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Workshop 7

*The author of this computation has been verified*
R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Tue, 21 Dec 2010 13:03:29 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07.htm/, Retrieved Tue, 21 Dec 2010 14:04:04 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
162556 807 213118 6282154 29790 444 81767 4321023 87550 412 153198 4111912 84738 428 -26007 223193 54660 315 126942 1491348 42634 168 157214 1629616 40949 263 129352 1398893 45187 267 234817 1926517 37704 228 60448 983660 16275 129 47818 1443586 25830 104 245546 1073089 12679 122 48020 984885 18014 393 -1710 1405225 43556 190 32648 227132 24811 280 95350 929118 6575 63 151352 1071292 7123 102 288170 638830 21950 265 114337 856956 37597 234 37884 992426 17821 277 122844 444477 12988 73 82340 857217 22330 67 79801 711969 13326 103 165548 702380 16189 290 116384 358589 7146 83 134028 297978 15824 56 63838 585715 27664 236 74996 657954 11920 73 31080 209458 8568 34 32168 786690 14416 139 49857 439798 3369 26 87161 688779 11819 70 106113 574339 6984 40 80570 741409 4519 42 102129 597793 2220 12 301670 644190 18562 211 102313 377934 10327 74 88577 640273 5336 80 112477 697458 2365 83 191778 550608 4069 131 79804 207393 8636 203 128294 301607 13718 56 96448 345783 4525 89 93 etc...
 
Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time24 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Wealth[t] = + 164987.400007445 + 22.0149248853323Costs[t] + 1009.42045030004Orders[t] + 1.56844194978589Dividends[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)164987.40000744530631.9488125.386100
Costs22.01492488533232.15473710.21700
Orders1009.42045030004349.6915332.88660.0040920.002046
Dividends1.568441949785890.4114543.8120.0001587.9e-05


Multiple Linear Regression - Regression Statistics
Multiple R0.809711850869305
R-squared0.655633281438196
Adjusted R-squared0.653213843134483
F-TEST (value)270.985740959813
F-TEST (DF numerator)3
F-TEST (DF denominator)427
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation253521.605610268
Sum Squared Residuals27444658326286


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162821544892511.044514111389642.95548589
243210231397241.485182812923781.51481719
341119122748557.469065191363354.53093481
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514913481885391.79407393-394043.794073932
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713988931534835.24065453-135942.240654525
819265171797587.90435393128929.095646071
99836601319995.16953308-336335.169533075
101443586728495.297759793715090.702240207
1110730891223737.28362890-150648.283628901
12984885642580.509993896342304.490006104
131405225955584.458125602449640.541874398
142271321366865.84664659-1139733.84664659
159291181143388.36733352-214270.367333516
161071292610715.845481399460576.154518601
17638830876738.512566066-237908.512566066
188569561095042.36778266-238086.367782665
199924261288305.77111718-295879.771117177
204444771029598.52400156-585121.524001557
21857217653750.447435412203466.552564588
22711969849375.078901879-137406.078901879
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25297978616303.088258834-318325.088258834
26585715670005.313800176-84290.3138001755
276579541129858.38077223-471904.380772226
28209458549840.173311854-340382.173311854
29786690438385.212375886348304.787624114
30439798700861.810036575-261063.810036575
31688779402107.582439218286671.417560782
32574339662273.309365818-87934.3093658184
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198315380260223.19519844555156.8048015549
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330315380260223.19519844555156.8048015549
331315380260223.19519844555156.8048015549
332315380260223.19519844555156.8048015549
333315380260223.19519844555156.8048015549
334313729265839.4710837647889.5289162397
335315388261265.60966727954122.3903327209
336315371271173.56341364044197.4365863604
337296139299313.731407372-3174.73140737241
338315380260223.19519844555156.8048015549
339313880262081.04947892651798.9505210738
340317698271522.78154962346175.2184503768
341295580282556.20371225513023.7962877450
342315380260223.19519844555156.8048015549
343315380260223.19519844555156.8048015549
344315380260223.19519844555156.8048015549
345308256287016.92940613721239.0705938630
346315380260223.19519844555156.8048015549
347303677263358.58860714340318.4113928571
348315380260223.19519844555156.8048015549
349315380260223.19519844555156.8048015549
350319369305431.20489355013937.7951064497
351318690266791.87929612351898.1207038767
352314049269243.68439137944805.3156086211
353325699281475.66341562644223.3365843735
354314210266314.18493072747895.8150692729
355315380260223.19519844555156.8048015549
356315380260223.19519844555156.8048015549
357322378315006.2349571397371.76504286072
358315380260223.19519844555156.8048015549
359315380260223.19519844555156.8048015549
360315380260223.19519844555156.8048015549
361315398264286.0288084351111.9711915698
362315380260223.19519844555156.8048015549
363315380260223.19519844555156.8048015549
364308336328679.509295498-20343.5092954984
365316386271568.90621498844817.0937850123
366315380260223.19519844555156.8048015549
367315380260223.19519844555156.8048015549
368315380260223.19519844555156.8048015549
369315380260223.19519844555156.8048015549
370315553272088.39197554843464.6080244521
371315380260223.19519844555156.8048015549
372323361275679.05770832547681.9422916746
373336639297262.39590790639376.604092094
374307424273512.66547351533911.3345264849
375315380260223.19519844555156.8048015549
376315380260223.19519844555156.8048015549
377295370266866.76272694328503.2372730566
378322340280206.76024220342133.2397577971
379319864319014.4135478849.586452199757
380315380260223.19519844555156.8048015549
381315380260223.19519844555156.8048015549
382317291310000.27600077290.72399930035
383280398256744.07517244123653.9248275591
384315380260223.19519844555156.8048015549
385317330277158.91980367840171.0801963224
386238125355402.379069021-117277.379069021
387327071264474.43168450162596.5683154994
388309038283305.76547485725732.2345251433
389314210264331.49283325849878.5071667419
390307930277534.63006271430395.3699372863
391322327282178.52436099640148.4756390037
392292136273998.45757869418137.5424213064
393263276282352.583727973-19076.5837279729
394367655293070.43968209474584.5603179058
395283910380626.417633505-96716.4176335046
396283587277119.9940120876467.00598791306
397243650382310.705186568-138660.705186568
398438493628037.225695208-189544.225695208
399296261283875.62575671212385.3742432883
400230621286116.218163418-55495.218163418
401304252301815.3365558572436.66344414331
402333505290887.37175561242617.6282443884
403296919277331.12082201119587.8791779890
404278990328553.022498365-49563.0224983647
405276898285889.942804402-8991.94280440196
406327007312992.10137337214014.8986266275
407317046296424.18810972720621.8118902731
408304555291301.49022352213253.5097764776
409298096275186.25567143522909.7443285651
410231861293758.064471114-61897.0644711136
411309422360785.872738027-51363.8727380273
412286963448725.752721732-161762.752721732
413269753295657.171890200-25904.1718902004
414448243388152.14366988960090.8563301112
415165404342925.340392579-177521.340392579
416204325303515.442312156-99190.4423121564
417407159315172.24452094291986.7554790585
418290476307853.155600713-17377.1556007128
419275311325718.038995901-50407.0389959008
420246541283940.379136836-37399.3791368363
421253468297728.134203149-44260.1342031488
422240897416294.025939821-175397.025939821
423-83265464603.056546323-547868.056546323
424-42143416411.322871671-458554.322871671
425272713321554.815091326-48841.8150913255
426215362465379.339600957-250017.339600957
42742754354608.700890617-311854.700890617
4283062751442227.08697415-1135952.08697415
429253537525677.758883616-272140.758883616
430372631708677.098877589-336046.098877589
431-7170675306.518688715-682476.518688715


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
712.43022520973283e-321.21511260486642e-32
818.73733347743257e-534.36866673871628e-53
912.60546020029725e-531.30273010014862e-53
1013.34347207775228e-751.67173603887614e-75
1113.78798325115966e-781.89399162557983e-78
1218.07044694451853e-844.03522347225926e-84
1313.22847771748853e-1051.61423885874427e-105
1412.61574216043962e-1071.30787108021981e-107
1518.42936411717439e-1164.21468205858719e-116
1612.05842398553173e-1231.02921199276587e-123
1711.76971596965708e-1338.8485798482854e-134
1811.34926693165129e-1396.74633465825644e-140
1911.6745544212806e-1448.372772106403e-145
2019.98050519024578e-1534.99025259512289e-153
2114.71453542909078e-1612.35726771454539e-161
2212.52269471976415e-1641.26134735988208e-164
2317.25435685470663e-1653.62717842735331e-165
2414.52380215170928e-1712.26190107585464e-171
2511.14818218549676e-1705.74091092748381e-171
2617.16104855043848e-1733.58052427521924e-173
2716.18797989256445e-1763.09398994628222e-176
2813.0890389684332e-1751.5445194842166e-175
2914.70567628395924e-1892.35283814197962e-189
3014.32802714575672e-1892.16401357287836e-189
3116.44123267206032e-1953.22061633603016e-195
3212.90418928668736e-1961.45209464334368e-196
3311.15266214761111e-2055.76331073805555e-206
3414.25020727727010e-2082.12510363863505e-208
3512.16546994692133e-2071.08273497346067e-207
3611.98338505143122e-2089.9169252571561e-209
3714.71510888091354e-2142.35755444045677e-214
3816.24283294989913e-2203.12141647494956e-220
3914.57711659949014e-2192.28855829974507e-219
4011.14345326939764e-2195.7172663469882e-220
4113.04307959762271e-2211.52153979881136e-221
4211.87423154151376e-2209.37115770756879e-221
4318.04893300920767e-2214.02446650460383e-221
4419.4019516982616e-2204.7009758491308e-220
4512.08760437889193e-2191.04380218944596e-219
4611.80737315160304e-2189.03686575801522e-219
4714.58286743457220e-2192.29143371728610e-219
4812.17289291785516e-2181.08644645892758e-218
4918.20437773510417e-2184.10218886755209e-218
5014.34100735568093e-2182.17050367784047e-218
5111.57393437103576e-2187.86967185517878e-219
5214.48245818669914e-2182.24122909334957e-218
5312.72974207842303e-2171.36487103921152e-217
5418.42052439169061e-2174.21026219584531e-217
5515.04889546485457e-2202.52444773242729e-220
5611.09777924650147e-2195.48889623250734e-220
5713.51478100408822e-2331.75739050204411e-233
5811.41503287593825e-2337.07516437969125e-234
5911.30034476741109e-2326.50172383705547e-233
6013.36346203475823e-2321.68173101737912e-232
6116.71022232118275e-2343.35511116059138e-234
6211.9703036016253e-2359.8515180081265e-236
6315.44604188610495e-2352.72302094305247e-235
6413.00096299274550e-2341.50048149637275e-234
6511.66961946274451e-2338.34809731372254e-234
6618.47187222743778e-2344.23593611371889e-234
6712.27178122646208e-2331.13589061323104e-233
6812.14068416244285e-2321.07034208122142e-232
6911.21350681274176e-2316.0675340637088e-232
7016.70100889953967e-2313.35050444976984e-231
7114.7189520411566e-2302.3594760205783e-230
7213.81374825903096e-2311.90687412951548e-231
7311.30941126528660e-2306.54705632643298e-231
7411.12306096153791e-2295.61530480768953e-230
7511.34855687779967e-2286.74278438899833e-229
7613.16144755490702e-2281.58072377745351e-228
7712.8521397169576e-2271.4260698584788e-227
7813.83406414499295e-2271.91703207249647e-227
7914.0326256918642e-2262.0163128459321e-226
8011.52430675455486e-2257.62153377277429e-226
8119.06839340449978e-2254.53419670224989e-225
8211.496333923466e-2247.48166961733e-225
8311.45843733131932e-2247.2921866565966e-225
8418.17352397920766e-2244.08676198960383e-224
8517.93979376684064e-2233.96989688342032e-223
8612.12220471639793e-2221.06110235819896e-222
8711.69309344872848e-2228.46546724364239e-223
8811.26637768190295e-2216.33188840951477e-222
8912.73690518068548e-2211.36845259034274e-221
9012.66262861639386e-2201.33131430819693e-220
9112.42051042646134e-2191.21025521323067e-219
9211.57694321068093e-2187.88471605340465e-219
9315.30707103448199e-2202.65353551724099e-220
9415.40043053086401e-2192.70021526543201e-219
9511.92337418061487e-2199.61687090307434e-220
9611.70725894554827e-2198.53629472774137e-220
9711.53280711549003e-2187.66403557745015e-219
9811.50576016872407e-2177.52880084362034e-218
9911.31767745842634e-2166.58838729213171e-217
10011.29552879995131e-2156.47764399975653e-216
10111.16998803188273e-2145.84994015941363e-215
10219.19038775043486e-2164.59519387521743e-216
10318.43138752814876e-2164.21569376407438e-216
10411.40360127379688e-2167.0180063689844e-217
10516.19138362331527e-2163.09569181165763e-216
10612.18747685119767e-2151.09373842559883e-215
10711.34598065916986e-2176.72990329584929e-218
10815.64811306151101e-2192.82405653075550e-219
10914.29809635084515e-2182.14904817542258e-218
11018.61883978201858e-2184.30941989100929e-218
11116.13343835040571e-2183.06671917520286e-218
11213.81010312870246e-2181.90505156435123e-218
11312.94605137953223e-2171.47302568976612e-217
11412.38717378362691e-2161.19358689181345e-216
11511.58419038722228e-2167.92095193611141e-217
11616.36420689503012e-2163.18210344751506e-216
11714.58479824946933e-2152.29239912473467e-215
11813.68536454608859e-2151.84268227304430e-215
11913.97777483039911e-2161.98888741519955e-216
12014.08740199340879e-2152.04370099670440e-215
12111.9751493276695e-2149.8757466383475e-215
12211.83253188917138e-2139.16265944585691e-214
12311.58916512356762e-2127.94582561783808e-213
12412.19785250285731e-2121.09892625142866e-212
12516.31575652032539e-2123.15787826016270e-212
12612.06231448635344e-2121.03115724317672e-212
12711.9257506391686e-2119.628753195843e-212
12811.9017495524042e-2109.508747762021e-211
12911.81825394649581e-2099.09126973247907e-210
13011.70949377524708e-2088.54746887623539e-209
13111.6683848021569e-2078.3419240107845e-208
13211.43497220606267e-2077.17486103031337e-208
13311.37297126098868e-2066.8648563049434e-207
13411.42286336139732e-2057.11431680698658e-206
13511.40727301278384e-2047.03636506391919e-205
13611.36331860206633e-2036.81659301033167e-204
13711.326767266966e-2026.63383633483e-203
13811.27420334273321e-2016.37101671366604e-202
13911.21843441120445e-2006.09217205602223e-201
14011.16263545684572e-1995.8131772842286e-200
14119.62111131797058e-1994.81055565898529e-199
14219.1801544985271e-1984.59007724926355e-198
14319.39831335421464e-1974.69915667710732e-197
14419.06428740153232e-1964.53214370076616e-196
14518.2958395643033e-1954.14791978215165e-195
14617.6065771008335e-1943.80328855041675e-194
14717.21228021659388e-1933.60614010829694e-193
14816.99539491220894e-1923.49769745610447e-192
14916.02248437603147e-1913.01124218801574e-191
15015.69280693583799e-1902.84640346791900e-190
15115.54245196397471e-1892.77122598198736e-189
15215.72113514034256e-1882.86056757017128e-188
15315.43377526245118e-1872.71688763122559e-187
15415.33120448722048e-1862.66560224361024e-186
15515.01212458925759e-1852.50606229462879e-185
15614.66351173976158e-1842.33175586988079e-184
15714.3305084949549e-1832.16525424747745e-183
15814.0665333336983e-1822.03326666684915e-182
15912.84408814169277e-1811.42204407084638e-181
16012.62528255502901e-1801.31264127751451e-180
16112.41762158222101e-1791.20881079111051e-179
16212.22098238254557e-1781.11049119127278e-178
16312.03522933957284e-1771.01761466978642e-177
16411.94369393567428e-1769.7184696783714e-177
16511.81307157505518e-1759.06535787527588e-176
16611.65306822700513e-1748.26534113502563e-175
16711.49638475819334e-1737.48192379096669e-174
16811.85432014574590e-1749.27160072872949e-175
16913.31027066911089e-1741.65513533455545e-174
17013.03296625819370e-1731.51648312909685e-173
17112.7708092216518e-1721.3854046108259e-172
17212.57888081638418e-1711.28944040819209e-171
17312.34156335014723e-1701.17078167507362e-170
17412.19785374018918e-1691.09892687009459e-169
17511.98256528344332e-1689.9128264172166e-169
17611.80835131781751e-1679.04175658908754e-168
17711.6988044754189e-1668.4940223770945e-167
17811.50777820229341e-1657.53889101146705e-166
17911.34052281753526e-1646.70261408767631e-165
18011.18795437675988e-1635.9397718837994e-164
18117.92351997940173e-1633.96175998970087e-163
18217.26115314314167e-1623.63057657157083e-162
18314.23234223868437e-1612.11617111934218e-161
18412.5723834094568e-1601.2861917047284e-160
18512.29646112744504e-1591.14823056372252e-159
18611.53310016667578e-1587.6655008333789e-159
18715.73439830092106e-1582.86719915046053e-158
18815.10012552089193e-1572.55006276044596e-157
18913.60527286898220e-1561.80263643449110e-156
19013.10590454990637e-1551.55295227495318e-155
19112.54314398317337e-1541.27157199158669e-154
19212.17544197713855e-1531.08772098856927e-153
19311.88594436763019e-1529.42972183815094e-153
19411.60147855489609e-1518.00739277448044e-152
19511.36069659758142e-1506.80348298790711e-151
19611.14705043074385e-1495.73525215371923e-150
19718.7985433808717e-1494.39927169043585e-149
19817.36010274556775e-1483.68005137278388e-148
19916.13425808801677e-1473.06712904400839e-147
20016.3524736327185e-1473.17623681635925e-147
20115.30737499355462e-1462.65368749677731e-146
20214.41776269893376e-1452.20888134946688e-145
20313.66354014241181e-1441.83177007120590e-144
20412.81196377065727e-1431.40598188532863e-143
20511.23668290642226e-1426.18341453211129e-143
20611.0289278809081e-1415.1446394045405e-142
20718.55982606203319e-1414.27991303101659e-141
20816.98878371791771e-1403.49439185895885e-140
20911.00620889542808e-1395.0310444771404e-140
21018.41272549168211e-1394.20636274584105e-139
21116.83844131271989e-1383.41922065635995e-138
21215.53716199847052e-1372.76858099923526e-137
21313.35602260125124e-1361.67801130062562e-136
21412.52318490810158e-1351.26159245405079e-135
21512.07225754378122e-1341.03612877189061e-134
21611.65689119001014e-1338.2844559500507e-134
21711.32338757114953e-1326.61693785574767e-133
21811.02226711530868e-1315.1113355765434e-132
21918.07449780603153e-1314.03724890301576e-131
22013.87021334746511e-1301.93510667373255e-130
22113.04890471233232e-1291.52445235616616e-129
22212.37949879982525e-1281.18974939991262e-128
22311.85068291489320e-1279.25341457446602e-128
22411.45254283621804e-1267.26271418109022e-127
22511.12007749353353e-1255.60038746766764e-126
22618.73063322540537e-1254.36531661270268e-125
22716.72910294811436e-1243.36455147405718e-124
22815.12134405581832e-1232.56067202790916e-123
22913.9211461920643e-1221.96057309603215e-122
23012.96014775018453e-1211.48007387509227e-121
23112.14888318752560e-1201.07444159376280e-120
23211.48285726507031e-1197.41428632535153e-120
23311.10613117076554e-1185.53065585382768e-119
23418.42612351011243e-1184.21306175505621e-118
23516.23235066937287e-1173.11617533468644e-117
23614.58917261643344e-1162.29458630821672e-116
23713.36578253849687e-1151.68289126924843e-115
23812.44762183545692e-1141.22381091772846e-114
23911.77982879615463e-1138.89914398077317e-114
24011.28870468561488e-1126.4435234280744e-113
24119.29101767452707e-1124.64550883726353e-112
24216.76425752119729e-1113.38212876059864e-111
24314.83463964143644e-1102.41731982071822e-110
24413.40768101798146e-1091.70384050899073e-109
24512.47349127219291e-1081.23674563609646e-108
24611.74432820495454e-1078.72164102477269e-108
24711.22474129777052e-1066.12370648885262e-107
24818.78431239128977e-1064.39215619564489e-106
24916.11322779103564e-1053.05661389551782e-105
25014.23558279659203e-1042.11779139829602e-104
25112.90197697138871e-1031.45098848569435e-103
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4000.9999998391529543.21694091331679e-071.60847045665840e-07
4010.9999995906489868.18702027212498e-074.09351013606249e-07
4020.99999912028841.75942320073177e-068.79711600365884e-07
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4040.99999494207271.01158546014143e-055.05792730070716e-06
4050.9999878004372322.43991255357350e-051.21995627678675e-05
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4230.8019672484088660.3960655031822680.198032751591134
4240.8245659667899470.3508680664201060.175434033210053


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level4100.980861244019139NOK
5% type I error level4140.99043062200957NOK
10% type I error level4140.99043062200957NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/1004921292936583.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/1004921292936583.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/1ulcq1292936583.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/1ulcq1292936583.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/2mvcb1292936583.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/2mvcb1292936583.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/3mvcb1292936583.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/3mvcb1292936583.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/4mvcb1292936583.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/4mvcb1292936583.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/5f4bw1292936583.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/5f4bw1292936583.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/6f4bw1292936583.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/6f4bw1292936583.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/7qdsz1292936583.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/7qdsz1292936583.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/8qdsz1292936583.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/8qdsz1292936583.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/904921292936583.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t129293660513keraz6qozip07/904921292936583.ps (open in new window)


 
Parameters (Session):
par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
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))
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$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$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')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$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()
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$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$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$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)
a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
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,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
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,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
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,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
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,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
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')
}
 




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Software written by Ed van Stee & Patrick Wessa


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