SimpleLinearRegression Object ( [n] => 25 [X] => Array ( [0] => 0 [1] => 0.25 [2] => 0.5 [3] => 0.75 [4] => 1 [5] => 1.25 [6] => 1.5 [7] => 1.75 [8] => 2 [9] => 2.25 [10] => 2.5 [11] => 2.75 [12] => 3 [13] => 3.25 [14] => 3.5 [15] => 3.75 [16] => 4 [17] => 4.25 [18] => 4.5 [19] => 4.75 [20] => 5 [21] => 5.25 [22] => 5.5 [23] => 5.75 [24] => 6 ) [Y] => Array ( [0] => -1.5528419686578 [1] => -1.7212463990472 [2] => -1.6575773191778 [3] => -1.5528419686578 [4] => -1.2518119729938 [5] => -1.0705810742857 [6] => -1.1549019599857 [7] => -1.0457574905607 [8] => -1.0457574905607 [9] => -0.97061622231479 [10] => -0.93181413825384 [11] => -0.83564714421556 [12] => -0.85078088734462 [13] => -0.79317412396815 [14] => -0.7594507517174 [15] => -0.65169513695184 [16] => -0.67778070526608 [17] => -0.63638802010786 [18] => -0.59687947882418 [19] => -0.49620931694282 [20] => -0.53910215724345 [21] => -0.4907974776689 [22] => -0.46218090492673 [23] => -0.36151074304536 [24] => -0.39577394691553 ) [ConfInt] => 95 [Alpha] => 0.975 [XMean] => 3 [YMean] => -0.90012475198537 [SumXX] => 81.25 [SumXY] => 17.07185157389 [SumYY] => 3.8738885260275 [Slope] => 0.21011509629404 [YInt] => -1.5304700408675 [PredictedY] => Array ( [0] => -1.5304700408675 [1] => -1.477941266794 [2] => -1.4254124927205 [3] => -1.3728837186469 [4] => -1.3203549445734 [5] => -1.2678261704999 [6] => -1.2152973964264 [7] => -1.1627686223529 [8] => -1.1102398482794 [9] => -1.0577110742059 [10] => -1.0051823001324 [11] => -0.95265352605888 [12] => -0.90012475198537 [13] => -0.84759597791186 [14] => -0.79506720383835 [15] => -0.74253842976484 [16] => -0.69000965569133 [17] => -0.63748088161782 [18] => -0.58495210754432 [19] => -0.53242333347081 [20] => -0.4798945593973 [21] => -0.42736578532379 [22] => -0.37483701125028 [23] => -0.32230823717677 [24] => -0.26977946310326 ) [Error] => Array ( [0] => -0.022371927790305 [1] => -0.2433051322532 [2] => -0.23216482645734 [3] => -0.17995825001083 [4] => 0.068542971579641 [5] => 0.19724509621422 [6] => 0.060395436440679 [7] => 0.11701113179224 [8] => 0.064482357718729 [9] => 0.087094851891105 [10] => 0.073368161878548 [11] => 0.11700638184332 [12] => 0.049343864640749 [13] => 0.05442185394371 [14] => 0.035616452120951 [15] => 0.090843292813003 [16] => 0.012228950425253 [17] => 0.0010928615099691 [18] => -0.011927371279866 [19] => 0.036214016527988 [20] => -0.059207597846154 [21] => -0.063431692345108 [22] => -0.087343893676445 [23] => -0.039202505868591 [24] => -0.12599448381227 ) [SquaredError] => Array ( [0] => 0.00050050315305463 [1] => 0.059197387380749 [2] => 0.053900506643965 [3] => 0.032384971746961 [4] => 0.0046981389529674 [5] => 0.038905627980558 [6] => 0.0036476087428601 [7] => 0.013691604963301 [8] => 0.0041579744569662 [9] => 0.0075855132259335 [10] => 0.0053828871774369 [11] => 0.013690493392064 [12] => 0.0024348169776846 [13] => 0.0029617381866705 [14] => 0.001268531661684 [15] => 0.008252503849109 [16] => 0.00014954722850329 [17] => 1.194346279972E-6 [18] => 0.00014226218564778 [19] => 0.0013114549930894 [20] => 0.0035055396427119 [21] => 0.0040235795937644 [22] => 0.0076289557625622 [23] => 0.0015368364663769 [24] => 0.01587460995112 ) [TotalError] => 3.8738885260275 [SumError] => -6.3837823915947E-15 [SumSquaredError] => 0.28683478866202 [ErrorVariance] => 0.012471077767914 [StdErr] => 0.11167397981586 [SlopeStdErr] => 0.012389115703422 [SlopeVal] => [YIntStdErr] => 0.043361904961978 [YIntTVal] => -35.295267636638 [R] => 0.96226653330541 [RSquared] => 0.92595688111961 [DF] => 23 [SlopeProb] => [YIntProb] => [AlphaTVal] => [ConfIntOfSlope] => 0 [RPath] => /usr/local/bin/R [format] => %01.2f [SlopeTVal] => 16.95965243395 ) SimpleLinearRegression Object ( [n] => 25 [X] => Array ( [0] => 0 [1] => 0.25 [2] => 0.5 [3] => 0.75 [4] => 1 [5] => 1.25 [6] => 1.5 [7] => 1.75 [8] => 2 [9] => 2.25 [10] => 2.5 [11] => 2.75 [12] => 3 [13] => 3.25 [14] => 3.5 [15] => 3.75 [16] => 4 [17] => 4.25 [18] => 4.5 [19] => 4.75 [20] => 5 [21] => 5.25 [22] => 5.5 [23] => 5.75 [24] => 6 ) [Y] => Array ( [0] => -1.7212463990472 [1] => -1.6575773191778 [2] => -1.5528419686578 [3] => -1.2518119729938 [4] => -1.0705810742857 [5] => -1.1549019599857 [6] => -1.0457574905607 [7] => -1.0457574905607 [8] => -0.97061622231479 [9] => -0.93181413825384 [10] => -0.83564714421556 [11] => -0.85078088734462 [12] => -0.79317412396815 [13] => -0.7594507517174 [14] => -0.65169513695184 [15] => -0.67778070526608 [16] => -0.63638802010786 [17] => -0.59687947882418 [18] => -0.49620931694282 [19] => -0.53910215724345 [20] => -0.4907974776689 [21] => -0.46218090492673 [22] => -0.36151074304536 [23] => -0.39577394691553 [24] => -0.23507701535011 ) [ConfInt] => 95 [Alpha] => 0.975 [XMean] => 3 [YMean] => -0.84741415385306 [SumXX] => 81.25 [SumXY] => 16.945663829611 [SumYY] => 3.8206770742039 [Slope] => 0.20856201636444 [YInt] => -1.4731002029464 [PredictedY] => Array ( [0] => -1.4731002029464 [1] => -1.4209596988553 [2] => -1.3688191947642 [3] => -1.3166786906731 [4] => -1.2645381865819 [5] => -1.2123976824908 [6] => -1.1602571783997 [7] => -1.1081166743086 [8] => -1.0559761702175 [9] => -1.0038356661264 [10] => -0.95169516203528 [11] => -0.89955465794417 [12] => -0.84741415385306 [13] => -0.79527364976195 [14] => -0.74313314567084 [15] => -0.69099264157973 [16] => -0.63885213748862 [17] => -0.58671163339751 [18] => -0.5345711293064 [19] => -0.48243062521529 [20] => -0.43029012112418 [21] => -0.37814961703307 [22] => -0.32600911294196 [23] => -0.27386860885085 [24] => -0.22172810475974 ) [Error] => Array ( [0] => -0.24814619610079 [1] => -0.23661762032252 [2] => -0.18402277389362 [3] => 0.064866717679255 [4] => 0.19395711229624 [5] => 0.05749572250509 [6] => 0.11449968783905 [7] => 0.062359183747938 [8] => 0.085359947902712 [9] => 0.072021527872554 [10] => 0.11604801781972 [11] => 0.048773770599552 [12] => 0.054240029884912 [13] => 0.035822898044552 [14] => 0.091438008719002 [15] => 0.013211936313651 [16] => 0.0024641173807657 [17] => -0.010167845426671 [18] => 0.038361812363582 [19] => -0.056671532028161 [20] => -0.060507356544717 [21] => -0.084031287893656 [22] => -0.035501630103403 [23] => -0.12190533806468 [24] => -0.013348910590372 ) [SquaredError] => Array ( [0] => 0.06157653463929 [1] => 0.055987898247092 [2] => 0.033864381311501 [3] => 0.0042076910624801 [4] => 0.037619361410295 [5] => 0.0033057581063823 [6] => 0.013110178515239 [7] => 0.0038886677977091 [8] => 0.0072863207059538 [9] => 0.0051871004770971 [10] => 0.013467142439886 [11] => 0.0023788806984977 [12] => 0.0029419808419161 [13] => 0.0012832800243103 [14] => 0.0083609094384964 [15] => 0.00017455526115596 [16] => 6.0718744661915E-6 [17] => 0.00010338508062067 [18] => 0.0014716286478187 [19] => 0.0032116625424189 [20] => 0.0036611401960294 [21] => 0.0070612573450664 [22] => 0.0012603657399988 [23] => 0.014860911448664 [24] => 0.00017819341394974 ) [TotalError] => 3.8206770742039 [SumError] => -1.1268763699945E-14 [SumSquaredError] => 0.28645525726634 [ErrorVariance] => 0.012454576402884 [StdErr] => 0.1116000734896 [SlopeStdErr] => 0.012380916532686 [SlopeVal] => [YIntStdErr] => 0.043333207864402 [YIntTVal] => -33.994718497555 [R] => 0.96178220074391 [RSquared] => 0.9250250016678 [DF] => 23 [SlopeProb] => [YIntProb] => [AlphaTVal] => [ConfIntOfSlope] => 0 [RPath] => /usr/local/bin/R [format] => %01.2f [SlopeTVal] => 16.845442404351 ) SimpleLinearRegression Object ( [n] => 25 [X] => Array ( [0] => 0 [1] => 0.25 [2] => 0.5 [3] => 0.75 [4] => 1 [5] => 1.25 [6] => 1.5 [7] => 1.75 [8] => 2 [9] => 2.25 [10] => 2.5 [11] => 2.75 [12] => 3 [13] => 3.25 [14] => 3.5 [15] => 3.75 [16] => 4 [17] => 4.25 [18] => 4.5 [19] => 4.75 [20] => 5 [21] => 5.25 [22] => 5.5 [23] => 5.75 [24] => 6 ) [Y] => Array ( [0] => -1.6575773191778 [1] => -1.5528419686578 [2] => -1.2518119729938 [3] => -1.0705810742857 [4] => -1.1549019599857 [5] => -1.0457574905607 [6] => -1.0457574905607 [7] => -0.97061622231479 [8] => -0.93181413825384 [9] => -0.83564714421556 [10] => -0.85078088734462 [11] => -0.79317412396815 [12] => -0.7594507517174 [13] => -0.65169513695184 [14] => -0.67778070526608 [15] => -0.63638802010786 [16] => -0.59687947882418 [17] => -0.49620931694282 [18] => -0.53910215724345 [19] => -0.4907974776689 [20] => -0.46218090492673 [21] => -0.36151074304536 [22] => -0.39577394691553 [23] => -0.23507701535011 [24] => -0.21183162885883 ) [ConfInt] => 95 [Alpha] => 0.975 [XMean] => 3 [YMean] => -0.78703756304553 [SumXX] => 81.25 [SumXY] => 16.012456607713 [SumYY] => 3.3699261096025 [Slope] => 0.197076389018 [YInt] => -1.3782667300995 [PredictedY] => Array ( [0] => -1.3782667300995 [1] => -1.328997632845 [2] => -1.2797285355905 [3] => -1.230459438336 [4] => -1.1811903410815 [5] => -1.131921243827 [6] => -1.0826521465725 [7] => -1.033383049318 [8] => -0.98411395206353 [9] => -0.93484485480903 [10] => -0.88557575755453 [11] => -0.83630666030003 [12] => -0.78703756304553 [13] => -0.73776846579103 [14] => -0.68849936853653 [15] => -0.63923027128203 [16] => -0.58996117402753 [17] => -0.54069207677303 [18] => -0.49142297951853 [19] => -0.44215388226403 [20] => -0.39288478500952 [21] => -0.34361568775502 [22] => -0.29434659050052 [23] => -0.24507749324602 [24] => -0.19580839599152 ) [Error] => Array ( [0] => -0.27931058907826 [1] => -0.22384433581275 [2] => 0.027916562596734 [3] => 0.15987836405033 [4] => 0.026288381095789 [5] => 0.086163753266357 [6] => 0.036894656011856 [7] => 0.062766827003241 [8] => 0.052299813809692 [9] => 0.099197710593467 [10] => 0.03479487020991 [11] => 0.043132536331879 [12] => 0.027586811328128 [13] => 0.086073328839189 [14] => 0.010718663270447 [15] => 0.0028422511741717 [16] => -0.0069183047966552 [17] => 0.044482759830207 [18] => -0.047679177724926 [19] => -0.048643595404872 [20] => -0.069296119917201 [21] => -0.017895055290338 [22] => -0.10142735641501 [23] => 0.010000477895912 [24] => -0.016023232867309 ) [SquaredError] => Array ( [0] => 0.078014405171244 [1] => 0.05010628667545 [2] => 0.00077933446721738 [3] => 0.025561091291409 [4] => 0.00069107898063746 [5] => 0.0074241923769456 [6] => 0.0013612156422332 [7] => 0.0039396745720548 [8] => 0.0027352705245285 [9] => 0.0098401857869853 [10] => 0.0012106829929245 [11] => 0.0018604156904209 [12] => 0.00076103215925375 [13] => 0.0074086179374592 [14] => 0.00011488974230523 [15] => 8.0783917370804E-6 [16] => 4.7862941259423E-5 [17] => 0.0019787159221119 [18] => 0.0022733039885251 [19] => 0.0023661993739128 [20] => 0.0048019522355791 [21] => 0.00032023300384426 [22] => 0.010287508629337 [23] => 0.00010000955814663 [24] => 0.00025674399152002 ) [TotalError] => 3.3699261096025 [SumError] => -6.2450045135165E-15 [SumSquaredError] => 0.21424898204704 [ErrorVariance] => 0.00931517313248 [StdErr] => 0.096515144575761 [SlopeStdErr] => 0.010707393926976 [SlopeVal] => [YIntStdErr] => 0.037475878744417 [YIntTVal] => -36.777435947513 [R] => 0.96768964054989 [RSquared] => 0.93642324042757 [DF] => 23 [SlopeProb] => [YIntProb] => [AlphaTVal] => [ConfIntOfSlope] => 0 [RPath] => /usr/local/bin/R [format] => %01.2f [SlopeTVal] => 18.405635429317 ) SimpleLinearRegression Object ( [n] => 25 [X] => Array ( [0] => 0 [1] => 0.25 [2] => 0.5 [3] => 0.75 [4] => 1 [5] => 1.25 [6] => 1.5 [7] => 1.75 [8] => 2 [9] => 2.25 [10] => 2.5 [11] => 2.75 [12] => 3 [13] => 3.25 [14] => 3.5 [15] => 3.75 [16] => 4 [17] => 4.25 [18] => 4.5 [19] => 4.75 [20] => 5 [21] => 5.25 [22] => 5.5 [23] => 5.75 [24] => 6 ) [Y] => Array ( [0] => -1.5528419686578 [1] => -1.2518119729938 [2] => -1.0705810742857 [3] => -1.1549019599857 [4] => -1.0457574905607 [5] => -1.0457574905607 [6] => -0.97061622231479 [7] => -0.93181413825384 [8] => -0.83564714421556 [9] => -0.85078088734462 [10] => -0.79317412396815 [11] => -0.7594507517174 [12] => -0.65169513695184 [13] => -0.67778070526608 [14] => -0.63638802010786 [15] => -0.59687947882418 [16] => -0.49620931694282 [17] => -0.53910215724345 [18] => -0.4907974776689 [19] => -0.46218090492673 [20] => -0.36151074304536 [21] => -0.39577394691553 [22] => -0.23507701535011 [23] => -0.21183162885883 [24] => -0.10182351650232 ) [ConfInt] => 95 [Alpha] => 0.975 [XMean] => 3 [YMean] => -0.72480741093851 [SumXX] => 81.25 [SumXY] => 15.238844539912 [SumYY] => 2.9847901363942 [Slope] => 0.187555009722 [YInt] => -1.2874724401045 [PredictedY] => Array ( [0] => -1.2874724401045 [1] => -1.240583687674 [2] => -1.1936949352435 [3] => -1.146806182813 [4] => -1.0999174303825 [5] => -1.053028677952 [6] => -1.0061399255215 [7] => -0.95925117309101 [8] => -0.91236242066051 [9] => -0.86547366823001 [10] => -0.81858491579951 [11] => -0.77169616336901 [12] => -0.72480741093851 [13] => -0.67791865850801 [14] => -0.63102990607751 [15] => -0.58414115364701 [16] => -0.53725240121651 [17] => -0.49036364878601 [18] => -0.44347489635551 [19] => -0.39658614392501 [20] => -0.34969739149451 [21] => -0.30280863906401 [22] => -0.25591988663351 [23] => -0.20903113420301 [24] => -0.16214238177251 ) [Error] => Array ( [0] => -0.26536952855327 [1] => -0.011228285319792 [2] => 0.1231138609578 [3] => -0.0080957771727357 [4] => 0.054159939821832 [5] => 0.0072711873913327 [6] => 0.035523703206718 [7] => 0.02743703483717 [8] => 0.076715276444946 [9] => 0.014692780885389 [10] => 0.025410791831359 [11] => 0.012245411651609 [12] => 0.073112273986671 [13] => 0.00013795324192956 [14] => -0.005358114030345 [15] => -0.012738325177171 [16] => 0.041043084273692 [17] => -0.048738508457441 [18] => -0.047322581313385 [19] => -0.065594761001714 [20] => -0.01181335155085 [21] => -0.092965307851517 [22] => 0.020842871283401 [23] => -0.0028004946558192 [24] => 0.06031886527019 ) [SquaredError] => Array ( [0] => 0.070420986684587 [1] => 0.00012607439122267 [2] => 0.015157022759937 [3] => 6.5541608030588E-5 [4] => 0.0029332990815045 [5] => 5.2870166079876E-5 [6] => 0.001261933489519 [7] => 0.00075279088065609 [8] => 0.0058852336400245 [9] => 0.00021587781014605 [10] => 0.00064570834149667 [11] => 0.00014995010651737 [12] => 0.005345404607502 [13] => 1.9031096958875E-8 [14] => 2.870938596218E-5 [15] => 0.00016226492831935 [16] => 0.0016845347666974 [17] => 0.002375442206656 [18] => 0.002239426702162 [19] => 0.004302672670872 [20] => 0.00013955527486398 [21] => 0.0086425484639274 [22] => 0.00043442528333644 [23] => 7.8427703172719E-6 [24] => 0.0036383655074833 ) [TotalError] => 2.9847901363942 [SumError] => -5.0792703376601E-15 [SumSquaredError] => 0.12666850055892 [ErrorVariance] => 0.0055073261112573 [StdErr] => 0.074211361065926 [SlopeStdErr] => 0.0082330113090821 [SlopeVal] => [YIntStdErr] => 0.028815539581787 [YIntTVal] => -44.679796345658 [R] => 0.97855097352631 [RSquared] => 0.95756200778928 [DF] => 23 [SlopeProb] => [YIntProb] => [AlphaTVal] => [ConfIntOfSlope] => 0 [RPath] => /usr/local/bin/R [format] => %01.2f [SlopeTVal] => 22.780851705512 ) SimpleLinearRegression Object ( [n] => 25 [X] => Array ( [0] => 0 [1] => 0.25 [2] => 0.5 [3] => 0.75 [4] => 1 [5] => 1.25 [6] => 1.5 [7] => 1.75 [8] => 2 [9] => 2.25 [10] => 2.5 [11] => 2.75 [12] => 3 [13] => 3.25 [14] => 3.5 [15] => 3.75 [16] => 4 [17] => 4.25 [18] => 4.5 [19] => 4.75 [20] => 5 [21] => 5.25 [22] => 5.5 [23] => 5.75 [24] => 6 ) [Y] => Array ( [0] => -1.2518119729938 [1] => -1.0705810742857 [2] => -1.1549019599857 [3] => -1.0457574905607 [4] => -1.0457574905607 [5] => -0.97061622231479 [6] => -0.93181413825384 [7] => -0.83564714421556 [8] => -0.85078088734462 [9] => -0.79317412396815 [10] => -0.7594507517174 [11] => -0.65169513695184 [12] => -0.67778070526608 [13] => -0.63638802010786 [14] => -0.59687947882418 [15] => -0.49620931694282 [16] => -0.53910215724345 [17] => -0.4907974776689 [18] => -0.46218090492673 [19] => -0.36151074304536 [20] => -0.39577394691553 [21] => -0.23507701535011 [22] => -0.21183162885883 [23] => -0.10182351650232 [24] => -0.10790539730952 ) [ConfInt] => 95 [Alpha] => 0.975 [XMean] => 3 [YMean] => -0.66700994808458 [SumXX] => 81.25 [SumXY] => 14.398438268212 [SumYY] => 2.5962033342276 [Slope] => 0.17721154791645 [YInt] => -1.1986445918339 [PredictedY] => Array ( [0] => -1.1986445918339 [1] => -1.1543417048548 [2] => -1.1100388178757 [3] => -1.0657359308966 [4] => -1.0214330439175 [5] => -0.97713015693837 [6] => -0.93282726995926 [7] => -0.88852438298015 [8] => -0.84422149600103 [9] => -0.79991860902192 [10] => -0.75561572204281 [11] => -0.71131283506369 [12] => -0.66700994808458 [13] => -0.62270706110547 [14] => -0.57840417412635 [15] => -0.53410128714724 [16] => -0.48979840016813 [17] => -0.44549551318901 [18] => -0.4011926262099 [19] => -0.35688973923079 [20] => -0.31258685225167 [21] => -0.26828396527256 [22] => -0.22398107829345 [23] => -0.17967819131434 [24] => -0.13537530433522 ) [Error] => Array ( [0] => -0.053167381159863 [1] => 0.083760630569116 [2] => -0.044863142110033 [3] => 0.019978440335922 [4] => -0.024324446643191 [5] => 0.0065139346235807 [6] => 0.0010131317054198 [7] => 0.052877238764582 [8] => -0.0065593913435881 [9] => 0.0067444850537686 [10] => -0.0038350296745946 [11] => 0.059617698111853 [12] => -0.010770757181501 [13] => -0.013680959002389 [14] => -0.018475304697829 [15] => 0.037891970204422 [16] => -0.049303757075325 [17] => -0.045301964479883 [18] => -0.060988278716825 [19] => -0.0046210038145746 [20] => -0.083187094663855 [21] => 0.03320694992245 [22] => 0.012149449434617 [23] => 0.077854674812012 [24] => 0.027469907025703 ) [SquaredError] => Array ( [0] => 0.0028267704193981 [1] => 0.007015843233336 [2] => 0.002012701519985 [3] => 0.000399138078256 [4] => 0.00059167870449744 [5] => 4.2431344280284E-5 [6] => 1.0264358525269E-6 [7] => 0.0027960023793666 [8] => 4.3025614798338E-5 [9] => 4.5488078640508E-5 [10] => 1.4707452605021E-5 [11] => 0.0035542699281561 [12] => 0.00011600921026286 [13] => 0.00018716863922505 [14] => 0.00034133688367761 [15] => 0.0014358014059728 [16] => 0.0024308604617426 [17] => 0.0020522679857366 [18] => 0.0037195701408411 [19] => 2.1353676254313E-5 [20] => 0.0069200927186132 [21] => 0.0011027015231521 [22] => 0.0001476091215643 [23] => 0.0060613503900842 [24] => 0.00075459579200077 ) [TotalError] => 2.5962033342276 [SumError] => -3.0114799542957E-15 [SumSquaredError] => 0.044633801138299 [ErrorVariance] => 0.0019406000494913 [StdErr] => 0.044052242275408 [SlopeStdErr] => 0.0048871574868661 [SlopeVal] => [YIntStdErr] => 0.017105051204031 [YIntTVal] => -70.075475222865 [R] => 0.99136675794443 [RSquared] => 0.98280804875725 [DF] => 23 [SlopeProb] => [YIntProb] => [AlphaTVal] => [ConfIntOfSlope] => 0 [RPath] => /usr/local/bin/R [format] => %01.2f [SlopeTVal] => 36.260658346431 ) SimpleLinearRegression Object ( [n] => 25 [X] => Array ( [0] => 0 [1] => 0.25 [2] => 0.5 [3] => 0.75 [4] => 1 [5] => 1.25 [6] => 1.5 [7] => 1.75 [8] => 2 [9] => 2.25 [10] => 2.5 [11] => 2.75 [12] => 3 [13] => 3.25 [14] => 3.5 [15] => 3.75 [16] => 4 [17] => 4.25 [18] => 4.5 [19] => 4.75 [20] => 5 [21] => 5.25 [22] => 5.5 [23] => 5.75 [24] => 6 ) [Y] => Array ( [0] => -1.0705810742857 [1] => -1.1549019599857 [2] => -1.0457574905607 [3] => -1.0457574905607 [4] => -0.97061622231479 [5] => -0.93181413825384 [6] => -0.83564714421556 [7] => -0.85078088734462 [8] => -0.79317412396815 [9] => -0.7594507517174 [10] => -0.65169513695184 [11] => -0.67778070526608 [12] => -0.63638802010786 [13] => -0.59687947882418 [14] => -0.49620931694282 [15] => -0.53910215724345 [16] => -0.4907974776689 [17] => -0.46218090492673 [18] => -0.36151074304536 [19] => -0.39577394691553 [20] => -0.23507701535011 [21] => -0.21183162885883 [22] => -0.10182351650232 [23] => -0.10790539730952 [24] => -0.056505484093897 ) [ConfInt] => 95 [Alpha] => 0.975 [XMean] => 3 [YMean] => -0.61919768852858 [SumXX] => 81.25 [SumXY] => 14.329345079229 [SumYY] => 2.569775322346 [Slope] => 0.17636117020589 [YInt] => -1.1482811991463 [PredictedY] => Array ( [0] => -1.1482811991463 [1] => -1.1041909065948 [2] => -1.0601006140433 [3] => -1.0160103214918 [4] => -0.97192002894037 [5] => -0.9278297363889 [6] => -0.88373944383742 [7] => -0.83964915128595 [8] => -0.79555885873448 [9] => -0.751468566183 [10] => -0.70737827363153 [11] => -0.66328798108006 [12] => -0.61919768852858 [13] => -0.57510739597711 [14] => -0.53101710342564 [15] => -0.48692681087416 [16] => -0.44283651832269 [17] => -0.39874622577122 [18] => -0.35465593321974 [19] => -0.31056564066827 [20] => -0.2664753481168 [21] => -0.22238505556532 [22] => -0.17829476301385 [23] => -0.13420447046238 [24] => -0.090114177910903 ) [Error] => Array ( [0] => 0.077700124860556 [1] => -0.050711053390953 [2] => 0.014343123482642 [3] => -0.029747169068832 [4] => 0.0013038066255798 [5] => -0.0039844018649414 [6] => 0.048092299621861 [7] => -0.01113173605867 [8] => 0.0023847347663266 [9] => -0.0079821855343968 [10] => 0.055683136679691 [11] => -0.014492724186024 [12] => -0.017190331579272 [13] => -0.021772082847072 [14] => 0.034807786482818 [15] => -0.052175346369289 [16] => -0.047960959346207 [17] => -0.063434679155509 [18] => -0.0068548098256192 [19] => -0.08520830624726 [20] => 0.031398332766685 [21] => 0.010553426706491 [22] => 0.076471246511527 [23] => 0.026299073152857 [24] => 0.033608693817006 ) [SquaredError] => Array ( [0] => 0.0060373094033461 [1] => 0.0025716109360201 [2] => 0.00020572519123831 [3] => 0.00088489406760966 [4] => 1.6999117169059E-6 [5] => 1.5875458221349E-5 [6] => 0.0023128692829188 [7] => 0.00012391554767989 [8] => 5.6869599057268E-6 [9] => 6.3715285905533E-5 [10] => 0.0031006117104891 [11] => 0.00021003905433216 [12] => 0.00029550749980532 [13] => 0.00047402359149976 [14] => 0.0012115819998334 [15] => 0.0027222667687552 [16] => 0.0023002536214085 [17] => 0.0040239585195624 [18] => 4.6988417745406E-5 [19] => 0.0072604554535268 [20] => 0.0009858553005275 [21] => 0.00011137481524928 [22] => 0.0058478515430267 [23] => 0.00069164124869934 [24] => 0.0011295443000853 ) [TotalError] => 2.569775322346 [SumError] => -3.663735981263E-15 [SumSquaredError] => 0.042635255889109 [ErrorVariance] => 0.0018537067777873 [StdErr] => 0.043054695188647 [SlopeStdErr] => 0.004776489573912 [SlopeVal] => [YIntStdErr] => 0.016717713508692 [YIntTVal] => -68.686498219343 [R] => 0.9916697816443 [RSquared] => 0.98340895582646 [DF] => 23 [SlopeProb] => [YIntProb] => [AlphaTVal] => [ConfIntOfSlope] => 0 [RPath] => /usr/local/bin/R [format] => %01.2f [SlopeTVal] => 36.922758330539 ) SimpleLinearRegression Object ( [n] => 25 [X] => Array ( [0] => 0 [1] => 0.25 [2] => 0.5 [3] => 0.75 [4] => 1 [5] => 1.25 [6] => 1.5 [7] => 1.75 [8] => 2 [9] => 2.25 [10] => 2.5 [11] => 2.75 [12] => 3 [13] => 3.25 [14] => 3.5 [15] => 3.75 [16] => 4 [17] => 4.25 [18] => 4.5 [19] => 4.75 [20] => 5 [21] => 5.25 [22] => 5.5 [23] => 5.75 [24] => 6 ) [Y] => Array ( [0] => -1.1549019599857 [1] => -1.0457574905607 [2] => -1.0457574905607 [3] => -0.97061622231479 [4] => -0.93181413825384 [5] => -0.83564714421556 [6] => -0.85078088734462 [7] => -0.79317412396815 [8] => -0.7594507517174 [9] => -0.65169513695184 [10] => -0.67778070526608 [11] => -0.63638802010786 [12] => -0.59687947882418 [13] => -0.49620931694282 [14] => -0.53910215724345 [15] => -0.4907974776689 [16] => -0.46218090492673 [17] => -0.36151074304536 [18] => -0.39577394691553 [19] => -0.23507701535011 [20] => -0.21183162885883 [21] => -0.10182351650232 [22] => -0.10790539730952 [23] => -0.056505484093897 [24] => -0.055024091587952 ) [ConfInt] => 95 [Alpha] => 0.975 [XMean] => 3 [YMean] => -0.57857540922067 [SumXX] => 81.25 [SumXY] => 14.55486986634 [SumYY] => 2.6430659694891 [Slope] => 0.17913685989342 [YInt] => -1.1159859889009 [PredictedY] => Array ( [0] => -1.1159859889009 [1] => -1.0712017739276 [2] => -1.0264175589542 [3] => -0.98163334398086 [4] => -0.93684912900751 [5] => -0.89206491403415 [6] => -0.8472806990608 [7] => -0.80249648408744 [8] => -0.75771226911409 [9] => -0.71292805414074 [10] => -0.66814383916738 [11] => -0.62335962419403 [12] => -0.57857540922067 [13] => -0.53379119424732 [14] => -0.48900697927397 [15] => 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0.00064741155605474 [2] => 0.00037403295454259 [3] => 0.00012137696980498 [4] => 2.5351131889519E-5 [5] => 0.0031829647513033 [6] => 1.2251318022207E-5 [7] => 8.6906398193793E-5 [8] => 3.0223217620138E-6 [9] => 0.0037494701474622 [10] => 9.2869188204258E-5 [11] => 0.00016973910008746 [12] => 0.00033503896405009 [13] => 0.0014123975017305 [14] => 0.0025095268557946 [15] => 0.002169203925338 [16] => 0.0039366031861702 [17] => 4.7010340144324E-5 [18] => 0.0073794675851598 [19] => 0.00090053342244033 [20] => 7.1741926144311E-5 [21] => 0.0054307994395395 [22] => 0.00052111129160009 [23] => 0.00086692325019919 [24] => 0.00019207914450204 ) [TotalError] => 2.6430659694891 [SumError] => -3.2265856653169E-15 [SumSquaredError] => 0.035752285475615 [ErrorVariance] => 0.0015544471945919 [StdErr] => 0.039426478343772 [SlopeStdErr] => 0.004373975054752 [SlopeVal] => [YIntStdErr] => 0.015308912691632 [YIntTVal] => -72.897795642333 [R] => 0.99321356063379 [RSquared] => 0.98647317702686 [DF] => 23 [SlopeProb] => [YIntProb] => [AlphaTVal] => [ConfIntOfSlope] => 0 [RPath] => /usr/local/bin/R [format] => %01.2f [SlopeTVal] => 40.955162672635 ) SimpleLinearRegression Object ( [n] => 25 [X] => Array ( [0] => 0 [1] => 0.25 [2] => 0.5 [3] => 0.75 [4] => 1 [5] => 1.25 [6] => 1.5 [7] => 1.75 [8] => 2 [9] => 2.25 [10] => 2.5 [11] => 2.75 [12] => 3 [13] => 3.25 [14] => 3.5 [15] => 3.75 [16] => 4 [17] => 4.25 [18] => 4.5 [19] => 4.75 [20] => 5 [21] => 5.25 [22] => 5.5 [23] => 5.75 [24] => 6 ) [Y] => Array ( [0] => -1.0457574905607 [1] => -1.0457574905607 [2] => -0.97061622231479 [3] => -0.93181413825384 [4] => -0.83564714421556 [5] => -0.85078088734462 [6] => -0.79317412396815 [7] => -0.7594507517174 [8] => -0.65169513695184 [9] => -0.67778070526608 [10] => -0.63638802010786 [11] => -0.59687947882418 [12] => -0.49620931694282 [13] => -0.53910215724345 [14] => -0.4907974776689 [15] => -0.46218090492673 [16] => -0.36151074304536 [17] => -0.39577394691553 [18] => -0.23507701535011 [19] => 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0.0050602896461398 ) [Error] => Array ( [0] => 0.021355405211687 [1] => -0.023318477514084 [2] => 0.0071489080060301 [3] => 0.0012771093412113 [4] => 0.052770220653716 [5] => -0.0070374052011123 [6] => 0.0058954754495866 [7] => -0.0050550350254344 [8] => 0.058026697014356 [9] => -0.012732754025657 [10] => -0.016013951593203 [11] => -0.0211792930353 [12] => 0.034816986120292 [13] => -0.052749736906112 [14] => -0.049118940057328 [15] => -0.065176250040927 [16] => -0.0091799708853351 [17] => -0.088117057481273 [18] => 0.027905991358374 [19] => 0.0064774951238824 [20] => 0.07181172475462 [21] => 0.021055961221653 [22] => 0.027781991711505 [23] => -0.015410498508321 [24] => 0.028765404307171 ) [SquaredError] => Array ( [0] => 0.00045605333175535 [1] => 0.00054375139357483 [2] => 5.1106885678681E-5 [3] => 1.6310082694091E-6 [4] => 0.0027846961878418 [5] => 4.9525071964642E-5 [6] => 3.4756630776678E-5 [7] => 2.5553379108368E-5 [8] => 0.0033670975663958 [9] => 0.00016212302507788 [10] => 0.00025644664562943 [11] => 0.0004485624534751 [12] => 0.0012122225225006 [13] => 0.002782534743664 [14] => 0.0024126702723553 [15] => 0.0042479435693975 [16] => 8.42718654556E-5 [17] => 0.007764615819158 [18] => 0.00077874435369365 [19] => 4.1957943079921E-5 [20] => 0.0051569238122334 [21] => 0.00044335350296777 [22] => 0.00077183906345811 [23] => 0.00023748346427496 [24] => 0.00082744848495498 ) [TotalError] => 2.6294258501315 [SumError] => -1.7139067942651E-15 [SumSquaredError] => 0.034943312996742 [ErrorVariance] => 0.0015192744781192 [StdErr] => 0.038977871646862 [SlopeStdErr] => 0.0043242066101912 [SlopeVal] => [YIntStdErr] => 0.015134723135669 [YIntTVal] => -70.507592785587 [R] => 0.993333110309 [RSquared] => 0.98671066803614 [DF] => 23 [SlopeProb] => [YIntProb] => [AlphaTVal] => [ConfIntOfSlope] => 0 [RPath] => /usr/local/bin/R [format] => %01.2f [SlopeTVal] => 41.324466430891 ) SimpleLinearRegression Object ( [n] => 25 [X] => Array ( [0] => 0 [1] => 0.25 [2] => 0.5 [3] => 0.75 [4] => 1 [5] => 1.25 [6] => 1.5 [7] => 1.75 [8] => 2 [9] => 2.25 [10] => 2.5 [11] => 2.75 [12] => 3 [13] => 3.25 [14] => 3.5 [15] => 3.75 [16] => 4 [17] => 4.25 [18] => 4.5 [19] => 4.75 [20] => 5 [21] => 5.25 [22] => 5.5 [23] => 5.75 [24] => 6 ) [Y] => Array ( [0] => -1.0457574905607 [1] => -0.97061622231479 [2] => -0.93181413825384 [3] => -0.83564714421556 [4] => -0.85078088734462 [5] => -0.79317412396815 [6] => -0.7594507517174 [7] => -0.65169513695184 [8] => -0.67778070526608 [9] => -0.63638802010786 [10] => -0.59687947882418 [11] => -0.49620931694282 [12] => -0.53910215724345 [13] => -0.4907974776689 [14] => -0.46218090492673 [15] => -0.36151074304536 [16] => -0.39577394691553 [17] => -0.23507701535011 [18] => -0.21183162885883 [19] => -0.10182351650232 [20] => -0.10790539730952 [21] => -0.056505484093897 [22] => -0.055024091587952 [23] => 0.03382569395331 [24] => -0.019996628416254 ) [ConfInt] => 95 [Alpha] => 0.975 [XMean] => 3 [YMean] => -0.48999586857733 [SumXX] => 81.25 [SumXY] => 14.379224550449 [SumYY] => 2.5835415692662 [Slope] => 0.17697507139014 [YInt] => -1.0209210827478 [PredictedY] => Array ( [0] => -1.0209210827478 [1] => -0.97667731490022 [2] => -0.93243354705269 [3] => -0.88818977920515 [4] => -0.84394601135762 [5] => -0.79970224351008 [6] => -0.75545847566255 [7] => -0.71121470781501 [8] => -0.66697093996748 [9] => -0.62272717211994 [10] => -0.57848340427241 [11] => -0.53423963642487 [12] => -0.48999586857733 [13] => -0.4457521007298 [14] => -0.40150833288226 [15] => -0.35726456503473 [16] => -0.31302079718719 [17] => -0.26877702933966 [18] => -0.22453326149212 [19] => -0.18028949364459 [20] => -0.13604572579705 [21] => -0.091801957949515 [22] => -0.047558190101979 [23] => -0.0033144222544434 [24] => 0.040929345593092 ) [Error] => Array ( [0] => -0.024836407812915 [1] => 0.0060610925854345 [2] => 0.00061940879885103 [3] => 0.052542634989591 [4] => -0.0068348759870017 [5] => 0.0065281195419326 [6] => -0.003992276054853 [7] => 0.059519570863172 [8] => -0.010809765298604 [9] => -0.013660847987915 [10] => -0.018396074551777 [11] => 0.038030319482051 [12] => -0.049106288666118 [13] => -0.045045376939098 [14] => -0.060672572044463 [15] => -0.004246178010635 [16] => -0.082753149728338 [17] => 0.033700013989545 [18] => 0.012701632633289 [19] => 0.078465977142262 [20] => 0.02814032848753 [21] => 0.035296473855617 [22] => -0.007465901485973 [23] => 0.037140116207754 [24] => -0.060925974009346 ) [SquaredError] => Array ( [0] => 0.00061684715304942 [1] => 3.6736843329209E-5 [2] => 3.8366726009407E-7 [3] => 0.0027607284916494 [4] => 4.6715529757693E-5 [5] => 4.2616344753762E-5 [6] => 1.5938268098152E-5 [7] => 0.0035425793157362 [8] => 0.00011685102581091 [9] => 0.00018661876774892 [10] => 0.00033841555891453 [11] => 0.0014463051999069 [12] => 0.0024114275865601 [13] => 0.0020290859835855 [14] => 0.0036811609984905 [15] => 1.8030027698001E-5 [16] => 0.0068480837899607 [17] => 0.0011356909428955 [18] => 0.00016133147155103 [19] => 0.00615690956889 [20] => 0.00079187808738612 [21] => 0.0012458410666403 [22] => 5.5739684998254E-5 [23] => 0.0013793882319255 [24] => 0.0037119743089875 ) [TotalError] => 2.5835415692662 [SumError] => -6.1131655293423E-15 [SumSquaredError] => 0.038777277915584 [ErrorVariance] => 0.0016859686050254 [StdErr] => 0.041060548036106 [SlopeStdErr] => 0.0045552588105487 [SlopeVal] => [YIntStdErr] => 0.015943405836921 [YIntTVal] => -64.034064815912 [R] => 0.99246695192957 [RSquared] => 0.98499065067236 [DF] => 23 [SlopeProb] => [YIntProb] => [AlphaTVal] => [ConfIntOfSlope] => 0 [RPath] => /usr/local/bin/R [format] => %01.2f [SlopeTVal] => 38.850717105319 ) SimpleLinearRegression Object ( [n] => 25 [X] => Array ( [0] => 0 [1] => 0.25 [2] => 0.5 [3] => 0.75 [4] => 1 [5] => 1.25 [6] => 1.5 [7] => 1.75 [8] => 2 [9] => 2.25 [10] => 2.5 [11] => 2.75 [12] => 3 [13] => 3.25 [14] => 3.5 [15] => 3.75 [16] => 4 [17] => 4.25 [18] => 4.5 [19] => 4.75 [20] => 5 [21] => 5.25 [22] => 5.5 [23] => 5.75 [24] => 6 ) [Y] => Array ( [0] => -0.97061622231479 [1] => -0.93181413825384 [2] => -0.83564714421556 [3] => -0.85078088734462 [4] => -0.79317412396815 [5] => -0.7594507517174 [6] => -0.65169513695184 [7] => -0.67778070526608 [8] => -0.63638802010786 [9] => -0.59687947882418 [10] => -0.49620931694282 [11] => -0.53910215724345 [12] => -0.4907974776689 [13] => -0.46218090492673 [14] => -0.36151074304536 [15] => -0.39577394691553 [16] => -0.23507701535011 [17] => -0.21183162885883 [18] => -0.10182351650232 [19] => -0.10790539730952 [20] => -0.056505484093897 [21] => -0.055024091587952 [22] => 0.03382569395331 [23] => -0.019996628416254 [24] => 0.011147360775797 ) [ConfInt] => 95 [Alpha] => 0.975 [XMean] => 3 [YMean] => -0.44771967452388 [SumXX] => 81.25 [SumXY] => 14.076428967063 [SumYY] => 2.481133210532 [Slope] => 0.17324835651769 [YInt] => -0.96746474407696 [PredictedY] => Array ( [0] => -0.96746474407696 [1] => -0.92415265494753 [2] => -0.88084056581811 [3] => -0.83752847668869 [4] => -0.79421638755926 [5] => -0.75090429842984 [6] => -0.70759220930042 [7] => -0.66428012017099 [8] => -0.62096803104157 [9] => -0.57765594191215 [10] => -0.53434385278272 [11] => -0.4910317636533 [12] => -0.44771967452388 [13] => -0.40440758539445 [14] => -0.36109549626503 [15] => -0.31778340713561 [16] => -0.27447131800618 [17] => -0.23115922887676 [18] => -0.18784713974734 [19] => -0.14453505061791 [20] => -0.10122296148849 [21] => -0.057910872359065 [22] => -0.014598783229642 [23] => 0.028713305899781 [24] => 0.072025395029204 ) [Error] => Array ( [0] => -0.0031514782378351 [1] => -0.0076614833063063 [2] => 0.045193421602546 [3] => -0.013252410655935 [4] => 0.0010422635911117 [5] => -0.0085464532875617 [6] => 0.055897072348576 [7] => -0.013500585095089 [8] => -0.015419989066287 [9] => -0.019223536912037 [10] => 0.038134535839903 [11] => -0.048070393590153 [12] => -0.043077803145022 [13] => -0.057773319532274 [14] => -0.00041524678033394 [15] => -0.077990539779924 [16] => 0.039394302656071 [17] => 0.019327600017926 [18] => 0.086023623245012 [19] => 0.036629653308392 [20] => 0.044717477394591 [21] => 0.0028867807711134 [22] => 0.048424477182952 [23] => -0.048709934316035 [24] => -0.060878034253407 ) [SquaredError] => Array ( [0] => 9.9318150835484E-6 [1] => 5.8698326452811E-5 [2] => 0.0020424453561455 [3] => 0.00017562638819353 [4] => 1.0863133933571E-6 [5] => 7.3041863796473E-5 [6] => 0.003124482697142 [7] => 0.00018226579790973 [8] => 0.00023777606280441 [9] => 0.00036954437140843 [10] => 0.0014542428237249 [11] => 0.0023107627399123 [12] => 0.0018556971238012 [13] => 0.0033377564497782 [14] => 1.7242988857771E-7 [15] => 0.006082524295164 [16] => 0.0015519110817581 [17] => 0.00037355612245295 [18] => 0.0074000637561998 [19] => 0.001341731501493 [20] => 0.0019996527845358 [21] => 8.3335032204699E-6 [22] => 0.0023449299904423 [23] => 0.0023726577010724 [24] => 0.003706135054559 ) [TotalError] => 2.481133210532 [SumError] => -3.5665914666083E-15 [SumSquaredError] => 0.042415026350333 [ErrorVariance] => 0.0018441315804492 [StdErr] => 0.04294335315796 [SlopeStdErr] => 0.0047641372846579 [SlopeVal] => [YIntStdErr] => 0.016674480496303 [YIntTVal] => -58.020682820762 [R] => 0.99141564350623 [RSquared] => 0.98290497818888 [DF] => 23 [SlopeProb] => [YIntProb] => [AlphaTVal] => [ConfIntOfSlope] => 0 [RPath] => /usr/local/bin/R [format] => %01.2f [SlopeTVal] => 36.365105824219 ) SimpleLinearRegression Object ( [n] => 25 [X] => Array ( [0] => 0 [1] => 0.25 [2] => 0.5 [3] => 0.75 [4] => 1 [5] => 1.25 [6] => 1.5 [7] => 1.75 [8] => 2 [9] => 2.25 [10] => 2.5 [11] => 2.75 [12] => 3 [13] => 3.25 [14] => 3.5 [15] => 3.75 [16] => 4 [17] => 4.25 [18] => 4.5 [19] => 4.75 [20] => 5 [21] => 5.25 [22] => 5.5 [23] => 5.75 [24] => 6 ) [Y] => Array ( [0] => -0.93181413825384 [1] => -0.83564714421556 [2] => -0.85078088734462 [3] => -0.79317412396815 [4] => -0.7594507517174 [5] => -0.65169513695184 [6] => -0.67778070526608 [7] => -0.63638802010786 [8] => -0.59687947882418 [9] => -0.49620931694282 [10] => -0.53910215724345 [11] => -0.4907974776689 [12] => -0.46218090492673 [13] => -0.36151074304536 [14] => -0.39577394691553 [15] => -0.23507701535011 [16] => -0.21183162885883 [17] => -0.10182351650232 [18] => -0.10790539730952 [19] => -0.056505484093897 [20] => -0.055024091587952 [21] => 0.03382569395331 [22] => -0.019996628416254 [23] => 0.011147360775797 [24] => 0.03181227133037 ) [ConfInt] => 95 [Alpha] => 0.975 [XMean] => 3 [YMean] => -0.40762253477807 [SumXX] => 81.25 [SumXY] => 13.815611024305 [SumYY] => 2.3974687825402 [Slope] => 0.17003828952991 [YInt] => -0.91773740336779 [PredictedY] => Array ( [0] => -0.91773740336779 [1] => -0.87522783098531 [2] => -0.83271825860283 [3] => -0.79020868622036 [4] => -0.74769911383788 [5] => -0.7051895414554 [6] => -0.66267996907293 [7] => -0.62017039669045 [8] => -0.57766082430797 [9] => -0.5351512519255 [10] => -0.49264167954302 [11] => -0.45013210716055 [12] => 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-0.070680062481278 ) [SquaredError] => Array ( [0] => 0.00019815446505219 [1] => 0.0015666307651648 [2] => 0.00032625855706361 [3] => 8.793821036037E-6 [4] => 0.00013810099285136 [5] => 0.002861651313191 [6] => 0.0002280322335752 [7] => 0.00026301130930874 [8] => 0.00036935668141333 [9] => 0.0015164743001952 [10] => 0.0021585759881522 [11] => 0.0016536723585815 [12] => 0.0029766157532778 [13] => 1.2975984247171E-5 [14] => 0.0053539303974094 [15] => 0.0020265124875642 [16] => 0.00066319725089604 [17] => 0.0086957781631044 [18] => 0.0019944890875622 [19] => 0.0028676072131341 [20] => 0.00015679708129783 [21] => 0.003464744142787 [22] => 0.0014039872207067 [23] => 0.0023848963569756 [24] => 0.0049956712323574 ) [TotalError] => 2.3974687825402 [SumError] => -1.6237011735143E-15 [SumSquaredError] => 0.048285915156905 [ErrorVariance] => 0.0020993876155176 [StdErr] => 0.045819074799887 [SlopeStdErr] => 0.0050831699564711 [SlopeVal] => [YIntStdErr] => 0.017791094847649 [YIntTVal] => -51.584088063533 [R] => 0.98987859213048 [RSquared] => 0.97985962715821 [DF] => 23 [SlopeProb] => [YIntProb] => [AlphaTVal] => [ConfIntOfSlope] => 0 [RPath] => /usr/local/bin/R [format] => %01.2f [SlopeTVal] => 33.451230430224 ) SimpleLinearRegression Object ( [n] => 25 [X] => Array ( [0] => 0 [1] => 0.25 [2] => 0.5 [3] => 0.75 [4] => 1 [5] => 1.25 [6] => 1.5 [7] => 1.75 [8] => 2 [9] => 2.25 [10] => 2.5 [11] => 2.75 [12] => 3 [13] => 3.25 [14] => 3.5 [15] => 3.75 [16] => 4 [17] => 4.25 [18] => 4.5 [19] => 4.75 [20] => 5 [21] => 5.25 [22] => 5.5 [23] => 5.75 [24] => 6 ) [Y] => Array ( [0] => -0.83564714421556 [1] => -0.85078088734462 [2] => -0.79317412396815 [3] => -0.7594507517174 [4] => -0.65169513695184 [5] => -0.67778070526608 [6] => -0.63638802010786 [7] => -0.59687947882418 [8] => -0.49620931694282 [9] => -0.53910215724345 [10] => -0.4907974776689 [11] => -0.46218090492673 [12] => -0.36151074304536 [13] => -0.39577394691553 [14] => -0.23507701535011 [15] => -0.21183162885883 [16] => -0.10182351650232 [17] => -0.10790539730952 [18] => -0.056505484093897 [19] => -0.055024091587952 [20] => 0.03382569395331 [21] => -0.019996628416254 [22] => 0.011147360775797 [23] => 0.03181227133037 [24] => 0.13417710757677 ) [ConfInt] => 95 [Alpha] => 0.975 [XMean] => 3 [YMean] => -0.36498288494484 [SumXX] => 81.25 [SumXY] => 13.737387240073 [SumYY] => 2.370785304394 [Slope] => 0.16907553526244 [YInt] => -0.87220949073216 [PredictedY] => Array ( [0] => -0.87220949073216 [1] => -0.82994060691655 [2] => -0.78767172310094 [3] => -0.74540283928533 [4] => -0.70313395546972 [5] => -0.66086507165411 [6] => -0.6185961878385 [7] => -0.57632730402289 [8] => -0.53405842020728 [9] => -0.49178953639167 [10] => -0.44952065257606 [11] => -0.40725176876045 [12] => -0.36498288494484 [13] => -0.32271400112924 [14] => -0.28044511731363 [15] => -0.23817623349802 [16] => -0.19590734968241 [17] => -0.1536384658668 [18] => -0.11136958205119 [19] => -0.069100698235578 [20] => -0.026831814419969 [21] => 0.015437069395641 [22] => 0.057705953211251 [23] => 0.09997483702686 [24] => 0.14224372084247 ) [Error] => Array ( [0] => 0.036562346516596 [1] => -0.02084028042807 [2] => -0.0055024008672101 [3] => -0.01404791243207 [4] => 0.051438818517882 [5] => -0.016915633611969 [6] => -0.017791832269354 [7] => -0.02055217480129 [8] => 0.037849103264464 [9] => -0.047312620851779 [10] => -0.041276825092833 [11] => -0.054929136166271 [12] => 0.0034721418994821 [13] => -0.073059945786295 [14] => 0.045368101963514 [15] => 0.026344604639184 [16] => 0.094083833180083 [17] => 0.045733068557278 [18] => 0.05486409795729 [19] => 0.014076606647626 [20] => 0.060657508373279 [21] => -0.035433697811895 [22] => -0.046558592435453 [23] => -0.06816256569649 [24] => -0.0080666132657033 ) [SquaredError] => Array ( [0] => 0.0013368051827997 [1] => 0.00043431728832061 [2] => 3.0276415303474E-5 [3] => 0.0001973438436991 [4] => 0.0026459520505156 [5] => 0.00028613866049438 [6] => 0.00031654929550081 [7] => 0.00042239188906276 [8] => 0.0014325546179241 [9] => 0.0022384840918642 [10] => 0.0017037762897443 [11] => 0.0030172099999728 [12] => 1.2055769370139E-5 [13] => 0.0053377556782963 [14] => 0.0020582646757718 [15] => 0.00069403819359491 [16] => 0.0088517676658577 [17] => 0.0020915135596646 [18] => 0.0030100692446671 [19] => 0.00019815085471199 [20] => 0.0036793333220544 [21] => 0.0012555469406247 [22] => 0.0021677025295706 [23] => 0.0046461353623283 [24] => 6.5070249578421E-5 ) [TotalError] => 2.370785304394 [SumError] => -2.9004576518332E-15 [SumSquaredError] => 0.048129203671293 [ErrorVariance] => 0.0020925740726649 [StdErr] => 0.045744661684888 [SlopeStdErr] => 0.0050749145625729 [SlopeVal] => [YIntStdErr] => 0.017762200969005 [YIntTVal] => -49.104809266271 [R] => 0.9897974772089 [RSquared] => 0.9796990458891 [DF] => 23 [SlopeProb] => [YIntProb] => [AlphaTVal] => [ConfIntOfSlope] => 0 [RPath] => /usr/local/bin/R [format] => %01.2f [SlopeTVal] => 33.315937278897 ) SimpleLinearRegression Object ( [n] => 25 [X] => Array ( [0] => 0 [1] => 0.25 [2] => 0.5 [3] => 0.75 [4] => 1 [5] => 1.25 [6] => 1.5 [7] => 1.75 [8] => 2 [9] => 2.25 [10] => 2.5 [11] => 2.75 [12] => 3 [13] => 3.25 [14] => 3.5 [15] => 3.75 [16] => 4 [17] => 4.25 [18] => 4.5 [19] => 4.75 [20] => 5 [21] => 5.25 [22] => 5.5 [23] => 5.75 [24] => 6 ) [Y] => Array ( [0] => -0.85078088734462 [1] => -0.79317412396815 [2] => -0.7594507517174 [3] => -0.65169513695184 [4] => -0.67778070526608 [5] => -0.63638802010786 [6] => -0.59687947882418 [7] => -0.49620931694282 [8] => -0.53910215724345 [9] => -0.4907974776689 [10] => -0.46218090492673 [11] => -0.36151074304536 [12] => -0.39577394691553 [13] => -0.23507701535011 [14] => -0.21183162885883 [15] => -0.10182351650232 [16] => -0.10790539730952 [17] => -0.056505484093897 [18] => -0.055024091587952 [19] => 0.03382569395331 [20] => -0.019996628416254 [21] => 0.011147360775797 [22] => 0.03181227133037 [23] => 0.13417710757677 [24] => 0.06707085604537 ) [ConfInt] => 95 [Alpha] => 0.975 [XMean] => 3 [YMean] => -0.32887416493441 [SumXX] => 81.25 [SumXY] => 13.503889620414 [SumYY] => 2.303334903023 [Slope] => 0.16620171840509 [YInt] => -0.82747932014969 [PredictedY] => Array ( [0] => -0.82747932014969 [1] => -0.78592889054842 [2] => -0.74437846094714 [3] => -0.70282803134587 [4] => -0.6612776017446 [5] => -0.61972717214332 [6] => -0.57817674254205 [7] => -0.53662631294078 [8] => -0.4950758833395 [9] => -0.45352545373823 [10] => -0.41197502413695 [11] => -0.37042459453568 [12] => -0.32887416493441 [13] => -0.28732373533313 [14] => -0.24577330573186 [15] => -0.20422287613059 [16] => -0.16267244652931 [17] => -0.12112201692804 [18] => -0.079571587326766 [19] => -0.038021157725492 [20] => 0.0035292718757812 [21] => 0.045079701477055 [22] => 0.086630131078328 [23] => 0.1281805606796 [24] => 0.16973099028088 ) [Error] => Array ( [0] => -0.02330156719493 [1] => -0.0072452334197334 [2] => -0.015072290770257 [3] => 0.05113289439403 [4] => -0.016503103521485 [5] => -0.016660847964533 [6] => -0.018702736282133 [7] => 0.040416995997957 [8] => -0.04402627390395 [9] => -0.037272023930669 [10] => -0.050205880789771 [11] => 0.0089138514903184 [12] => -0.066899781981122 [13] => 0.052246719983022 [14] => 0.033941676873028 [15] => 0.10239935962826 [16] => 0.054767049219794 [17] => 0.064616532834142 [18] => 0.024547495738814 [19] => 0.071846851678803 [20] => -0.023525900292035 [21] => -0.033932340701257 [22] => -0.054817859747958 [23] => 0.0059965468971644 [24] => -0.10266013423551 ) [SquaredError] => Array ( [0] => 0.00054296303373982 [1] => 5.2493407306421E-5 [2] => 0.00022717394906318 [3] => 0.0026145728891111 [4] => 0.00027235242584084 [5] => 0.00027758385489728 [6] => 0.00034979234443902 [7] => 0.0016335335654988 [8] => 0.0019383127938657 [9] => 0.0013892037678884 [10] => 0.0025206304658767 [11] => 7.9456748391451E-5 [12] => 0.0044755808291217 [13] => 0.0027297197489843 [14] => 0.001152037428953 [15] => 0.010485628852278 [16] => 0.0029994296802433 [17] => 0.0041752963155058 [18] => 0.00060257954704708 [19] => 0.0051619700961559 [20] => 0.00055346798455077 [21] => 0.0011514037454662 [22] => 0.0030049977473468 [23] => 3.5958574689893E-5 [24] => 0.010539103161252 ) [TotalError] => 2.303334903023 [SumError] => -3.4278135885302E-15 [SumSquaredError] => 0.058965242957514 [ErrorVariance] => 0.0025637062155441 [StdErr] => 0.050633054574498 [SlopeStdErr] => 0.0056172330615913 [SlopeVal] => [YIntStdErr] => 0.01966031571557 [YIntTVal] => -42.088811396573 [R] => 0.98711704305162 [RSquared] => 0.97440005668298 [DF] => 23 [SlopeProb] => [YIntProb] => [AlphaTVal] => [ConfIntOfSlope] => 0 [RPath] => /usr/local/bin/R [format] => %01.2f [SlopeTVal] => 29.58782670805 ) SimpleLinearRegression Object ( [n] => 25 [X] => Array ( [0] => 0 [1] => 0.25 [2] => 0.5 [3] => 0.75 [4] => 1 [5] => 1.25 [6] => 1.5 [7] => 1.75 [8] => 2 [9] => 2.25 [10] => 2.5 [11] => 2.75 [12] => 3 [13] => 3.25 [14] => 3.5 [15] => 3.75 [16] => 4 [17] => 4.25 [18] => 4.5 [19] => 4.75 [20] => 5 [21] => 5.25 [22] => 5.5 [23] => 5.75 [24] => 6 ) [Y] => Array ( [0] => -0.79317412396815 [1] => -0.7594507517174 [2] => -0.65169513695184 [3] => -0.67778070526608 [4] => -0.63638802010786 [5] => -0.59687947882418 [6] => -0.49620931694282 [7] => -0.53910215724345 [8] => -0.4907974776689 [9] => -0.46218090492673 [10] => -0.36151074304536 [11] => -0.39577394691553 [12] => -0.23507701535011 [13] => -0.21183162885883 [14] => -0.10182351650232 [15] => -0.10790539730952 [16] => -0.056505484093897 [17] => -0.055024091587952 [18] => 0.03382569395331 [19] => -0.019996628416254 [20] => 0.011147360775797 [21] => 0.03181227133037 [22] => 0.13417710757677 [23] => 0.06707085604537 [24] => 0.1215598441875 ) [ConfInt] => 95 [Alpha] => 0.975 [XMean] => 3 [YMean] => -0.28998053567312 [SumXX] => 81.25 [SumXY] => 13.158994799946 [SumYY] => 2.1960212127718 [Slope] => 0.16195685907626 [YInt] => -0.77585111290191 [PredictedY] => Array ( [0] => -0.77585111290191 [1] => 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0.10717858963267 [15] => 0.060607494056405 [16] => 0.071518192502961 [17] => 0.032510370239841 [18] => 0.080870941012037 [19] => -0.013440596126593 [20] => -0.022785821703608 [21] => -0.042610125918101 [22] => 0.019265495559229 [23] => -0.088329970741233 [24] => -0.074330197368168 ) [SquaredError] => Array ( [0] => 0.00030008671240091 [1] => 0.00058027286701795 [2] => 0.0018643005141555 [3] => 0.00054743068385581 [4] => 0.00050596952155845 [5] => 0.00055104932240255 [6] => 0.0013473676814465 [7] => 0.0021786067554287 [8] => 0.0015101060445112 [9] => 0.0025738093804876 [10] => 8.9268902096057E-5 [11] => 0.0042646380770287 [12] => 0.0030143965438593 [13] => 0.0014182524049411 [14] => 0.011487250075648 [15] => 0.0036732683357972 [16] => 0.0051148518588906 [17] => 0.0010569241731315 [18] => 0.0065401091001724 [19] => 0.00018064962423819 [20] => 0.0005191936707086 [21] => 0.0018156228307564 [22] => 0.00037115931914268 [23] => 0.0078021837311471 [24] => 0.0055249782407909 ) [TotalError] => 2.1960212127718 [SumError] => 1.0824674490095E-15 [SumSquaredError] => 0.064831746371614 [ErrorVariance] => 0.0028187715813745 [StdErr] => 0.053092104699046 [SlopeStdErr] => 0.0058900401789143 [SlopeVal] => [YIntStdErr] => 0.0206151406262 [YIntTVal] => -37.635014330966 [R] => 0.98512823124885 [RSquared] => 0.97047763200348 [DF] => 23 [SlopeProb] => [YIntProb] => [AlphaTVal] => [ConfIntOfSlope] => 0 [RPath] => /usr/local/bin/R [format] => %01.2f [SlopeTVal] => 27.496732476639 ) SimpleLinearRegression Object ( [n] => 25 [X] => Array ( [0] => 0 [1] => 0.25 [2] => 0.5 [3] => 0.75 [4] => 1 [5] => 1.25 [6] => 1.5 [7] => 1.75 [8] => 2 [9] => 2.25 [10] => 2.5 [11] => 2.75 [12] => 3 [13] => 3.25 [14] => 3.5 [15] => 3.75 [16] => 4 [17] => 4.25 [18] => 4.5 [19] => 4.75 [20] => 5 [21] => 5.25 [22] => 5.5 [23] => 5.75 [24] => 6 ) [Y] => Array ( [0] => -0.7594507517174 [1] => -0.65169513695184 [2] => -0.67778070526608 [3] => -0.63638802010786 [4] => -0.59687947882418 [5] => -0.49620931694282 [6] => 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-0.056866223644877 [24] => -0.096122336806629 ) [SquaredError] => Array ( [0] => 0.0012240353680391 [1] => 0.0011231402563655 [2] => 0.0010130468365983 [3] => 0.00088160445432365 [4] => 0.00086667807118689 [5] => 0.0010223783792402 [6] => 0.0025174605135564 [7] => 0.001691326072154 [8] => 0.0026796437302827 [9] => 9.3098827869644E-5 [10] => 0.0040794463455243 [11] => 0.0033143365357735 [12] => 0.0017271960372841 [13] => 0.012613883653061 [14] => 0.0044854568434862 [15] => 0.0062595556039163 [16] => 0.001709213279554 [17] => 0.0082694115836845 [18] => 4.5887228214193E-6 [19] => 0.00010514973349622 [20] => 0.00083206039050522 [21] => 0.0011739714016392 [22] => 0.0051982800225743 [23] => 0.0032337673916292 [24] => 0.0092395036331671 ) [TotalError] => 2.0787133804265 [SumError] => 2.0261570199409E-15 [SumSquaredError] => 0.075358233687733 [ErrorVariance] => 0.0032764449429449 [StdErr] => 0.057240238844234 [SlopeStdErr] => 0.0063502343437751 [SlopeVal] => [YIntStdErr] => 0.022225820203213 [YIntTVal] => -32.595626539947 [R] => 0.98170650168474 [RSquared] => 0.96374765545009 [DF] => 23 [SlopeProb] => [YIntProb] => [AlphaTVal] => [ConfIntOfSlope] => 0 [RPath] => /usr/local/bin/R [format] => %01.2f [SlopeTVal] => 24.727347708189 ) SimpleLinearRegression Object ( [n] => 25 [X] => Array ( [0] => 0 [1] => 0.25 [2] => 0.5 [3] => 0.75 [4] => 1 [5] => 1.25 [6] => 1.5 [7] => 1.75 [8] => 2 [9] => 2.25 [10] => 2.5 [11] => 2.75 [12] => 3 [13] => 3.25 [14] => 3.5 [15] => 3.75 [16] => 4 [17] => 4.25 [18] => 4.5 [19] => 4.75 [20] => 5 [21] => 5.25 [22] => 5.5 [23] => 5.75 [24] => 6 ) [Y] => Array ( [0] => -0.65169513695184 [1] => -0.67778070526608 [2] => -0.63638802010786 [3] => -0.59687947882418 [4] => -0.49620931694282 [5] => -0.53910215724345 [6] => -0.4907974776689 [7] => -0.46218090492673 [8] => -0.36151074304536 [9] => -0.39577394691553 [10] => -0.23507701535011 [11] => -0.21183162885883 [12] => -0.10182351650232 [13] => -0.10790539730952 [14] => -0.056505484093897 [15] => 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GURUFOCUS.COM » STOCK LIST » Technology » Software » Shopify Inc (NYSE:SHOP) » Definitions » Intrinsic Value: Projected FCF

Shopify (Shopify) Intrinsic Value: Projected FCF : $8.84 (As of May. 16, 2024)


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What is Shopify Intrinsic Value: Projected FCF?

Since the intrinsic value calculations based on Discounted Cash Flow Intrinsic Value: DCF (FCF Based), or Discounted Earnings Intrinsic Value: DCF (Earnings Based) cannot be applied to companies without consistent revenue and earnings, GuruFocus developed a valuation model based on normalized Free Cash Flow and Book Value of the company. The details of how we calculate the intrinsic value of stocks are described in detail here.

As of today (2024-05-16), Shopify's Intrinsic Value: Projected FCF is $8.84. The stock price of Shopify is $58.44. Therefore, Shopify's Price-to-Intrinsic-Value-Projected-FCF of today is 6.6.

The historical rank and industry rank for Shopify's Intrinsic Value: Projected FCF or its related term are showing as below:

SHOP' s Price-to-Projected-FCF Range Over the Past 10 Years
Min: 2.05   Med: 13.33   Max: 31.75
Current: 6.61

During the past 12 years, the highest Price-to-Intrinsic-Value-Projected-FCF of Shopify was 31.75. The lowest was 2.05. And the median was 13.33.

SHOP's Price-to-Projected-FCF is ranked worse than
87.92% of 1275 companies
in the Software industry
Industry Median: 1.6 vs SHOP: 6.61

Shopify Intrinsic Value: Projected FCF Historical Data

The historical data trend for Shopify's Intrinsic Value: Projected FCF can be seen below:

* For Operating Data section: All numbers are indicated by the unit behind each term and all currency related amount are in USD.
* For other sections: All numbers are in millions except for per share data, ratio, and percentage. All currency related amount are indicated in the company's associated stock exchange currency.

* Premium members only.

Shopify Intrinsic Value: Projected FCF Chart

Shopify Annual Data
Trend Dec14 Dec15 Dec16 Dec17 Dec18 Dec19 Dec20 Dec21 Dec22 Dec23
Intrinsic Value: Projected FCF
Get a 7-Day Free Trial Premium Member Only Premium Member Only 1.97 4.76 8.49 6.37 8.19

Shopify Quarterly Data
Jun19 Sep19 Dec19 Mar20 Jun20 Sep20 Dec20 Mar21 Jun21 Sep21 Dec21 Mar22 Jun22 Sep22 Dec22 Mar23 Jun23 Sep23 Dec23 Mar24
Intrinsic Value: Projected FCF Get a 7-Day Free Trial Premium Member Only Premium Member Only Premium Member Only Premium Member Only Premium Member Only Premium Member Only Premium Member Only Premium Member Only Premium Member Only Premium Member Only Premium Member Only Premium Member Only 6.58 6.19 7.16 8.19 8.84

Competitive Comparison of Shopify's Intrinsic Value: Projected FCF

For the Software - Application subindustry, Shopify's Price-to-Projected-FCF, along with its competitors' market caps and Price-to-Projected-FCF data, can be viewed below:

* Competitive companies are chosen from companies within the same industry, with headquarter located in same country, with closest market capitalization; x-axis shows the market cap, and y-axis shows the term value; the bigger the dot, the larger the market cap. Note that "N/A" values will not show up in the chart.

Shopify's Price-to-Projected-FCF Distribution in the Software Industry

For the Software industry and Technology sector, Shopify's Price-to-Projected-FCF distribution charts can be found below:

* The bar in red indicates where Shopify's Price-to-Projected-FCF falls into.


Shopify Intrinsic Value: Projected FCF Calculation

Since the intrinsic value calculations based on Discounted Cash Flow Intrinsic Value: DCF (FCF Based), or Discounted Earnings Intrinsic Value: DCF (Earnings Based) cannot be applied to companies without consistent revenue and earnings, GuruFocus developed a valuation model based on normalized Free Cash Flow and Book Value of the company.

The details of how we calculate the intrinsic value of stocks are described in detail here.

This method smooths out the free cash flow over the past 6-7 years, multiplies the results by a growth multiple, and adds a portion of Total Stockholders Equity.

Intrinsic Value: Projected FCF = ( Growth Multiple * Free Cash Flow (6 year avg) + 0.8 * Total Stockholders Equity (most recent) ) / Shares Outstanding (Diluted Average)

In the case of negative Total Stockholders Equity, the following formula is used (see Explanation section below for the reason):

Intrinsic Value: Projected FCF = ( Growth Multiple * Free Cash Flow (6 year avg) + Total Stockholders Equity (most recent) / 0.8 ) / Shares Outstanding (Diluted Average)


Add all the Free Cash Flow together and divide 6 will get Shopify's Free Cash Flow(6 year avg) = $287.18.

Shopify's Intrinsic Value: Projected FCF for today is calculated as

Intrinsic Value: Projected FCF=(Growth Multiple*Free Cash Flow (6 year avg)+Total Stockholders Equity (Mar24)*0.8)/Shares Outstanding (Diluted Average)
=(14.862653310476*287.18128+8893*0.8)/1287.377
=8.84

* For Operating Data section: All numbers are indicated by the unit behind each term and all currency related amount are in USD.
* For other sections: All numbers are in millions except for per share data, ratio, and percentage. All currency related amount are indicated in the company's associated stock exchange currency.

Shopify  (NYSE:SHOP) Intrinsic Value: Projected FCF Explanation

The growth multiple is capped between 8.35 and 17.74.

Total Stockholders Equity weighting is more art than science and it should always be revisited in more detail when researching a company. Weightings from 0% to 100% to more than 100% are possible. 80% was chosen as a happy median after taking the above ideas into consideration.

Shopify's Price-to-Intrinsic-Value-Projected-FCF for today is calculated as

Price-to-Intrinsic-Value-Projected-FCF=Share Price/Intrinsic Value: Projected FCF
=58.44/8.8417579325238
=6.61

* For Operating Data section: All numbers are indicated by the unit behind each term and all currency related amount are in USD.
* For other sections: All numbers are in millions except for per share data, ratio, and percentage. All currency related amount are indicated in the company's associated stock exchange currency.

Shopify Intrinsic Value: Projected FCF Related Terms

Thank you for viewing the detailed overview of Shopify's Intrinsic Value: Projected FCF provided by GuruFocus.com. Please click on the following links to see related term pages.

Shopify (Shopify) Business Description

Industry
GURUFOCUS.COM » STOCK LIST » Technology » Software » Shopify Inc (NYSE:SHOP) » Definitions » Intrinsic Value: Projected FCF
Comparable Companies
CDNS WDAY ROP SNOW TEAM ADSK TTD UBER DDOG ANSS CRM XTER:SAP INTU NOW XPAR:DSY TSX:CSU FICO HUBS ZM SHSE:688111
Traded in Other Exchanges
SHOP:Mexico 307:Germany 307:Germany SHOP:Canada S2HO34:Brazil
Address
151 O'Connor Street, Ground Floor, Ottawa, ON, CAN, K2P2L8
Website
https://www.shopify.com
Shopify offers an e-commerce platform primarily to small and medium-size businesses. The firm has two segments. The subscription solutions segment allows Shopify merchants to conduct e-commerce on a variety of platforms, including the company's website, physical stores, pop-up stores, kiosks, social networks (Facebook), and Amazon. The merchant solutions segment offers add-on products for the platform that facilitate e-commerce and include Shopify Payments, Shopify Shipping, and Shopify Capital.

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