*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, 14 Dec 2010 15:02:34 +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/14/t1292339097ygk25wh37tu6agw.htm/, Retrieved Tue, 14 Dec 2010 16:05:15 +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/14/t1292339097ygk25wh37tu6agw.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 «

5 1 4 1 5 1 6 1 6 1 6 1 7 1 8 1 7 1 8 1 7 1 8 1 8 1 9 1 9 1 8 1 9 1 9 1 10 1 11 1 12 1 13 1 13 1 13 1 14 1 14 1 15 1 15 1 16 1 16 1 17 1 18 1 19 1 20 1 22 1 20 1 22 1 25 1 24 1 25 1 28 1 26 1 27 1 26 1 25 1 27 1 28 1 30 1 31 1 32 1 34 1 34 1 33 1 32 1 34 1 36 1 37 1 40 1 38 1 38 1 36 1 40 1 40 1 42 1 44 1 45 1 47 1 49 1 47 1 49 1 52 1 50 1 50 1 57 1 58 1 58 1 58 1 61 1 61 1 64 1 68 1 40 1 34 1 46 1 36 1 34 1 45 1 55 1 50 1 56 1 72 1 76 1 78 1 77 1 90 1 88 1 97 1 93 1 84 1 67 1 72 1 75 1 71 1 75 1 90 1 78 1 73 1 62 1 65 1 61 1 58 1 33 1 39 1 56 1 79 1 82 1 79 1 73 1 87 1 85 1 83 1 82 1 83 1 92 1 95 1 97 1 87 1 84 1 84 1 89 1 103 1 106 1 109 1 106 1 105 1 115 1 120 1 124 1 121 1 131 1 139 1 133 1 119 1 123 1 120 1 128 1 134 1 126 1 115 1 106 1 99 1 100 1 99 1 99 1 100 1 100 1 108 1 109 1 115 1 114 1 108 1 113 1 118 1 122 1 118 1 121 1 118 1 121 1 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 14 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation CO2-uitstoot[t] = + 108.750000000000 -47.4999999999996Dummy[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) 108.750000000000 19.510276 5.574 0 0 Dummy -47.4999999999996 19.735836 -2.4068 0.01714 0.00857 Multiple Linear Regression - Regression Statistics Multiple R 0.179494911537252 R-squared 0.0322184232677658 Adjusted R-squared 0.0266564601830978 F-TEST (value) 5.79263522200973 F-TEST (DF numerator) 1 F-TEST (DF denominator) 174 p-value 0.0171398615537401 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 39.0205516141925 Sum Squared Residuals 264933 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 5 61.2500000000013 -56.2500000000013 2 4 61.25 -57.25 3 5 61.25 -56.25 4 6 61.25 -55.25 5 6 61.25 -55.25 6 6 61.25 -55.25 7 7 61.25 -54.25 8 8 61.25 -53.25 9 7 61.25 -54.25 10 8 61.25 -53.25 11 7 61.25 -54.25 12 8 61.25 -53.25 13 8 61.25 -53.25 14 9 61.25 -52.25 15 9 61.25 -52.25 16 8 61.25 -53.25 17 9 61.25 -52.25 18 9 61.25 -52.25 19 10 61.25 -51.25 20 11 61.25 -50.25 21 12 61.25 -49.25 22 13 61.25 -48.25 23 13 61.25 -48.25 24 13 61.25 -48.25 25 14 61.25 -47.25 26 14 61.25 -47.25 27 15 61.25 -46.25 28 15 61.25 -46.25 29 16 61.25 -45.25 30 16 61.25 -45.25 31 17 61.25 -44.25 32 18 61.25 -43.25 33 19 61.25 -42.25 34 20 61.25 -41.25 35 22 61.25 -39.25 36 20 61.25 -41.25 37 22 61.25 -39.25 38 25 61.25 -36.25 39 24 61.25 -37.25 40 25 61.25 -36.25 41 28 61.25 -33.25 42 26 61.25 -35.25 43 27 61.25 -34.25 44 26 61.25 -35.25 45 25 61.25 -36.25 46 27 61.25 -34.25 47 28 61.25 -33.25 48 30 61.25 -31.25 49 31 61.25 -30.25 50 32 61.25 -29.25 51 34 61.25 -27.25 52 34 61.25 -27.25 53 33 61.25 -28.25 54 32 61.25 -29.25 55 34 61.25 -27.25 56 36 61.25 -25.25 57 37 61.25 -24.25 58 40 61.25 -21.25 59 38 61.25 -23.25 60 38 61.25 -23.25 61 36 61.25 -25.25 62 40 61.25 -21.25 63 40 61.25 -21.25 64 42 61.25 -19.25 65 44 61.25 -17.25 66 45 61.25 -16.25 67 47 61.25 -14.25 68 49 61.25 -12.2500000000000 69 47 61.25 -14.25 70 49 61.25 -12.2500000000000 71 52 61.25 -9.24999999999999 72 50 61.25 -11.2500000000000 73 50 61.25 -11.2500000000000 74 57 61.25 -4.24999999999999 75 58 61.25 -3.24999999999999 76 58 61.25 -3.24999999999999 77 58 61.25 -3.24999999999999 78 61 61.25 -0.249999999999987 79 61 61.25 -0.249999999999987 80 64 61.25 2.75000000000001 81 68 61.25 6.75000000000001 82 40 61.25 -21.25 83 34 61.25 -27.25 84 46 61.25 -15.25 85 36 61.25 -25.25 86 34 61.25 -27.25 87 45 61.25 -16.25 88 55 61.25 -6.24999999999999 89 50 61.25 -11.2500000000000 90 56 61.25 -5.24999999999999 91 72 61.25 10.7500000000000 92 76 61.25 14.75 93 78 61.25 16.75 94 77 61.25 15.75 95 90 61.25 28.75 96 88 61.25 26.75 97 97 61.25 35.75 98 93 61.25 31.75 99 84 61.25 22.75 100 67 61.25 5.75000000000001 101 72 61.25 10.7500000000000 102 75 61.25 13.75 103 71 61.25 9.75000000000001 104 75 61.25 13.75 105 90 61.25 28.75 106 78 61.25 16.75 107 73 61.25 11.75 108 62 61.25 0.750000000000012 109 65 61.25 3.75000000000001 110 61 61.25 -0.249999999999987 111 58 61.25 -3.24999999999999 112 33 61.25 -28.25 113 39 61.25 -22.25 114 56 61.25 -5.24999999999999 115 79 61.25 17.75 116 82 61.25 20.75 117 79 61.25 17.75 118 73 61.25 11.75 119 87 61.25 25.75 120 85 61.25 23.75 121 83 61.25 21.75 122 82 61.25 20.75 123 83 61.25 21.75 124 92 61.25 30.75 125 95 61.25 33.75 126 97 61.25 35.75 127 87 61.25 25.75 128 84 61.25 22.75 129 84 61.25 22.75 130 89 61.25 27.75 131 103 61.25 41.75 132 106 61.25 44.75 133 109 61.25 47.75 134 106 61.25 44.75 135 105 61.25 43.75 136 115 61.25 53.75 137 120 61.25 58.75 138 124 61.25 62.75 139 121 61.25 59.75 140 131 61.25 69.75 141 139 61.25 77.75 142 133 61.25 71.75 143 119 61.25 57.75 144 123 61.25 61.75 145 120 61.25 58.75 146 128 61.25 66.75 147 134 61.25 72.75 148 126 61.25 64.75 149 115 61.25 53.75 150 106 61.25 44.75 151 99 61.25 37.75 152 100 61.25 38.75 153 99 61.25 37.75 154 99 61.25 37.75 155 100 61.25 38.75 156 100 61.25 38.75 157 108 61.25 46.75 158 109 61.25 47.75 159 115 61.25 53.75 160 114 61.25 52.75 161 108 61.25 46.75 162 113 61.25 51.75 163 118 61.25 56.75 164 122 61.25 60.75 165 118 61.25 56.75 166 121 61.25 59.75 167 118 61.25 56.75 168 121 61.25 59.75 169 121 61.25 59.75 170 112 61.25 50.75 171 119 61.25 57.75 172 116 61.25 54.75 173 110 108.750000000000 1.25000000000035 174 111 108.750000000000 2.25000000000035 175 106 108.750000000000 -2.74999999999965 176 108 108.750000000000 -0.749999999999654 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 2.21515374435362e-05 4.43030748870724e-05 0.999977848462556 6 6.57679846073014e-07 1.31535969214603e-06 0.999999342320154 7 5.28665283840725e-08 1.05733056768145e-07 0.999999947133472 8 9.2552174220246e-09 1.85104348440492e-08 0.999999990744783 9 4.32125950972923e-10 8.64251901945846e-10 0.999999999567874 10 4.06797294499577e-11 8.13594588999154e-11 0.99999999995932 11 1.73165959924573e-12 3.46331919849146e-12 0.999999999998268 12 1.33580949459035e-13 2.6716189891807e-13 0.999999999999866 13 9.3254265079507e-15 1.86508530159014e-14 0.99999999999999 14 1.45122719679986e-15 2.90245439359972e-15 0.999999999999999 15 1.78968072354009e-16 3.57936144708018e-16 1 16 1.03623208263145e-17 2.07246416526291e-17 1 17 1.08900305901702e-18 2.17800611803405e-18 1 18 1.05451795687361e-19 2.10903591374723e-19 1 19 2.17132290648130e-20 4.34264581296260e-20 1 20 9.39846507534834e-21 1.87969301506967e-20 1 21 7.22398483383618e-21 1.44479696676724e-20 1 22 8.11307871163928e-21 1.62261574232786e-20 1 23 5.11921906194582e-21 1.02384381238916e-20 1 24 2.32749031594420e-21 4.65498063188839e-21 1 25 1.60008941994935e-21 3.20017883989869e-21 1 26 8.28786280260547e-22 1.65757256052109e-21 1 27 6.1790746375843e-22 1.23581492751686e-21 1 28 3.59970128628876e-22 7.19940257257751e-22 1 29 2.90520461862356e-22 5.81040923724712e-22 1 30 1.88762325740179e-22 3.77524651480358e-22 1 31 1.64790922930060e-22 3.29581845860119e-22 1 32 1.85259380913129e-22 3.70518761826258e-22 1 33 2.56696060002164e-22 5.13392120004328e-22 1 34 4.21000610075682e-22 8.42001220151364e-22 1 35 1.21628420903586e-21 2.43256841807172e-21 1 36 1.16692001928720e-21 2.33384003857440e-21 1 37 1.91949672135533e-21 3.83899344271067e-21 1 38 7.4382572825094e-21 1.48765145650188e-20 1 39 1.40429100460229e-20 2.80858200920457e-20 1 40 2.90870497471626e-20 5.81740994943252e-20 1 41 1.19776980268728e-19 2.39553960537456e-19 1 42 2.05419851298607e-19 4.10839702597213e-19 1 43 3.87921632389118e-19 7.75843264778237e-19 1 44 5.1294048585935e-19 1.0258809717187e-18 1 45 5.24576013100672e-19 1.04915202620134e-18 1 46 7.42006165874424e-19 1.48401233174885e-18 1 47 1.18038529429858e-18 2.36077058859716e-18 1 48 2.54537298537122e-18 5.09074597074245e-18 1 49 5.90258607341175e-18 1.18051721468235e-17 1 50 1.45678024048871e-17 2.91356048097742e-17 1 51 4.57837499770713e-17 9.15674999541427e-17 1 52 1.22160299254624e-16 2.44320598509247e-16 1 53 2.46369430264126e-16 4.92738860528251e-16 1 54 4.046766765073e-16 8.093533530146e-16 1 55 8.30018523542417e-16 1.66003704708483e-15 1 56 2.09603731219791e-15 4.19207462439582e-15 0.999999999999998 57 5.53340347328189e-15 1.10668069465638e-14 0.999999999999994 58 2.00590496250471e-14 4.01180992500942e-14 0.99999999999998 59 4.87868414019478e-14 9.75736828038955e-14 0.999999999999951 60 1.10526351011024e-13 2.21052702022048e-13 0.99999999999989 61 1.96566028145473e-13 3.93132056290947e-13 0.999999999999803 62 5.00843799090325e-13 1.00168759818065e-12 0.9999999999995 63 1.19512967999511e-12 2.39025935999021e-12 0.999999999998805 64 3.26621351701694e-12 6.53242703403388e-12 0.999999999996734 65 1.00384910971045e-11 2.0076982194209e-11 0.999999999989962 66 3.08350311643699e-11 6.16700623287398e-11 0.999999999969165 67 1.03281140911377e-10 2.06562281822753e-10 0.999999999896719 68 3.69166656072939e-10 7.38333312145877e-10 0.999999999630833 69 9.93017440700323e-10 1.98603488140065e-09 0.999999999006983 70 2.86345554774254e-09 5.72691109548508e-09 0.999999997136545 71 9.37493082252903e-09 1.87498616450581e-08 0.999999990625069 72 2.39569929837117e-08 4.79139859674235e-08 0.999999976043007 73 5.71408412039269e-08 1.14281682407854e-07 0.999999942859159 74 1.94600739194468e-07 3.89201478388936e-07 0.99999980539926 75 6.10386959143069e-07 1.22077391828614e-06 0.99999938961304 76 1.67565952450866e-06 3.35131904901732e-06 0.999998324340476 77 4.12247700287878e-06 8.24495400575757e-06 0.999995877522997 78 1.06133542880592e-05 2.12267085761184e-05 0.999989386645712 79 2.44746861810533e-05 4.89493723621066e-05 0.99997552531382 80 5.8052945137189e-05 0.000116105890274378 0.999941947054863 81 0.000145400174204447 0.000290800348408895 0.999854599825795 82 0.000214291550964192 0.000428583101928385 0.999785708449036 83 0.000366725346144124 0.000733450692288248 0.999633274653856 84 0.000561375888565755 0.00112275177713151 0.999438624111434 85 0.00101280766585171 0.00202561533170341 0.998987192334148 86 0.00203893974340069 0.00407787948680137 0.9979610602566 87 0.00349362041610453 0.00698724083220906 0.996506379583896 88 0.00585235420922787 0.0117047084184557 0.994147645790772 89 0.00980835938368469 0.0196167187673694 0.990191640616315 90 0.0161400588469416 0.0322801176938832 0.983859941153058 91 0.0298031331990613 0.0596062663981226 0.970196866800939 92 0.0531043069577585 0.106208613915517 0.946895693042241 93 0.0875088870510508 0.175017774102102 0.91249111294895 94 0.129240591677241 0.258481183354481 0.87075940832276 95 0.21025934587545 0.4205186917509 0.78974065412455 96 0.292695101140985 0.585390202281969 0.707304898859015 97 0.412202198773495 0.824404397546989 0.587797801226505 98 0.505356138330019 0.989287723339962 0.494643861669981 99 0.56093254604404 0.87813490791192 0.43906745395596 100 0.600009131553663 0.799981736892674 0.399990868446337 101 0.636162495858386 0.727675008283229 0.363837504141614 102 0.670217136354961 0.659565727290078 0.329782863645039 103 0.702725261747504 0.594549476504993 0.297274738252496 104 0.732067658921743 0.535864682156513 0.267932341078257 105 0.768970778512557 0.462058442974885 0.231029221487443 106 0.7909063194266 0.418187361146802 0.209093680573401 107 0.81247115862623 0.375057682747541 0.187528841373770 108 0.846492910464911 0.307014179070178 0.153507089535089 109 0.874293579145106 0.251412841709787 0.125706420854894 110 0.906095166375592 0.187809667248816 0.0939048336244078 111 0.938193224405907 0.123613551188186 0.0618067755940932 112 0.989028191692501 0.0219436166149978 0.0109718083074989 113 0.998942444450507 0.00211511109898566 0.00105755554949283 114 0.999826947237963 0.000346105524074244 0.000173052762037122 115 0.999913040961887 0.000173918076224945 8.69590381124727e-05 116 0.999953478560975 9.3042878049021e-05 4.65214390245105e-05 117 0.999979474740173 4.10505196545407e-05 2.05252598272704e-05 118 0.999994759337411 1.04813251776211e-05 5.24066258881055e-06 119 0.999997185555284 5.62888943094964e-06 2.81444471547482e-06 120 0.999998684906054 2.63018789101220e-06 1.31509394550610e-06 121 0.99999950213906 9.95721879213316e-07 4.97860939606658e-07 122 0.99999984834229 3.0331541980334e-07 1.5165770990167e-07 123 0.999999957614864 8.4770271149888e-08 4.2385135574944e-08 124 0.999999977620547 4.47589067030498e-08 2.23794533515249e-08 125 0.999999985996353 2.80072946716819e-08 1.40036473358409e-08 126 0.999999990177621 1.96447575885374e-08 9.8223787942687e-09 127 0.99999999711756 5.76487897224073e-09 2.88243948612037e-09 128 0.999999999570982 8.58036511488627e-10 4.29018255744314e-10 129 0.999999999961213 7.75749938838031e-11 3.87874969419015e-11 130 0.999999999994663 1.06737009186413e-11 5.33685045932067e-12 131 0.999999999995684 8.63120749831982e-12 4.31560374915991e-12 132 0.999999999995544 8.91154924579267e-12 4.45577462289634e-12 133 0.999999999994433 1.11345943286651e-11 5.56729716433256e-12 134 0.999999999993804 1.23912278095893e-11 6.19561390479466e-12 135 0.999999999993462 1.30752742613853e-11 6.53763713069263e-12 136 0.999999999989688 2.06247294420310e-11 1.03123647210155e-11 137 0.999999999985081 2.98369641058637e-11 1.49184820529318e-11 138 0.999999999982464 3.50716688248063e-11 1.75358344124031e-11 139 0.999999999973066 5.38690588169696e-11 2.69345294084848e-11 140 0.999999999984386 3.12287842639898e-11 1.56143921319949e-11 141 0.999999999998344 3.31265670952792e-12 1.65632835476396e-12 142 0.9999999999995 1.00151060402466e-12 5.00755302012328e-13 143 0.999999999998903 2.19380248220309e-12 1.09690124110155e-12 144 0.999999999998299 3.40269301240709e-12 1.70134650620354e-12 145 0.999999999996398 7.20502932898122e-12 3.60251466449061e-12 146 0.999999999997363 5.27389055984386e-12 2.63694527992193e-12 147 0.999999999999661 6.77757149127059e-13 3.38878574563529e-13 148 0.999999999999768 4.64010339395512e-13 2.32005169697756e-13 149 0.999999999999214 1.57273683061881e-12 7.86368415309403e-13 150 0.99999999999741 5.17814238580329e-12 2.58907119290164e-12 151 0.999999999996792 6.41614922562455e-12 3.20807461281228e-12 152 0.999999999995911 8.17696536718644e-12 4.08848268359322e-12 153 0.999999999996773 6.45411703992099e-12 3.22705851996050e-12 154 0.999999999998409 3.18277663782822e-12 1.59138831891411e-12 155 0.999999999999479 1.04170206653072e-12 5.20851033265358e-13 156 0.999999999999964 7.13894103647753e-14 3.56947051823876e-14 157 0.99999999999995 9.89403131971075e-14 4.94701565985537e-14 158 0.99999999999993 1.4066873748133e-13 7.0334368740665e-14 159 0.999999999999444 1.11246427117080e-12 5.56232135585401e-13 160 0.999999999996355 7.29012358115776e-12 3.64506179057888e-12 161 0.999999999999119 1.76279830234039e-12 8.81399151170196e-13 162 0.999999999997869 4.2622871731719e-12 2.13114358658595e-12 163 0.999999999973663 5.26738543735646e-11 2.63369271867823e-11 164 0.999999999840905 3.18189308518936e-10 1.59094654259468e-10 165 0.999999997964574 4.07085303369621e-09 2.03542651684810e-09 166 0.9999999838497 3.23006002549004e-08 1.61503001274502e-08 167 0.999999797620107 4.04759785781145e-07 2.02379892890573e-07 168 0.999998639892827 2.72021434644747e-06 1.36010717322374e-06 169 0.999994279510577 1.14409788451142e-05 5.72048942255708e-06 170 0.999980288601388 3.94227972238932e-05 1.97113986119466e-05 171 0.99975266597555 0.000494668048901318 0.000247334024450659 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 142 0.850299401197605 NOK 5% type I error level 146 0.874251497005988 NOK 10% type I error level 147 0.880239520958084 NOK

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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Software written by Ed van Stee & Patrick Wessa

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