Multiple Regression 1

*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: Mon, 28 Dec 2009 10:13:22 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm.htm/, Retrieved Mon, 28 Dec 2009 18:15:11 +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/2009/Dec/28/t1262020498oqt61qujoqlm3lm.htm/}, year = {2009}, } @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 = {2009}, 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:

Geen seasonal dummies Geen lineaire trend

Dataseries X:

» Textbox « » Textfile « » CSV «

4.6 11.7 4.5 11.4 4.4 11.2 4.4 11.1 4.3 10.8 4.1 10.4 3.9 10.1 3.7 9.8 3.6 9.7 3.9 10.3 4.2 10.9 4.2 10.8 4.1 10.6 4.1 10.4 4.1 10.3 4.1 10.2 4.1 10 4 9.7 3.9 9.4 3.8 9.2 3.8 9.1 4 9.6 4.4 10.2 4.6 10.2 4.6 10 4.6 9.9 4.7 9.9 4.8 9.9 4.8 9.7 4.7 9.5 4.7 9.4 4.7 9.3 4.6 9.3 5 9.9 5.4 10.5 5.5 10.6 5.6 10.6 5.6 10.5 5.8 10.6 6 10.8 6.1 10.8 6.1 10.7 6 10.6 6 10.6 6.1 10.8 6.5 11.4 7.1 12.2 7.4 12.4 7.4 12.4 7.5 12.3 7.6 12.4 7.8 12.5 7.8 12.5 7.7 12.4 7.6 12.3 7.5 12.2 7.3 12.1 7.6 12.6 8 13.2 8 13.4 7.9 13.2 7.8 12.9 7.7 12.8 7.8 12.7 7.7 12.6 7.5 12.4 7.3 12.1 7.1 12 7 11.9 7.3 12.5 7.8 13.2 7.9 13.4 7.9 13.3 7.8 13 7.8 12.9 7.9 13 7.8 12.9 7.6 12.6 7.4 12.4 7.2 12.1 6.9 11.9 7.1 12.3 7.5 13 7.6 13 7.4 12.6 7.3 12.2 7.2 12.1 7.3 12 7.2 11.8 7.1 11.6 7 11.4 6.9 11.2 6.8 11.2 7.2 11.8 7.6 12.5 7.7 12.6 7.6 12.4 7.5 12.1 7.5 12 7.6 12 7.6 11.9 7.6 11.8 7.5 11.5 7.3 11.3 7.2 11.2 7.4 11.6 8 12.2 8.2 12.2 8 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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 8 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 4.74758616822106 + 0.191586205017679X[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 4.74758616822106 0.449235 10.5682 0 0 X 0.191586205017679 0.04426 4.3286 2.2e-05 1.1e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.270150291019032 R-squared 0.0729811797376678 Adjusted R-squared 0.069086142677742 F-TEST (value) 18.7369667129839 F-TEST (DF numerator) 1 F-TEST (DF denominator) 238 p-value 2.21094861694304e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.17651453917370 Sum Squared Residuals 329.436377691129 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4.6 6.98914476692795 -2.38914476692795 2 4.5 6.9316689054226 -2.43166890542260 3 4.4 6.89335166441906 -2.49335166441906 4 4.4 6.8741930439173 -2.47419304391730 5 4.3 6.81671718241199 -2.51671718241199 6 4.1 6.74008270040492 -2.64008270040492 7 3.9 6.68260683889962 -2.78260683889962 8 3.7 6.62513097739431 -2.92513097739431 9 3.6 6.60597235689255 -3.00597235689255 10 3.9 6.72092407990315 -2.82092407990315 11 4.2 6.83587580291376 -2.63587580291376 12 4.2 6.81671718241199 -2.61671718241199 13 4.1 6.77839994140846 -2.67839994140846 14 4.1 6.74008270040492 -2.64008270040492 15 4.1 6.72092407990315 -2.62092407990315 16 4.1 6.70176545940139 -2.60176545940139 17 4.1 6.66344821839785 -2.56344821839785 18 4 6.60597235689255 -2.60597235689255 19 3.9 6.54849649538724 -2.64849649538724 20 3.8 6.5101792543837 -2.71017925438371 21 3.8 6.49102063388194 -2.69102063388194 22 4 6.58681373639078 -2.58681373639078 23 4.4 6.70176545940139 -2.30176545940139 24 4.6 6.70176545940139 -2.10176545940139 25 4.6 6.66344821839785 -2.06344821839785 26 4.6 6.64428959789608 -2.04428959789608 27 4.7 6.64428959789608 -1.94428959789608 28 4.8 6.64428959789608 -1.84428959789608 29 4.8 6.60597235689255 -1.80597235689255 30 4.7 6.56765511588901 -1.86765511588901 31 4.7 6.54849649538724 -1.84849649538724 32 4.7 6.52933787488547 -1.82933787488547 33 4.6 6.52933787488547 -1.92933787488548 34 5 6.64428959789608 -1.64428959789608 35 5.4 6.75924132090669 -1.35924132090669 36 5.5 6.77839994140846 -1.27839994140846 37 5.6 6.77839994140846 -1.17839994140846 38 5.6 6.75924132090669 -1.15924132090669 39 5.8 6.77839994140846 -0.978399941408458 40 6 6.81671718241199 -0.816717182411993 41 6.1 6.81671718241199 -0.716717182411994 42 6.1 6.79755856191023 -0.697558561910226 43 6 6.77839994140846 -0.778399941408457 44 6 6.77839994140846 -0.778399941408457 45 6.1 6.81671718241199 -0.716717182411994 46 6.5 6.9316689054226 -0.431668905422601 47 7.1 7.08493786943674 0.0150621305632556 48 7.4 7.12325511044028 0.276744889559720 49 7.4 7.12325511044028 0.276744889559720 50 7.5 7.10409648993851 0.395903510061488 51 7.6 7.12325511044028 0.47674488955972 52 7.8 7.14241373094205 0.657586269057952 53 7.8 7.14241373094205 0.657586269057952 54 7.7 7.12325511044028 0.57674488955972 55 7.6 7.10409648993851 0.495903510061488 56 7.5 7.08493786943674 0.415062130563256 57 7.3 7.06577924893498 0.234220751065024 58 7.6 7.16157235144382 0.438427648556184 59 8 7.27652407445442 0.723475925545577 60 8 7.31484131545796 0.685158684542041 61 7.9 7.27652407445442 0.623475925545577 62 7.8 7.21904821294912 0.58095178705088 63 7.7 7.19988959244735 0.500110407552648 64 7.8 7.18073097194558 0.619269028054416 65 7.7 7.16157235144382 0.538427648556185 66 7.5 7.12325511044028 0.37674488955972 67 7.3 7.06577924893498 0.234220751065024 68 7.1 7.04662062843321 0.0533793715667914 69 7 7.02746200793144 -0.0274620079314404 70 7.3 7.14241373094205 0.157586269057952 71 7.8 7.27652407445442 0.523475925545577 72 7.9 7.31484131545796 0.585158684542041 73 7.9 7.2956826949562 0.604317305043809 74 7.8 7.23820683345089 0.561793166549112 75 7.8 7.21904821294912 0.58095178705088 76 7.9 7.23820683345089 0.661793166549113 77 7.8 7.21904821294912 0.58095178705088 78 7.6 7.16157235144382 0.438427648556184 79 7.4 7.12325511044028 0.276744889559720 80 7.2 7.06577924893498 0.134220751065024 81 6.9 7.02746200793144 -0.12746200793144 82 7.1 7.10409648993851 -0.00409648993851244 83 7.5 7.23820683345089 0.261793166549113 84 7.6 7.23820683345089 0.361793166549112 85 7.4 7.16157235144382 0.238427648556185 86 7.3 7.08493786943674 0.215062130563256 87 7.2 7.06577924893498 0.134220751065024 88 7.3 7.04662062843321 0.253379371566792 89 7.2 7.00830338742967 0.191696612570328 90 7.1 6.96998614642614 0.130013853573863 91 7 6.9316689054226 0.0683310945773992 92 6.9 6.89335166441906 0.00664833558093553 93 6.8 6.89335166441906 -0.093351664419065 94 7.2 7.00830338742967 0.191696612570328 95 7.6 7.14241373094205 0.457586269057952 96 7.7 7.16157235144382 0.538427648556185 97 7.6 7.12325511044028 0.47674488955972 98 7.5 7.06577924893498 0.434220751065024 99 7.5 7.04662062843321 0.453379371566792 100 7.6 7.04662062843321 0.553379371566791 101 7.6 7.02746200793144 0.572537992068559 102 7.6 7.00830338742967 0.591696612570327 103 7.5 6.95082752592437 0.549172474075631 104 7.3 6.91251028492083 0.387489715079167 105 7.2 6.89335166441906 0.306648335580935 106 7.4 6.96998614642614 0.430013853573864 107 8 7.08493786943674 0.915062130563256 108 8.2 7.08493786943674 1.11506213056326 109 8 6.9891447669279 1.01085523307210 110 7.7 6.89335166441906 0.806648335580935 111 7.7 6.85503442341553 0.844965576584471 112 7.8 6.83587580291376 0.964124197086239 113 7.8 6.81671718241199 0.983282817588007 114 7.7 6.75924132090669 0.94075867909331 115 7.5 6.70176545940139 0.798234540598614 116 7.3 6.66344821839785 0.63655178160215 117 7.1 6.64428959789608 0.455710402103917 118 7.1 6.72092407990315 0.379075920096846 119 7.2 6.79755856191023 0.402441438089775 120 6.8 6.74008270040492 0.059917299595078 121 6.6 6.68260683889962 -0.0826068388996182 122 6.4 6.60597235689255 -0.205972356892546 123 6.4 6.54849649538724 -0.148496495387242 124 6.5 6.4527033928784 0.0472966071215969 125 6.3 6.35691029036956 -0.0569102903695637 126 5.9 6.29943442886426 -0.399434428864259 127 5.5 6.3377516698678 -0.837751669867796 128 5.2 6.29943442886426 -1.09943442886426 129 4.9 6.28027580836249 -1.38027580836249 130 5.4 6.41438615187487 -1.01438615187487 131 5.8 6.5101792543837 -0.710179254383707 132 5.7 6.47186201338017 -0.771862013380171 133 5.6 6.4527033928784 -0.852703392878403 134 5.5 6.37606891087133 -0.876068910871331 135 5.4 6.29943442886426 -0.89943442886426 136 5.4 6.18448270585365 -0.784482705853652 137 5.4 6.10784822384658 -0.70784822384658 138 5.5 6.06953098284304 -0.569530982843045 139 5.8 6.10784822384658 -0.307848223846581 140 5.7 6.08868960334481 -0.388689603344813 141 5.4 6.03121374183951 -0.631213741839509 142 5.6 6.08868960334481 -0.488689603344813 143 5.8 6.14616546485012 -0.346165464850117 144 6.2 6.22279994685719 -0.0227999468571879 145 6.8 6.35691029036956 0.443089709630436 146 6.7 6.35691029036956 0.343089709630437 147 6.7 6.43354477237664 0.266455227623365 148 6.4 6.49102063388194 -0.0910206338819384 149 6.3 6.47186201338017 -0.171862013380171 150 6.3 6.3952275313731 -0.0952275313730994 151 6.4 6.26111718786072 0.138882812139276 152 6.3 6.22279994685719 0.0772000531428117 153 6 6.24195856735896 -0.241958567358956 154 6.3 6.5101792543837 -0.210179254383707 155 6.3 6.54849649538724 -0.248496495387243 156 6.6 6.5101792543837 0.089820745616293 157 7.5 6.41438615187487 1.08561384812513 158 7.8 6.35691029036956 1.44308970963044 159 7.9 6.3952275313731 1.50477246862690 160 7.8 6.47186201338017 1.32813798661983 161 7.6 6.49102063388194 1.10897936611806 162 7.5 6.41438615187487 1.08561384812513 163 7.6 6.31859304936603 1.28140695063397 164 7.5 6.26111718786072 1.23888281213928 165 7.3 6.26111718786072 1.03888281213928 166 7.6 6.49102063388194 1.10897936611806 167 7.5 6.54849649538724 0.951503504612757 168 7.6 6.54849649538724 1.05150350461276 169 7.9 6.49102063388194 1.40897936611806 170 7.9 6.47186201338017 1.42813798661983 171 8.1 6.52933787488547 1.57066212511452 172 8.2 6.64428959789608 1.55571040210392 173 8 6.62513097739431 1.37486902260569 174 7.5 6.52933787488548 0.970662125114525 175 6.8 6.3377516698678 0.462248330132204 176 6.5 6.2802758083625 0.219724191637508 177 6.6 6.37606891087133 0.223931089128668 178 7.6 6.74008270040492 0.859917299595078 179 8 6.8741930439173 1.12580695608270 180 8.1 6.83587580291376 1.26412419708624 181 7.7 6.66344821839785 1.03655178160215 182 7.5 6.5101792543837 0.989820745616293 183 7.6 6.5101792543837 1.08982074561629 184 7.8 6.56765511588901 1.23234488411099 185 7.8 6.58681373639078 1.21318626360922 186 7.8 6.56765511588901 1.23234488411099 187 7.5 6.49102063388194 1.00897936611806 188 7.5 6.4527033928784 1.04729660712160 189 7.1 6.47186201338017 0.628137986619829 190 7.5 6.68260683889962 0.817393161100382 191 7.5 6.72092407990315 0.779075920096846 192 7.6 6.70176545940139 0.898234540598614 193 7.7 6.58681373639078 1.11318626360922 194 7.7 6.5101792543837 1.18982074561629 195 7.9 6.52933787488547 1.37066212511453 196 8.1 6.54849649538724 1.55150350461276 197 8.2 6.54849649538724 1.65150350461276 198 8.2 6.5101792543837 1.68982074561629 199 8.2 6.47186201338017 1.72813798661983 200 7.9 6.47186201338017 1.42813798661983 201 7.3 6.47186201338017 0.828137986619829 202 6.9 6.62513097739431 0.274869022605686 203 6.6 6.66344821839785 -0.0634482183978504 204 6.7 6.62513097739431 0.0748690226056858 205 6.9 6.52933787488548 0.370662125114526 206 7 6.47186201338017 0.528137986619829 207 7.1 6.47186201338017 0.628137986619829 208 7.2 6.49102063388194 0.708979366118061 209 7.1 6.49102063388194 0.608979366118061 210 6.9 6.49102063388194 0.408979366118062 211 7 6.5101792543837 0.489820745616293 212 6.8 6.43354477237664 0.366455227623365 213 6.4 6.3377516698678 0.0622483301322047 214 6.7 6.35691029036956 0.343089709630437 215 6.6 6.29943442886426 0.30056557113574 216 6.4 6.22279994685719 0.177200053142812 217 6.3 6.26111718786072 0.0388828121392759 218 6.2 6.26111718786072 -0.0611171878607238 219 6.5 6.2802758083625 0.219724191637508 220 6.8 6.26111718786072 0.538882812139276 221 6.8 6.20364132635542 0.59635867364458 222 6.4 6.10784822384658 0.29215177615342 223 6.1 6.05037236234128 0.0496276376587228 224 5.8 5.99289650083597 -0.192896500835973 225 6.1 6.06953098284304 0.0304690171569548 226 7.2 6.31859304936603 0.881406950633973 227 7.3 6.41438615187487 0.885613848125133 228 6.9 6.3377516698678 0.562248330132205 229 6.1 6.26111718786072 -0.161117187860724 230 5.8 6.18448270585365 -0.384482705853652 231 6.2 6.24195856735896 -0.0419585673589558 232 7.1 6.3377516698678 0.762248330132204 233 7.7 6.35691029036956 1.34308970963044 234 7.9 6.31859304936603 1.58140695063397 235 7.7 6.22279994685719 1.47720005314281 236 7.4 6.12700684434835 1.27299315565165 237 7.5 6.14616546485012 1.35383453514988 238 8 6.29943442886426 1.70056557113574 239 8.1 6.37606891087133 1.72393108912867 240 8 6.35691029036956 1.64308970963044 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 4.85145898654541e-06 9.70291797309082e-06 0.999995148541013 6 3.48039564654272e-07 6.96079129308545e-07 0.999999651960435 7 1.63848540333619e-07 3.27697080667239e-07 0.99999983615146 8 5.05539358383386e-08 1.01107871676677e-07 0.999999949446064 9 1.23580185254628e-08 2.47160370509257e-08 0.999999987641981 10 1.44159725291968e-09 2.88319450583936e-09 0.999999998558403 11 1.48891686491936e-10 2.97783372983871e-10 0.999999999851108 12 9.55062693232865e-12 1.91012538646573e-11 0.99999999999045 13 6.13352316095586e-13 1.22670463219117e-12 0.999999999999387 14 1.28763543521463e-13 2.57527087042927e-13 0.999999999999871 15 7.29335416051722e-14 1.45867083210344e-13 0.999999999999927 16 7.77525464859269e-14 1.55505092971854e-13 0.999999999999922 17 2.99487828540151e-13 5.98975657080302e-13 0.9999999999997 18 4.74392857637203e-13 9.48785715274406e-13 0.999999999999526 19 3.8174997778556e-13 7.6349995557112e-13 0.999999999999618 20 1.36582774422425e-13 2.73165548844851e-13 0.999999999999863 21 5.36194594198388e-14 1.07238918839678e-13 0.999999999999946 22 2.50258247769499e-14 5.00516495538998e-14 0.999999999999975 23 1.79757569489105e-13 3.59515138978209e-13 0.99999999999982 24 1.05525965944253e-11 2.11051931888506e-11 0.999999999989447 25 2.07651322489073e-10 4.15302644978146e-10 0.999999999792349 26 1.70986161124605e-09 3.41972322249210e-09 0.999999998290138 27 1.49236547277999e-08 2.98473094555998e-08 0.999999985076345 28 1.27057811394214e-07 2.54115622788427e-07 0.999999872942189 29 7.26354182488725e-07 1.45270836497745e-06 0.999999273645818 30 1.96044464260780e-06 3.92088928521561e-06 0.999998039555357 31 4.35294140602958e-06 8.70588281205917e-06 0.999995647058594 32 8.31146432922384e-06 1.66229286584477e-05 0.999991688535671 33 1.14544538081461e-05 2.29089076162921e-05 0.999988545546192 34 4.06874969466253e-05 8.13749938932506e-05 0.999959312503053 35 0.00039550463506285 0.0007910092701257 0.999604495364937 36 0.00252355109964719 0.00504710219929437 0.997476448900353 37 0.011501393427083 0.023002786854166 0.988498606572917 38 0.0344503855074459 0.0689007710148919 0.965549614492554 39 0.0952432041139023 0.190486408227805 0.904756795886098 40 0.215648868137384 0.431297736274768 0.784351131862616 41 0.381425601031058 0.762851202062116 0.618574398968942 42 0.54780835513932 0.90438328972136 0.45219164486068 43 0.675635668137974 0.648728663724052 0.324364331862026 44 0.774613077497713 0.450773845004574 0.225386922502287 45 0.845943463606756 0.308113072786488 0.154056536393244 46 0.895538495075172 0.208923009849657 0.104461504924828 47 0.923768499066974 0.152463001866053 0.0762315009330263 48 0.939769690986644 0.120460618026712 0.0602303090133561 49 0.94516524560689 0.109669508786221 0.0548347543931104 50 0.950925453430767 0.0981490931384651 0.0490745465692326 51 0.952548376295643 0.094903247408713 0.0474516237043565 52 0.953883667027468 0.0922326659450632 0.0461163329725316 53 0.952637403450912 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0.697723911365146 106 0.322143966082241 0.644287932164483 0.677856033917759 107 0.324321393181114 0.648642786362229 0.675678606818886 108 0.337331143325069 0.674662286650138 0.662668856674931 109 0.385884779781525 0.771769559563049 0.614115220218475 110 0.467597015120273 0.935194030240545 0.532402984879727 111 0.57237205697725 0.8552558860455 0.42762794302275 112 0.688082850568572 0.623834298862855 0.311917149431428 113 0.788888665739691 0.422222668520617 0.211111334260309 114 0.876814090046319 0.246371819907362 0.123185909953681 115 0.934910053683137 0.130179892633727 0.0650899463168633 116 0.966039961383897 0.0679200772322062 0.0339600386161031 117 0.98098820451692 0.0380235909661588 0.0190117954830794 118 0.986434311554944 0.0271313768901127 0.0135656884450563 119 0.98887529983702 0.0222494003259601 0.0111247001629801 120 0.991427218263984 0.0171455634720322 0.00857278173601609 121 0.993921169194458 0.0121576616110847 0.00607883080554237 122 0.99610933885003 0.0077813222999385 0.00389066114996925 123 0.99767980149651 0.00464039700698045 0.00232019850349022 124 0.998853425705816 0.00229314858836788 0.00114657429418394 125 0.999477435164346 0.00104512967130862 0.00052256483565431 126 0.999730665163686 0.00053866967262789 0.000269334836313945 127 0.99985401379887 0.000291972402258043 0.000145986201129022 128 0.999931908558316 0.000136182883368573 6.80914416842865e-05 129 0.99997688370928 4.62325814398680e-05 2.31162907199340e-05 130 0.999991283296703 1.74334065947834e-05 8.71670329739171e-06 131 0.999996332216847 7.33556630506664e-06 3.66778315253332e-06 132 0.99999862452236 2.75095528015152e-06 1.37547764007576e-06 133 0.999999578555323 8.42889353826396e-07 4.21444676913198e-07 134 0.999999869888571 2.60222857972436e-07 1.30111428986218e-07 135 0.99999995892569 8.21486219493483e-08 4.10743109746741e-08 136 0.999999983006066 3.39878675232325e-08 1.69939337616163e-08 137 0.99999999194469 1.61106209835774e-08 8.05531049178871e-09 138 0.999999995596544 8.80691286338756e-09 4.40345643169378e-09 139 0.999999997147374 5.70525243799244e-09 2.85262621899622e-09 140 0.999999998066959 3.86608267630544e-09 1.93304133815272e-09 141 0.999999998823708 2.35258327483562e-09 1.17629163741781e-09 142 0.999999999231379 1.53724296502941e-09 7.68621482514703e-10 143 0.999999999455527 1.08894628256925e-09 5.44473141284625e-10 144 0.999999999526165 9.47670492206882e-10 4.73835246103441e-10 145 0.9999999995244 9.51198432985463e-10 4.75599216492732e-10 146 0.999999999502533 9.94934885176215e-10 4.97467442588108e-10 147 0.999999999477072 1.04585560515901e-09 5.22927802579507e-10 148 0.999999999631398 7.37204521684145e-10 3.68602260842073e-10 149 0.99999999977391 4.52178107221255e-10 2.26089053610628e-10 150 0.999999999829853 3.40294116606390e-10 1.70147058303195e-10 151 0.999999999820553 3.5889452713117e-10 1.79447263565585e-10 152 0.999999999811976 3.76047256957822e-10 1.88023628478911e-10 153 0.999999999863786 2.72428757578708e-10 1.36214378789354e-10 154 0.99999999993759 1.24821873667375e-10 6.24109368336875e-11 155 0.999999999979116 4.17676494127058e-11 2.08838247063529e-11 156 0.999999999985068 2.98645949930518e-11 1.49322974965259e-11 157 0.999999999985453 2.90943295215688e-11 1.45471647607844e-11 158 0.999999999993229 1.35421601939122e-11 6.77108009695608e-12 159 0.99999999999684 6.3192845067191e-12 3.15964225335955e-12 160 0.999999999997278 5.44418499788714e-12 2.72209249894357e-12 161 0.999999999996593 6.81434482199582e-12 3.40717241099791e-12 162 0.999999999995932 8.13588725529895e-12 4.06794362764947e-12 163 0.999999999996964 6.07201150684352e-12 3.03600575342176e-12 164 0.99999999999778 4.44085399554497e-12 2.22042699777249e-12 165 0.99999999999757 4.8613468469324e-12 2.4306734234662e-12 166 0.99999999999652 6.95937835529344e-12 3.47968917764672e-12 167 0.99999999999414 1.17205245812212e-11 5.86026229061058e-12 168 0.999999999990535 1.89298603359029e-11 9.46493016795143e-12 169 0.999999999990749 1.85030565811905e-11 9.25152829059526e-12 170 0.999999999991514 1.69711694133020e-11 8.48558470665102e-12 171 0.999999999993362 1.32760092590090e-11 6.63800462950451e-12 172 0.999999999993163 1.36747152324452e-11 6.83735761622262e-12 173 0.99999999999087 1.82602060647168e-11 9.13010303235841e-12 174 0.999999999983421 3.31584817985632e-11 1.65792408992816e-11 175 0.99999999996851 6.29820707522728e-11 3.14910353761364e-11 176 0.99999999994645 1.07100058192745e-10 5.35500290963724e-11 177 0.999999999918108 1.63784030308862e-10 8.18920151544311e-11 178 0.999999999850486 2.99028926841644e-10 1.49514463420822e-10 179 0.99999999972317 5.53658412751391e-10 2.76829206375695e-10 180 0.999999999497908 1.00418449558308e-09 5.02092247791541e-10 181 0.999999999065728 1.86854427407547e-09 9.34272137037733e-10 182 0.99999999831466 3.37068187375101e-09 1.68534093687550e-09 183 0.999999997141136 5.71772701780412e-09 2.85886350890206e-09 184 0.999999995498722 9.0025570754488e-09 4.5012785377244e-09 185 0.999999992692264 1.46154711282727e-08 7.30773556413635e-09 186 0.999999988559697 2.28806060211859e-08 1.14403030105930e-08 187 0.99999997981187 4.03762594746546e-08 2.01881297373273e-08 188 0.999999966109152 6.77816968644544e-08 3.38908484322272e-08 189 0.999999936171432 1.27657136463078e-07 6.38285682315389e-08 190 0.999999882100976 2.3579804876025e-07 1.17899024380125e-07 191 0.99999979102393 4.17952139249108e-07 2.08976069624554e-07 192 0.99999961948699 7.61026020774062e-07 3.80513010387031e-07 193 0.999999340913545 1.31817291006464e-06 6.59086455032322e-07 194 0.999998967213771 2.06557245749459e-06 1.03278622874729e-06 195 0.99999862999159 2.74001681838286e-06 1.37000840919143e-06 196 0.9999985758491 2.84830180016836e-06 1.42415090008418e-06 197 0.999998823854164 2.35229167136789e-06 1.17614583568395e-06 198 0.999999222923194 1.55415361127086e-06 7.77076805635428e-07 199 0.99999960703576 7.85928482027645e-07 3.92964241013822e-07 200 0.99999965325541 6.93489179399218e-07 3.46744589699609e-07 201 0.999999339709295 1.32058140896539e-06 6.60290704482695e-07 202 0.999998775322956 2.44935408763152e-06 1.22467704381576e-06 203 0.999998657874706 2.68425058817684e-06 1.34212529408842e-06 204 0.99999847040832 3.05918335920213e-06 1.52959167960106e-06 205 0.99999743658719 5.1268256211709e-06 2.56341281058545e-06 206 0.999995091023976 9.81795204794252e-06 4.90897602397126e-06 207 0.999990376517023 1.92469659546143e-05 9.62348297730715e-06 208 0.999981188172578 3.76236548444568e-05 1.88118274222284e-05 209 0.999965342499405 6.93150011899551e-05 3.46575005949776e-05 210 0.999947604054967 0.000104791890065512 5.23959450327559e-05 211 0.99992517202762 0.000149655944758595 7.48279723792975e-05 212 0.999900744996152 0.000198510007695296 9.92550038476478e-05 213 0.999890637497578 0.000218725004843616 0.000109362502421808 214 0.99984737940094 0.000305241198118877 0.000152620599059438 215 0.999765131146089 0.000469737707822688 0.000234868853911344 216 0.999608745385022 0.000782509229956718 0.000391254614978359 217 0.999518129760926 0.000963740478148255 0.000481870239074128 218 0.99952039467974 0.000959210640519418 0.000479605320259709 219 0.999376213735844 0.00124757252831234 0.000623786264156168 220 0.998860864397493 0.00227827120501469 0.00113913560250734 221 0.997780316150172 0.00443936769965632 0.00221968384982816 222 0.99575217418922 0.00849565162155786 0.00424782581077893 223 0.99216998822003 0.0156600235599406 0.0078300117799703 224 0.98654876480237 0.0269024703952589 0.0134512351976294 225 0.978824490587287 0.0423510188254256 0.0211755094127128 226 0.964284103855097 0.0714317922898066 0.0357158961449033 227 0.94580668048935 0.108386639021298 0.0541933195106492 228 0.92800859397385 0.143982812052299 0.0719914060261494 229 0.950113046316774 0.099773907366452 0.049886953683226 230 0.984220237606974 0.0315595247860517 0.0157797623930258 231 0.9993843597864 0.00123128042720080 0.000615640213600401 232 0.999988425646396 2.31487072079172e-05 1.15743536039586e-05 233 0.999999040867836 1.91826432712840e-06 9.59132163564199e-07 234 0.999985781893246 2.84362135071819e-05 1.42181067535909e-05 235 0.999710108916896 0.000579782166207412 0.000289891083103706 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 138 0.597402597402597 NOK 5% type I error level 148 0.64069264069264 NOK 10% type I error level 156 0.675324675324675 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/10mxcc1262020392.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/10mxcc1262020392.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/1xbqn1262020392.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/1xbqn1262020392.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/2wx0h1262020392.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/2wx0h1262020392.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/3gnkq1262020392.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/3gnkq1262020392.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/496bw1262020392.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/496bw1262020392.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/53ryy1262020392.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/53ryy1262020392.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/6izev1262020392.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/6izev1262020392.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/7eilp1262020392.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/7eilp1262020392.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/8bo871262020392.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/8bo871262020392.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/93o6p1262020392.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t1262020498oqt61qujoqlm3lm/93o6p1262020392.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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

library(lattice) 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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