]
[ROW][C]Blocked Bootstrap Plot -- Central Tendency[/C][C]Compute[/C][/ROW]
[ROW][C](Partial) Autocorrelation Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Spectral Analysis[/C][C]Compute[/C][/ROW]
[ROW][C]Tukey lambda PPCC Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Box-Cox Normality Plot[/C][C]Compute[/C][/ROW]
[ROW][C]Summary Statistics[/C][C]Compute[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=4

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

As an alternative you can also use a QR Code:

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

Menu of Residual Diagnostics
Description	Link
Histogram	Compute
Central Tendency	Compute
QQ Plot	Compute
Kernel Density Plot	Compute
Skewness/Kurtosis Test	Compute
Skewness-Kurtosis Plot	Compute
Harrell-Davis Plot	Compute
Bootstrap Plot -- Central Tendency	Compute
Blocked Bootstrap Plot -- Central Tendency	Compute
(Partial) Autocorrelation Plot	Compute
Spectral Analysis	Compute
Tukey lambda PPCC Plot	Compute
Box-Cox Normality Plot	Compute
Summary Statistics	Compute

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	44.5	43.51	0.9915
2	44.3	43.64	0.6628
3	44.2	43.97	0.2339
4	42.3	44.16	-1.858
5	42.6	43.77	-1.166
6	42.4	43.41	-1.01
7	42.9	43.3	-0.4006
8	44	43.49	0.5105
9	43.5	42.87	0.6269
10	44.8	44.19	0.6069
11	43.9	44.12	-0.2163
12	43.6	43.2	0.3951
13	42.1	43.2	-1.102
14	43	43.67	-0.6688
15	42	42.82	-0.8189
16	43.8	42.93	0.8672
17	45.2	43.39	1.813
18	45	43.59	1.412
19	44.7	42.84	1.861
20	43.4	43.13	0.2736
21	44.4	43.57	0.8252
22	42.9	42.83	0.07178
23	42.3	43.66	-1.359
24	43.3	43.52	-0.2181
25	41.5	42.85	-1.353
26	39	39.74	-0.7385
27	42.2	43.22	-1.018
28	43.95	42.89	1.064
29	41.2	43.67	-2.473
30	45.3	43.56	1.744
31	43.4	42.96	0.4418

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 &  44.5 &  43.51 &  0.9915 \tabularnewline
2 &  44.3 &  43.64 &  0.6628 \tabularnewline
3 &  44.2 &  43.97 &  0.2339 \tabularnewline
4 &  42.3 &  44.16 & -1.858 \tabularnewline
5 &  42.6 &  43.77 & -1.166 \tabularnewline
6 &  42.4 &  43.41 & -1.01 \tabularnewline
7 &  42.9 &  43.3 & -0.4006 \tabularnewline
8 &  44 &  43.49 &  0.5105 \tabularnewline
9 &  43.5 &  42.87 &  0.6269 \tabularnewline
10 &  44.8 &  44.19 &  0.6069 \tabularnewline
11 &  43.9 &  44.12 & -0.2163 \tabularnewline
12 &  43.6 &  43.2 &  0.3951 \tabularnewline
13 &  42.1 &  43.2 & -1.102 \tabularnewline
14 &  43 &  43.67 & -0.6688 \tabularnewline
15 &  42 &  42.82 & -0.8189 \tabularnewline
16 &  43.8 &  42.93 &  0.8672 \tabularnewline
17 &  45.2 &  43.39 &  1.813 \tabularnewline
18 &  45 &  43.59 &  1.412 \tabularnewline
19 &  44.7 &  42.84 &  1.861 \tabularnewline
20 &  43.4 &  43.13 &  0.2736 \tabularnewline
21 &  44.4 &  43.57 &  0.8252 \tabularnewline
22 &  42.9 &  42.83 &  0.07178 \tabularnewline
23 &  42.3 &  43.66 & -1.359 \tabularnewline
24 &  43.3 &  43.52 & -0.2181 \tabularnewline
25 &  41.5 &  42.85 & -1.353 \tabularnewline
26 &  39 &  39.74 & -0.7385 \tabularnewline
27 &  42.2 &  43.22 & -1.018 \tabularnewline
28 &  43.95 &  42.89 &  1.064 \tabularnewline
29 &  41.2 &  43.67 & -2.473 \tabularnewline
30 &  45.3 &  43.56 &  1.744 \tabularnewline
31 &  43.4 &  42.96 &  0.4418 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=5

[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] 44.5[/C][C] 43.51[/C][C] 0.9915[/C][/ROW]
[ROW][C]2[/C][C] 44.3[/C][C] 43.64[/C][C] 0.6628[/C][/ROW]
[ROW][C]3[/C][C] 44.2[/C][C] 43.97[/C][C] 0.2339[/C][/ROW]
[ROW][C]4[/C][C] 42.3[/C][C] 44.16[/C][C]-1.858[/C][/ROW]
[ROW][C]5[/C][C] 42.6[/C][C] 43.77[/C][C]-1.166[/C][/ROW]
[ROW][C]6[/C][C] 42.4[/C][C] 43.41[/C][C]-1.01[/C][/ROW]
[ROW][C]7[/C][C] 42.9[/C][C] 43.3[/C][C]-0.4006[/C][/ROW]
[ROW][C]8[/C][C] 44[/C][C] 43.49[/C][C] 0.5105[/C][/ROW]
[ROW][C]9[/C][C] 43.5[/C][C] 42.87[/C][C] 0.6269[/C][/ROW]
[ROW][C]10[/C][C] 44.8[/C][C] 44.19[/C][C] 0.6069[/C][/ROW]
[ROW][C]11[/C][C] 43.9[/C][C] 44.12[/C][C]-0.2163[/C][/ROW]
[ROW][C]12[/C][C] 43.6[/C][C] 43.2[/C][C] 0.3951[/C][/ROW]
[ROW][C]13[/C][C] 42.1[/C][C] 43.2[/C][C]-1.102[/C][/ROW]
[ROW][C]14[/C][C] 43[/C][C] 43.67[/C][C]-0.6688[/C][/ROW]
[ROW][C]15[/C][C] 42[/C][C] 42.82[/C][C]-0.8189[/C][/ROW]
[ROW][C]16[/C][C] 43.8[/C][C] 42.93[/C][C] 0.8672[/C][/ROW]
[ROW][C]17[/C][C] 45.2[/C][C] 43.39[/C][C] 1.813[/C][/ROW]
[ROW][C]18[/C][C] 45[/C][C] 43.59[/C][C] 1.412[/C][/ROW]
[ROW][C]19[/C][C] 44.7[/C][C] 42.84[/C][C] 1.861[/C][/ROW]
[ROW][C]20[/C][C] 43.4[/C][C] 43.13[/C][C] 0.2736[/C][/ROW]
[ROW][C]21[/C][C] 44.4[/C][C] 43.57[/C][C] 0.8252[/C][/ROW]
[ROW][C]22[/C][C] 42.9[/C][C] 42.83[/C][C] 0.07178[/C][/ROW]
[ROW][C]23[/C][C] 42.3[/C][C] 43.66[/C][C]-1.359[/C][/ROW]
[ROW][C]24[/C][C] 43.3[/C][C] 43.52[/C][C]-0.2181[/C][/ROW]
[ROW][C]25[/C][C] 41.5[/C][C] 42.85[/C][C]-1.353[/C][/ROW]
[ROW][C]26[/C][C] 39[/C][C] 39.74[/C][C]-0.7385[/C][/ROW]
[ROW][C]27[/C][C] 42.2[/C][C] 43.22[/C][C]-1.018[/C][/ROW]
[ROW][C]28[/C][C] 43.95[/C][C] 42.89[/C][C] 1.064[/C][/ROW]
[ROW][C]29[/C][C] 41.2[/C][C] 43.67[/C][C]-2.473[/C][/ROW]
[ROW][C]30[/C][C] 45.3[/C][C] 43.56[/C][C] 1.744[/C][/ROW]
[ROW][C]31[/C][C] 43.4[/C][C] 42.96[/C][C] 0.4418[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=5

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	44.5	43.51	0.9915
2	44.3	43.64	0.6628
3	44.2	43.97	0.2339
4	42.3	44.16	-1.858
5	42.6	43.77	-1.166
6	42.4	43.41	-1.01
7	42.9	43.3	-0.4006
8	44	43.49	0.5105
9	43.5	42.87	0.6269
10	44.8	44.19	0.6069
11	43.9	44.12	-0.2163
12	43.6	43.2	0.3951
13	42.1	43.2	-1.102
14	43	43.67	-0.6688
15	42	42.82	-0.8189
16	43.8	42.93	0.8672
17	45.2	43.39	1.813
18	45	43.59	1.412
19	44.7	42.84	1.861
20	43.4	43.13	0.2736
21	44.4	43.57	0.8252
22	42.9	42.83	0.07178
23	42.3	43.66	-1.359
24	43.3	43.52	-0.2181
25	41.5	42.85	-1.353
26	39	39.74	-0.7385
27	42.2	43.22	-1.018
28	43.95	42.89	1.064
29	41.2	43.67	-2.473
30	45.3	43.56	1.744
31	43.4	42.96	0.4418

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
7	0.03674	0.07347	0.9633
8	0.1709	0.3418	0.8291
9	0.08745	0.1749	0.9126
10	0.4008	0.8016	0.5992
11	0.2774	0.5548	0.7226
12	0.1776	0.3551	0.8224
13	0.1796	0.3592	0.8204
14	0.1349	0.2698	0.8651
15	0.1181	0.2362	0.8819
16	0.1106	0.2212	0.8894
17	0.1531	0.3062	0.8469
18	0.1344	0.2688	0.8656
19	0.1644	0.3288	0.8356
20	0.1137	0.2275	0.8863
21	0.1007	0.2014	0.8993
22	0.08797	0.1759	0.912
23	0.0703	0.1406	0.9297
24	0.05371	0.1074	0.9463

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
7 &  0.03674 &  0.07347 &  0.9633 \tabularnewline
8 &  0.1709 &  0.3418 &  0.8291 \tabularnewline
9 &  0.08745 &  0.1749 &  0.9126 \tabularnewline
10 &  0.4008 &  0.8016 &  0.5992 \tabularnewline
11 &  0.2774 &  0.5548 &  0.7226 \tabularnewline
12 &  0.1776 &  0.3551 &  0.8224 \tabularnewline
13 &  0.1796 &  0.3592 &  0.8204 \tabularnewline
14 &  0.1349 &  0.2698 &  0.8651 \tabularnewline
15 &  0.1181 &  0.2362 &  0.8819 \tabularnewline
16 &  0.1106 &  0.2212 &  0.8894 \tabularnewline
17 &  0.1531 &  0.3062 &  0.8469 \tabularnewline
18 &  0.1344 &  0.2688 &  0.8656 \tabularnewline
19 &  0.1644 &  0.3288 &  0.8356 \tabularnewline
20 &  0.1137 &  0.2275 &  0.8863 \tabularnewline
21 &  0.1007 &  0.2014 &  0.8993 \tabularnewline
22 &  0.08797 &  0.1759 &  0.912 \tabularnewline
23 &  0.0703 &  0.1406 &  0.9297 \tabularnewline
24 &  0.05371 &  0.1074 &  0.9463 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=6

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]7[/C][C] 0.03674[/C][C] 0.07347[/C][C] 0.9633[/C][/ROW]
[ROW][C]8[/C][C] 0.1709[/C][C] 0.3418[/C][C] 0.8291[/C][/ROW]
[ROW][C]9[/C][C] 0.08745[/C][C] 0.1749[/C][C] 0.9126[/C][/ROW]
[ROW][C]10[/C][C] 0.4008[/C][C] 0.8016[/C][C] 0.5992[/C][/ROW]
[ROW][C]11[/C][C] 0.2774[/C][C] 0.5548[/C][C] 0.7226[/C][/ROW]
[ROW][C]12[/C][C] 0.1776[/C][C] 0.3551[/C][C] 0.8224[/C][/ROW]
[ROW][C]13[/C][C] 0.1796[/C][C] 0.3592[/C][C] 0.8204[/C][/ROW]
[ROW][C]14[/C][C] 0.1349[/C][C] 0.2698[/C][C] 0.8651[/C][/ROW]
[ROW][C]15[/C][C] 0.1181[/C][C] 0.2362[/C][C] 0.8819[/C][/ROW]
[ROW][C]16[/C][C] 0.1106[/C][C] 0.2212[/C][C] 0.8894[/C][/ROW]
[ROW][C]17[/C][C] 0.1531[/C][C] 0.3062[/C][C] 0.8469[/C][/ROW]
[ROW][C]18[/C][C] 0.1344[/C][C] 0.2688[/C][C] 0.8656[/C][/ROW]
[ROW][C]19[/C][C] 0.1644[/C][C] 0.3288[/C][C] 0.8356[/C][/ROW]
[ROW][C]20[/C][C] 0.1137[/C][C] 0.2275[/C][C] 0.8863[/C][/ROW]
[ROW][C]21[/C][C] 0.1007[/C][C] 0.2014[/C][C] 0.8993[/C][/ROW]
[ROW][C]22[/C][C] 0.08797[/C][C] 0.1759[/C][C] 0.912[/C][/ROW]
[ROW][C]23[/C][C] 0.0703[/C][C] 0.1406[/C][C] 0.9297[/C][/ROW]
[ROW][C]24[/C][C] 0.05371[/C][C] 0.1074[/C][C] 0.9463[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=6

As an alternative you can also use a QR Code:

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

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
7	0.03674	0.07347	0.9633
8	0.1709	0.3418	0.8291
9	0.08745	0.1749	0.9126
10	0.4008	0.8016	0.5992
11	0.2774	0.5548	0.7226
12	0.1776	0.3551	0.8224
13	0.1796	0.3592	0.8204
14	0.1349	0.2698	0.8651
15	0.1181	0.2362	0.8819
16	0.1106	0.2212	0.8894
17	0.1531	0.3062	0.8469
18	0.1344	0.2688	0.8656
19	0.1644	0.3288	0.8356
20	0.1137	0.2275	0.8863
21	0.1007	0.2014	0.8993
22	0.08797	0.1759	0.912
23	0.0703	0.1406	0.9297
24	0.05371	0.1074	0.9463

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	1	0.0555556	OK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 &  0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 1 & 0.0555556 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=7

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C] 0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]1[/C][C]0.0555556[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=7

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=7

As an alternative you can also use a QR Code:

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	1	0.0555556	OK

Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted RESET test data: mylm RESET = 0.90321, df1 = 2, df2 = 25, p-value = 0.4181
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors RESET test data: mylm RESET = 0.67924, df1 = 6, df2 = 21, p-value = 0.668
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components RESET test data: mylm RESET = 0.98183, df1 = 2, df2 = 25, p-value = 0.3886

\begin{tabular}{lllllllll}
\hline
Ramsey RESET F-Test for powers (2 and 3) of fitted values \tabularnewline
> reset_test_fitted
	RESET test
data:  mylm
RESET = 0.90321, df1 = 2, df2 = 25, p-value = 0.4181
 \tabularnewline
Ramsey RESET F-Test for powers (2 and 3) of regressors \tabularnewline
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0.67924, df1 = 6, df2 = 21, p-value = 0.668
 \tabularnewline
Ramsey RESET F-Test for powers (2 and 3) of principal components \tabularnewline
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.98183, df1 = 2, df2 = 25, p-value = 0.3886
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=8

[TABLE]
[ROW][C]Ramsey RESET F-Test for powers (2 and 3) of fitted values[/C][/ROW]
[ROW][C]> reset_test_fitted
	RESET test
data:  mylm
RESET = 0.90321, df1 = 2, df2 = 25, p-value = 0.4181
[/C][/ROW]
[ROW][C]Ramsey RESET F-Test for powers (2 and 3) of regressors[/C][/ROW]
[ROW][C]> reset_test_regressors
	RESET test
data:  mylm
RESET = 0.67924, df1 = 6, df2 = 21, p-value = 0.668
[/C][/ROW]
[ROW][C]Ramsey RESET F-Test for powers (2 and 3) of principal components[/C][/ROW]
[ROW][C]> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.98183, df1 = 2, df2 = 25, p-value = 0.3886
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=8

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=8

As an alternative you can also use a QR Code:

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

Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted RESET test data: mylm RESET = 0.90321, df1 = 2, df2 = 25, p-value = 0.4181
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors RESET test data: mylm RESET = 0.67924, df1 = 6, df2 = 21, p-value = 0.668
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components RESET test data: mylm RESET = 0.98183, df1 = 2, df2 = 25, p-value = 0.3886

Variance Inflation Factors (Multicollinearity)
> vif `Solids,` `Osmo,` t 15.466179 15.411955 1.014185

\begin{tabular}{lllllllll}
\hline
Variance Inflation Factors (Multicollinearity) \tabularnewline
> vif
`Solids,`   `Osmo,`         t 
15.466179 15.411955  1.014185 
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=9

[TABLE]
[ROW][C]Variance Inflation Factors (Multicollinearity)[/C][/ROW]
[ROW][C]> vif
`Solids,`   `Osmo,`         t 
15.466179 15.411955  1.014185 
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=9

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=9

As an alternative you can also use a QR Code:

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

Variance Inflation Factors (Multicollinearity)
> vif `Solids,` `Osmo,` t 15.466179 15.411955 1.014185

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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Figure 10

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ; par4 = 0 ; par5 = 0 ; par6 = 12 ;

Parameters (R input):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ; par4 = 0 ; par5 = 0 ; par6 = 12 ;

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

library(lattice)
library(lmtest)
library(car)
library(MASS)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
mywarning <- ''
par6 <- as.numeric(par6)
if(is.na(par6)) {
par6 <- 12
mywarning = 'Warning: you did not specify the seasonality. The seasonal period was set to s = 12.'
}
par1 <- as.numeric(par1)
if(is.na(par1)) {
par1 <- 1
mywarning = 'Warning: you did not specify the column number of the endogenous series! The first column was selected by default.'
}
if (par4=='') par4 <- 0
par4 <- as.numeric(par4)
if (!is.numeric(par4)) par4 <- 0
if (par5=='') par5 <- 0
par5 <- as.numeric(par5)
if (!is.numeric(par5)) par5 <- 0
x <- na.omit(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'){
(n <- n -1)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'Seasonal Differences (s)'){
(n <- n - par6)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-Bs)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+par6,j] - x[i,j]
}
}
x <- x2
}
if (par3 == 'First and Seasonal Differences (s)'){
(n <- n -1)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
(n <- n - par6)
x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-Bs)',colnames(x),sep='')))
for (i in 1:n) {
for (j in 1:k) {
x2[i,j] <- x[i+par6,j] - x[i,j]
}
}
x <- x2
}
if(par4 > 0) {
x2 <- array(0, dim=c(n-par4,par4), dimnames=list(1:(n-par4), paste(colnames(x)[par1],'(t-',1:par4,')',sep='')))
for (i in 1:(n-par4)) {
for (j in 1:par4) {
x2[i,j] <- x[i+par4-j,par1]
}
}
x <- cbind(x[(par4+1):n,], x2)
n <- n - par4
}
if(par5 > 0) {
x2 <- array(0, dim=c(n-par5*par6,par5), dimnames=list(1:(n-par5*par6), paste(colnames(x)[par1],'(t-',1:par5,'s)',sep='')))
for (i in 1:(n-par5*par6)) {
for (j in 1:par5) {
x2[i,j] <- x[i+par5*par6-j*par6,par1]
}
}
x <- cbind(x[(par5*par6+1):n,], x2)
n <- n - par5*par6
}
if (par2 == 'Include Seasonal Dummies'){
x2 <- array(0, dim=c(n,par6-1), dimnames=list(1:n, paste('M', seq(1:(par6-1)), sep ='')))
for (i in 1:(par6-1)){
x2[seq(i,n,par6),i] <- 1
}
x <- cbind(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[n,]))
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
print(x)
(k <- length(x[n,]))
head(x)
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
sresid <- studres(mylm)
hist(sresid, freq=FALSE, main='Distribution of Studentized Residuals')
xfit<-seq(min(sresid),max(sresid),length=40)
yfit<-dnorm(xfit)
lines(xfit, yfit)
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqPlot(mylm, main='QQ Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
print(z)
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$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$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), sep=' ')
if (rownames(mysum$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.row.start(a)
a<-table.element(a, mywarning)
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,'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$coefficients)[i],header=TRUE)
a<-table.element(a,formatC(signif(mysum$coefficients[i,1],5),format='g',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,2],5),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,3],4),format='e',flag='+'))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4],4),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$coefficients[i,4]/2,4),format='g',flag=' '))
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,formatC(signif(sqrt(mysum$r.squared),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a,formatC(signif(mysum$adj.r.squared,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a,formatC(signif(mysum$fstatistic[1],6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[2],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[3],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a,formatC(signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a,formatC(signif(mysum$sigma,6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a,formatC(signif(sum(myerror*myerror),6),format='g',flag=' '))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
myr <- as.numeric(mysum$resid)
myr
a <-table.start()
a <- table.row.start(a)
a <- table.element(a,'Menu of Residual Diagnostics',2,TRUE)
a <- table.row.end(a)
a <- table.row.start(a)
a <- table.element(a,'Description',1,TRUE)
a <- table.element(a,'Link',1,TRUE)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Histogram',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_histogram.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_centraltendency.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'QQ Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_fitdistrnorm.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Kernel Density Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_density.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Skewness/Kurtosis Test',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_skewness_kurtosis.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Skewness-Kurtosis Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_skewness_kurtosis_plot.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Harrell-Davis Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_harrell_davis.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Bootstrap Plot -- Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_bootstrapplot1.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Blocked Bootstrap Plot -- Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_bootstrapplot.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'(Partial) Autocorrelation Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_autocorrelation.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Spectral Analysis',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_spectrum.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Tukey lambda PPCC Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_tukeylambda.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Box-Cox Normality Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_boxcoxnorm.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <- table.element(a,'Summary Statistics',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_summary1.wasp?convertgetintopost=1&data=',paste(as.character(mysum$resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable7.tab')
if(n < 200) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,formatC(signif(x[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(x[i]-mysum$resid[i],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(mysum$resid[i],6),format='g',flag=' '))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,1],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,2],6),format='g',flag=' '))
a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,3],6),format='g',flag=' '))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,signif(numsignificant1,6))
a<-table.element(a,formatC(signif(numsignificant1/numgqtests,6),format='g',flag=' '))
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,signif(numsignificant5,6))
a<-table.element(a,signif(numsignificant5/numgqtests,6))
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,signif(numsignificant10,6))
a<-table.element(a,signif(numsignificant10/numgqtests,6))
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of fitted values',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_fitted <- resettest(mylm,power=2:3,type='fitted')
a<-table.element(a,paste('',RC.texteval('reset_test_fitted'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of regressors',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_regressors <- resettest(mylm,power=2:3,type='regressor')
a<-table.element(a,paste('',RC.texteval('reset_test_regressors'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Ramsey RESET F-Test for powers (2 and 3) of principal components',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
reset_test_principal_components <- resettest(mylm,power=2:3,type='princomp')
a<-table.element(a,paste('',RC.texteval('reset_test_principal_components'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable8.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variance Inflation Factors (Multicollinearity)',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
vif <- vif(mylm)
a<-table.element(a,paste('',RC.texteval('vif'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable9.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code