[{"data":1,"prerenderedAt":327},["ShallowReactive",2],{"/matrix/forecast-compound-growth":3,"/matrix/forecast-compound-growth-surround":316},{"id":4,"title":5,"body":6,"description":284,"extension":285,"meta":286,"navigation":303,"path":79,"seo":313,"stem":314,"__hash__":315},"content/matrix/forecast-compound-growth.md","Matrix Extension Dictionary: forecast-compound-growth",{"type":7,"value":8,"toc":273},"minimark",[9],[10,11,15,16,15,26,47,51,61,99,111,144,169],"div",{"className":12,"id":14},[13],"dict_entry","forecast-compound-growth","\n  ",[17,18,20,21,15],"h3",{"id":19},"matrixforecast-compound-growth","\n    ",[22,23,25],"a",{"href":24},"#forecast-compound-growth","matrix:forecast-compound-growth",[27,28,32],"h4",{"id":29,"className":30},"matrixforecast-compound-growth-data-list",[31],"section-heading",[22,33,20,37,15],{"className":34,"href":36},[35],"section-anchor","#----matrixforecast-compound-growth-data-list--",[38,39,42,43],"span",{"className":40},[41],"prim_example","matrix:forecast-compound-growth ",[44,45,46],"i",{},"data-list",[48,49,50],"p",{},"Reports a four-element list of the form:",[52,53,54],"tt",{},[38,55,56,57],{}," forecast constant growth-proportion R",[58,59,60],"sup",{},"2",[48,62,63,64,76,77,84,85,89,90,94,95,98],{},"Whereas ",[65,66,69],"primitive",{"displayText":67,"permalink":68},"matrix:forecast-linear-growth","/matrix/forecast-linear-growth",[22,70,67],{"className":71,"dataDisplayText":67,"href":68,"rel":73,"target":75,"title":67},[72],"netlogo-wiki-link",[74],"noopener","_self","\nassumes growth by a constant absolute amount each period, ",[65,78,80],{"displayText":25,"permalink":79},"/matrix/forecast-compound-growth",[22,81,25],{"className":82,"dataDisplayText":25,"href":79,"rel":83,"target":75,"title":25},[72],[74],"\nassumes that Y grows by a constant ",[86,87,88],"strong",{},"proportion"," each period.\nThe ",[91,92,93],"em",{},"constant"," and ",[91,96,97],{},"growth-proportion"," are the parameters\nof the trend-line",[52,100,101,102,104,105,107,110],{},"\nY = \n",[91,103,93],{},"\n * \n",[91,106,97],{},[58,108,109],{},"\nt\n","\n.\n",[48,112,113,114,116,117,120,121,127,128,130,131,137,138,140,141,143],{},"Note that the growth proportion is typically interpreted as\n",[91,115,97],{}," = ",[91,118,119],{},"(1.0 + growth-rate)",". Therefore,\nif ",[65,122,123],{"displayText":25,"permalink":79},[22,124,25],{"className":125,"dataDisplayText":25,"href":79,"rel":126,"target":75,"title":25},[72],[74],"\nreturns a ",[91,129,97],{}," of 1.10, that implies that Y\ngrows by (1.10 - 1.0) = 10% each period. Note that if growth is\nnegative, ",[65,132,133],{"displayText":25,"permalink":79},[22,134,25],{"className":135,"dataDisplayText":25,"href":79,"rel":136,"target":75,"title":25},[72],[74],"\nwill return a ",[91,139,97],{}," of less than one. E.g., a\n",[91,142,97],{}," of 0.90 implies a growth rate of -10%.",[48,145,146,149,150,158,159,165,166,168],{},[86,147,148],{},"NOTE:"," The compound growth forecast is achieved by taking the\nln of Y. (See ",[65,151,154],{"displayText":152,"permalink":153},"matrix:regress","/matrix/regress",[22,155,152],{"className":156,"dataDisplayText":152,"href":153,"rel":157,"target":75,"title":152},[72],[74],", below.)\nBecause it is impossible to take the natural log of zero or a\nnegative number, ",[65,160,161],{"displayText":25,"permalink":79},[22,162,25],{"className":163,"dataDisplayText":25,"href":79,"rel":164,"target":75,"title":25},[72],[74],"\nwill result in an error if it finds a zero or negative number in\n",[91,167,46],{},".",[170,171,172],"pre",{},[173,174,175,181,184,189,190,194,195,189,200,189,204,189,208,189,212,189,216,220,221,223,194,227,189,231,189,235,189,239,220,243,245,249,251,255,257,261,263,267,269],"code",{},[38,176,180],{"className":177},[178,179],"token","comment",";; a compound growth extrapolation of the next item in the list.",[182,183],"br",{},[38,185,188],{"className":186},[178,187],"command","print"," ",[38,191,25],{"className":192},[178,193],"variable"," [",[38,196,199],{"className":197},[178,198],"number","20",[38,201,203],{"className":202},[178,198],"25",[38,205,207],{"className":206},[178,198],"28",[38,209,211],{"className":210},[178,198],"32",[38,213,215],{"className":214},[178,198],"35",[38,217,219],{"className":218},[178,198],"39","]",[182,222],{},[38,224,226],{"className":225},[178,193],"=>",[38,228,230],{"className":229},[178,198],"45.60964465307147",[38,232,234],{"className":233},[178,198],"21.15254147944863",[38,236,238],{"className":237},[178,198],"1.136621034423892",[38,240,242],{"className":241},[178,198],"0.9760867518334806",[182,244],{},[38,246,248],{"className":247},[178,179],";; These results tell us:",[182,250],{},[38,252,254],{"className":253},[178,179],";; * the next predicted value is approximately 45.610",[182,256],{},[38,258,260],{"className":259},[178,179],";; * the compound growth trend line is given by Y = 21.1525 * 1.1366 ^ t",[182,262],{},[38,264,266],{"className":265},[178,179],";; * Y grows by approximately 13.66% each period",[182,268],{},[38,270,272],{"className":271},[178,179],";; * the R^2 value is roughly 0.9761 (a good fit)",{"title":274,"searchDepth":275,"depth":276,"links":277},"",5,3,[278],{"id":19,"depth":276,"text":279,"children":280},"\n    matrix:forecast-compound-growth\n  ",[281],{"id":29,"depth":282,"text":283},4,"\n    matrix:forecast-compound-growth data-list\n  ","Documentation for the forecast-compound-growth primitive.","md",{"source":287,"metadataOutputPath":288,"projectConfig":289,"language":296,"inheritFrom":304,"output":303,"version":290,"layout":305,"dictionaryDisplayName":306,"dictionaryHomeDirectory":307,"indexFileURI":308,"currentItemId":14,"currentItemLabel":25,"primRoot":309,"icon":310,"extensionName":311,"assetsRoot":291},"../../external/extensions/matrix/matrix/forecast-compound-growth.md","content/matrix/forecast-compound-growth.metadata.yaml",{"version":290,"projectRoot":168,"scanRoot":291,"outputRoot":292,"defaults":293,"engine":299,"partials":300,"dedupeIdenticalDiskWrites":303},"7.0.4","/home/runner/work/Helio/Helio/external/extensions/matrix","content",{"inheritFrom":294,"language":296,"output":297,"extension":285,"title":298,"version":290},[295],0,"en",false,"NetLogo User Manual","mustache",{"directoryPaths":301,"extensions":302},[168],[299,285],true,[295],"catalog","Matrix Extension Dictionary","/matrix.html","/_index/extensions/matrix.txt","matrix","i-mdi-matrix",{"shortName":309,"fullName":312},"Matrix",{"title":5,"description":284},"matrix/forecast-compound-growth","agwPt6g8X-Qnad8Y0O_vKrmJbmLOyzwtUiory3V7OFU",[317,322],{"title":318,"path":319,"stem":320,"description":321},"Matrix Extension Dictionary: eigenvectors","/matrix/eigenvectors","matrix/eigenvectors","Documentation for the eigenvectors primitive.",{"title":323,"path":324,"stem":325,"description":326},"Matrix Extension Dictionary: forecast-continuous-growth","/matrix/forecast-continuous-growth","matrix/forecast-continuous-growth","Documentation for the forecast-continuous-growth primitive.",1777657876684]