*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: Fri, 24 Dec 2010 15:58:02 +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/24/t12932061598f9ssu6fski7u25.htm/, Retrieved Fri, 24 Dec 2010 16:56:02 +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/24/t12932061598f9ssu6fski7u25.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 «

15 2 0 0 9 12 1 1 2 9 9 1 2 1 9 10 0 0 0 9 13 0 0 0 9 16 1 0 0 9 14 0 0 0 9 16 1 1 0 9 10 0 0 0 9 8 2 0 1 10 12 1 0 0 10 15 0 0 0 10 14 0 1 0 10 14 1 1 2 10 12 1 2 1 10 12 0 0 0 10 10 0 0 0 10 4 0 0 0 10 14 0 1 0 10 15 0 0 0 10 16 0 0 0 10 12 0 1 0 10 12 0 0 0 10 12 0 0 1 10 12 1 0 1 9 12 0 0 0 9 11 3 2 1 9 11 1 0 0 9 11 1 1 0 9 11 1 1 0 9 11 3 1 1 9 11 0 0 0 9 15 0 0 0 9 15 0 0 0 9 9 0 0 0 9 16 0 0 0 9 13 0 2 1 9 9 1 0 0 9 16 0 0 0 9 12 0 0 0 9 15 0 0 2 9 5 0 0 0 9 11 2 2 0 9 17 2 2 0 9 9 0 1 1 9 13 0 0 0 9 16 0 0 0 10 16 0 0 0 10 14 2 0 2 10 16 1 0 0 10 11 0 0 0 10 11 0 0 0 10 11 0 0 0 10 12 0 0 0 10 12 1 1 1 10 12 0 0 0 10 14 0 0 0 10 10 2 0 0 10 9 0 2 0 10 12 0 0 1 10 10 0 0 0 10 14 0 0 0 10 8 0 0 0 10 16 1 0 0 10 14 1 0 0 10 14 0 0 0 10 12 0 0 0 10 14 1 0 0 10 7 1 1 1 10 19 0 0 0 10 15 0 0 0 10 8 0 0 0 10 10 0 0 0 10 13 0 0 0 10 13 0 0 0 9 10 0 0 0 9 12 0 0 0 9 15 0 1 1 9 7 1 0 0 9 14 0 0 0 9 10 0 0 0 9 6 0 3 0 9 11 2 0 0 9 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 10 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Popularity[t] = + 11.3072637357884 + 0.102867075172939B[t] -0.12047308800788`2B`[t] + 0.193536916246143`3B`[t] + 0.0624951815495436Month[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) 11.3072637357884 1.949911 5.7989 0 0 B 0.102867075172939 0.21303 0.4829 0.629528 0.314764 `2B` -0.12047308800788 0.22302 -0.5402 0.589458 0.294729 `3B` 0.193536916246143 0.224721 0.8612 0.389782 0.194891 Month 0.0624951815495436 0.18697 0.3343 0.738417 0.369209 Multiple Linear Regression - Regression Statistics Multiple R 0.0633220517929962 R-squared 0.00400968224327489 Adjusted R-squared -0.00896739030078675 F-TEST (value) 0.308982031938302 F-TEST (DF numerator) 4 F-TEST (DF denominator) 307 p-value 0.871893926998178 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.94501866374813 Sum Squared Residuals 2662.65242345622 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15 12.0754545200802 2.92454547991977 2 12 12.2391881893916 -0.239188189391637 3 9 11.9251781851376 -2.92517818513761 4 10 11.8697203697343 -1.86972036973429 5 13 11.8697203697343 1.13027963026571 6 16 11.9725874449072 4.02741255509277 7 14 11.8697203697343 2.13027963026571 8 16 11.8521143568993 4.14788564310065 9 10 11.8697203697343 -1.86972036973429 10 8 12.3314866178759 -4.33148661787586 11 12 12.0350826264568 -0.035082626456775 12 15 11.9322155512838 3.06778444871616 13 14 11.811742463276 2.18825753672404 14 14 12.3016833709412 1.69831662905882 15 12 11.9876733666872 0.0123266333128423 16 12 11.9322155512838 0.0677844487161643 17 10 11.9322155512838 -1.93221555128384 18 4 11.9322155512838 -7.93221555128384 19 14 11.811742463276 2.18825753672404 20 15 11.9322155512838 3.06778444871616 21 16 11.9322155512838 4.06778444871616 22 12 11.811742463276 0.188257536724044 23 12 11.9322155512838 0.0677844487161643 24 12 12.12575246753 -0.125752467529979 25 12 12.1661243611534 -0.166124361153374 26 12 11.8697203697343 0.130279630265708 27 11 12.1309123354835 -1.13091233548349 28 11 11.9725874449072 -0.972587444907232 29 11 11.8521143568994 -0.852114356899351 30 11 11.8521143568994 -0.852114356899351 31 11 12.2513854234914 -1.25138542349137 32 11 11.8697203697343 -0.869720369734292 33 15 11.8697203697343 3.13027963026571 34 15 11.8697203697343 3.13027963026571 35 9 11.8697203697343 -2.86972036973429 36 16 11.8697203697343 4.13027963026571 37 13 11.8223111099647 1.17768889003532 38 9 11.9725874449072 -2.97258744490723 39 16 11.8697203697343 4.13027963026571 40 12 11.8697203697343 0.130279630265708 41 15 12.2567942022266 2.74320579777342 42 5 11.8697203697343 -6.86972036973429 43 11 11.8345083440644 -0.83450834406441 44 17 11.8345083440644 5.16549165593559 45 9 11.9427841979726 -2.94278419797255 46 13 11.8697203697343 1.13027963026571 47 16 11.9322155512838 4.06778444871616 48 16 11.9322155512838 4.06778444871616 49 14 12.525023534122 1.474976465878 50 16 12.0350826264568 3.96491737354323 51 11 11.9322155512838 -0.932215551283836 52 11 11.9322155512838 -0.932215551283836 53 11 11.9322155512838 -0.932215551283836 54 12 11.9322155512838 0.0677844487161643 55 12 12.108146454695 -0.108146454695038 56 12 11.9322155512838 0.0677844487161643 57 14 11.9322155512838 2.06778444871616 58 10 12.1379497016297 -2.13794970162971 59 9 11.6912693752681 -2.69126937526808 60 12 12.12575246753 -0.125752467529979 61 10 11.9322155512838 -1.93221555128384 62 14 11.9322155512838 2.06778444871616 63 8 11.9322155512838 -3.93221555128383 64 16 12.0350826264568 3.96491737354323 65 14 12.0350826264568 1.96491737354322 66 14 11.9322155512838 2.06778444871616 67 12 11.9322155512838 0.0677844487161643 68 14 12.0350826264568 1.96491737354322 69 7 12.108146454695 -5.10814645469504 70 19 11.9322155512838 7.06778444871617 71 15 11.9322155512838 3.06778444871616 72 8 11.9322155512838 -3.93221555128383 73 10 11.9322155512838 -1.93221555128384 74 13 11.9322155512838 1.06778444871616 75 13 11.8697203697343 1.13027963026571 76 10 11.8697203697343 -1.86972036973429 77 12 11.8697203697343 0.130279630265708 78 15 11.9427841979726 3.05721580202745 79 7 11.9725874449072 -4.97258744490723 80 14 11.8697203697343 2.13027963026571 81 10 11.8697203697343 -1.86972036973429 82 6 11.5083011057107 -5.50830110571065 83 11 12.0754545200802 -1.07545452008017 84 12 11.8697203697343 0.130279630265708 85 14 12.2567942022266 1.74320579777342 86 12 11.8697203697343 0.130279630265708 87 14 11.8697203697343 2.13027963026571 88 11 11.8345083440644 -0.83450834406441 89 10 12.1661243611534 -2.16612436115337 90 13 12.0632572859804 0.936742714019565 91 8 11.8697203697343 -3.86972036973429 92 9 11.8697203697343 -2.86972036973429 93 6 11.9322155512838 -5.93221555128383 94 12 12.4221564589491 -0.422156458949061 95 14 11.9322155512838 2.06778444871616 96 11 11.9322155512838 -0.932215551283836 97 8 12.2286195427029 -4.22861954270292 98 7 11.9322155512838 -4.93221555128383 99 9 11.8848062915142 -2.88480629151422 100 14 12.0174766136218 1.98252338637817 101 13 11.9322155512838 1.06778444871616 102 15 11.9322155512838 3.06778444871616 103 5 11.9322155512838 -6.93221555128383 104 15 12.1203436887948 2.87965631120523 105 13 11.811742463276 1.18825753672404 106 12 11.9322155512838 0.0677844487161643 107 6 12.0350826264568 -6.03508262645677 108 7 11.9322155512838 -4.93221555128383 109 13 11.9322155512838 1.06778444871616 110 16 11.9146095384489 4.08539046155111 111 10 11.9322155512838 -1.93221555128384 112 16 11.9322155512838 4.06778444871616 113 15 11.9322155512838 3.06778444871616 114 8 11.9322155512838 -3.93221555128383 115 11 11.9322155512838 -0.932215551283836 116 13 11.7643332035063 1.23566679649366 117 16 12.0350826264568 3.96491737354323 118 11 11.9322155512838 -0.932215551283836 119 14 11.9322155512838 2.06778444871616 120 9 12.0174766136218 -3.01747661362183 121 8 11.9322155512838 -3.93221555128383 122 8 12.2286195427029 -4.22861954270292 123 11 12.1379497016297 -1.13794970162971 124 12 11.9322155512838 0.0677844487161643 125 11 12.3436838519756 -1.34368385197559 126 14 12.1988162957682 1.80118370423176 127 11 12.0174766136218 -1.01747661362183 128 14 11.9322155512838 2.06778444871616 129 13 12.4045504461141 0.59544955388588 130 12 11.9322155512838 0.0677844487161643 131 4 11.9322155512838 -7.93221555128384 132 15 12.211013529868 2.78898647013202 133 10 11.9322155512838 -1.93221555128384 134 13 11.9876733666872 1.01232663331284 135 15 12.3016833709412 2.69831662905882 136 12 11.9876733666872 0.0123266333128423 137 13 11.9322155512838 1.06778444871616 138 8 11.9322155512838 -3.93221555128383 139 10 12.1379497016297 -2.13794970162971 140 15 11.9322155512838 3.06778444871616 141 16 11.9322155512838 4.06778444871616 142 16 11.9322155512838 4.06778444871616 143 14 11.9322155512838 2.06778444871616 144 14 12.108146454695 1.89185354530496 145 12 12.108146454695 -0.108146454695038 146 15 12.1363211142187 2.8636788857813 147 13 12.0456512731455 0.954348726854506 148 16 11.9322155512838 4.06778444871616 149 14 11.9322155512838 2.06778444871616 150 8 11.9322155512838 -3.93221555128383 151 16 11.811742463276 4.18825753672405 152 16 12.108146454695 3.89185354530496 153 12 11.9322155512838 0.0677844487161643 154 11 11.7643332035063 -0.764333203506339 155 16 12.108146454695 3.89185354530496 156 9 11.9322155512838 -2.93221555128384 157 15 12.5577154687369 2.44228453126313 158 12 12.0975778080063 -0.0975778080063186 159 9 12.6781885567447 -3.67818855674475 160 10 11.7361585439827 -1.73615854398268 161 13 12.5577154687369 0.442284531263133 162 16 11.9771047199984 4.02289528000156 163 14 11.8566316319906 2.14336836800944 164 16 12.3939817994254 3.6060182005746 165 10 12.1706416362446 -2.17064163624458 166 8 11.9947107328334 -3.99471073283338 167 12 12.0799717951714 -0.0799717951713778 168 15 12.4846516404986 2.5153483595014 169 14 12.0975778080063 1.90242219199368 170 14 12.0975778080063 1.90242219199368 171 12 12.2911147242525 -0.291114724252461 172 12 11.9473014730638 0.0526985269362379 173 10 11.8268283850559 -1.82682838505588 174 4 11.7537645568176 -7.75376455681762 175 14 11.9473014730638 2.05269852693624 176 15 11.9947107328334 3.00528926716662 177 16 12.0975778080063 3.90242219199368 178 12 12.2004448831793 -0.200444883179258 179 12 11.9947107328334 0.00528926716662068 180 12 11.8742376448255 0.125762355174501 181 12 11.7537645568176 0.246235443182381 182 12 12.0975778080063 -0.0975778080063186 183 11 11.9771047199984 -0.977104719998439 184 11 12.3033119583522 -1.3033119583522 185 11 12.4548483935639 -1.45484839356393 186 11 12.2613114773178 -1.26131147731779 187 11 12.0975778080063 -1.09757780800632 188 11 12.3939817994254 -1.3939817994254 189 15 12.0975778080063 2.90242219199368 190 15 12.2911147242525 2.70888527574754 191 9 12.1408383893099 -3.1408383893099 192 16 11.9473014730638 4.05269852693624 193 13 12.1882476490795 0.811752350920478 194 9 11.9594987071635 -2.9594987071635 195 16 11.8566316319906 4.14336836800944 196 12 12.0975778080063 -0.0975778080063186 197 15 12.0799717951714 2.92002820482862 198 5 11.6332914688097 -6.63329146880974 199 11 11.8566316319906 -0.856631631990559 200 17 12.2004448831793 4.79955511682074 201 9 11.9473014730638 -2.94730147306376 202 13 12.2004448831793 0.799555116820742 203 16 12.0677745610716 3.93222543892836 204 16 11.8742376448255 4.1257623551745 205 14 11.9771047199984 2.02289528000156 206 16 12.0677745610716 3.93222543892836 207 11 12.0975778080063 -1.09757780800632 208 11 12.2613114773178 -1.26131147731779 209 11 12.0501685482367 -1.0501685482367 210 12 12.0975778080063 -0.0975778080063186 211 12 12.1706416362446 -0.170641636244581 212 12 11.9771047199984 0.0228952800015615 213 14 12.1706416362446 1.82935836375542 214 10 12.4846516404986 -2.4846516404986 215 9 11.8742376448255 -2.8742376448255 216 12 11.8742376448255 0.125762355174501 217 10 12.0975778080063 -2.09757780800632 218 14 11.9594987071635 2.0405012928365 219 8 12.0975778080063 -4.09757780800632 220 16 11.9473014730638 4.05269852693624 221 14 12.4548483935639 1.54515160643607 222 14 12.1882476490795 1.81175235092048 223 12 11.8742376448255 0.125762355174501 224 14 11.8742376448255 2.1257623551745 225 7 11.8742376448255 -4.8742376448255 226 19 12.0799717951714 6.92002820482862 227 15 12.3817845653257 2.61821543467433 228 8 11.9947107328334 -3.99471073283338 229 10 12.0975778080063 -2.09757780800632 230 13 11.9771047199984 1.02289528000156 231 13 12.6781885567447 0.321811443255253 232 10 12.2911147242525 -2.29111472425246 233 12 12.0975778080063 -0.0975778080063186 234 15 12.1882476490795 2.81175235092048 235 7 12.1882476490795 -5.18824764907952 236 14 12.1882476490795 1.81175235092048 237 10 12.1706416362446 -2.17064163624458 238 6 12.2004448831793 -6.20044488317926 239 11 11.9771047199984 -0.977104719998439 240 12 11.9594987071635 0.0405012928365023 241 14 12.1828388703443 1.81716112965568 242 12 11.8566316319906 0.143368368009442 243 14 12.2613114773178 1.73868852268221 244 11 12.2735087114175 -1.27350871141752 245 10 12.0975778080063 -2.09757780800632 246 13 12.2613114773178 0.738688522682215 247 8 12.1882476490795 -4.18824764907952 248 9 12.9745925481638 -3.97459254816383 249 6 11.9771047199984 -5.97710471999844 250 12 12.0975778080063 -0.0975778080063186 251 14 11.9947107328334 2.00528926716662 252 11 11.9594987071635 -0.959498707163498 253 8 12.1882476490795 -4.18824764907952 254 7 12.0975778080063 -5.09757780800632 255 9 11.7537645568176 -2.75376455681762 256 14 12.1828388703443 1.81716112965568 257 13 11.9947107328334 1.00528926716662 258 15 12.2613114773178 2.73868852268222 259 5 12.3641785524907 -7.36417855249072 260 15 12.1408383893099 2.8591616106901 261 13 11.8742376448255 1.1257623551745 262 12 12.1882476490795 -0.188247649079522 263 6 12.0975778080063 -6.09757780800632 264 7 12.0975778080063 -5.09757780800632 265 13 12.3033119583522 0.696688041647803 266 16 12.2004448831793 3.79955511682074 267 10 11.8742376448255 -1.8742376448255 268 16 12.0975778080063 3.90242219199368 269 15 12.0975778080063 2.90242219199368 270 8 12.2911147242525 -4.29111472425246 271 11 12.0975778080063 -1.09757780800632 272 13 12.3641785524907 0.635821447509276 273 16 11.9473014730638 4.05269852693624 274 11 12.4548483935639 -1.45484839356393 275 14 12.0677745610716 1.93222543892836 276 9 12.3817845653257 -3.38178456532567 277 8 11.936732826375 -3.93673282637504 278 8 12.2629400647288 -4.2629400647288 279 11 11.7986537255322 -0.798653725532222 280 12 11.8162597383672 0.183740261632837 281 11 12.1424669767209 -1.14246697672092 282 14 12.1600729895559 1.83992701044414 283 11 12.1600729895559 -1.16007298955586 284 14 12.039599901548 1.96040009845202 285 13 12.2507428306291 0.749257169370934 286 12 12.039599901548 -0.039599901547982 287 4 12.1600729895559 -8.16007298955586 288 15 12.0572059143829 2.94279408561708 289 10 12.2507428306291 -2.25074283062907 290 13 12.0572059143829 0.942794085617077 291 15 12.4442797468752 2.55572025312479 292 12 12.0572059143829 -0.0572059143829229 293 13 12.1600729895559 0.839927010444138 294 8 12.0572059143829 -4.05720591438292 295 10 12.2507428306291 -2.25074283062907 296 15 12.1600729895559 2.83992701044414 297 16 11.936732826375 4.06326717362496 298 16 12.1600729895559 3.83992701044414 299 14 12.0572059143829 1.94279408561708 300 14 12.1600729895559 1.83992701044414 301 12 12.0572059143829 -0.0572059143829229 302 15 12.0572059143829 2.94279408561708 303 13 12.2507428306291 0.749257169370934 304 16 12.1600729895559 3.83992701044414 305 14 12.2507428306291 1.74925716937093 306 8 12.0572059143829 -4.05720591438292 307 16 12.0572059143829 3.94279408561708 308 16 12.353609905802 3.646390094198 309 12 11.936732826375 0.0632671736249572 310 11 12.0572059143829 -1.05720591438292 311 16 12.0572059143829 3.94279408561708 312 9 12.0572059143829 -3.05720591438292 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.5852358720493 0.8295282559014 0.4147641279507 9 0.531038364751206 0.937923270497587 0.468961635248794 10 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288 0.781915112115255 0.43616977576949 0.218084887884745 289 0.784442691279104 0.431114617441791 0.215557308720895 290 0.734500264036957 0.530999471926086 0.265499735963043 291 0.688101302845654 0.623797394308693 0.311898697154346 292 0.616946903271448 0.766106193457104 0.383053096728552 293 0.580746655767736 0.838506688464528 0.419253344232264 294 0.679495246315543 0.641009507368913 0.320504753684457 295 0.687629899858119 0.624740200283763 0.312370100141881 296 0.608415044623794 0.783169910752413 0.391584955376206 297 0.610832656511974 0.778334686976052 0.389167343488026 298 0.527539903005558 0.944920193988884 0.472460096994442 299 0.451356260605888 0.902712521211776 0.548643739394112 300 0.36525214297778 0.73050428595556 0.63474785702222 301 0.267009588057952 0.534019176115905 0.732990411942048 302 0.23519632468928 0.47039264937856 0.76480367531072 303 0.146313445215414 0.292626890430827 0.853686554784586 304 0.0843557529104866 0.168711505820973 0.915644247089513 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 0 0 OK

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

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

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

library(lattice) 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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