{"version":9,"randomSeed":"52f14dc98b1be89bc063fedcd903d661","graph":{"viewport":{"xmin":-0.23818579423035202,"ymin":-0.8295294414902286,"xmax":3.209207025322897,"ymax":3.4283654876934424}},"expressions":{"list":[{"type":"text","id":"11","text":"datasets, intended to be mostly but not unambiguously negatively correlated"},{"type":"expression","id":"1","color":"#c74440","latex":"A=\\left[1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,1,1,0,0\\right]","labelSize":"medium"},{"type":"expression","id":"5","color":"#000000","latex":"B=\\left[0,1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1\\right]"},{"type":"text","id":"9","text":"https://en.wikipedia.org/wiki/Correlation#Pearson%27s_product-moment_coefficient"},{"type":"expression","id":"12","color":"#000000","latex":"E\\left(v\\right)=\\frac{1}{\\operatorname{length}\\left(v\\right)}\\sum_{k=1}^{\\operatorname{length}\\left(v\\right)}v\\left[k\\right]","labelSize":"medium"},{"type":"expression","id":"13","color":"#c74440","latex":"\\frac{E\\left(A\\cdot B\\right)-E\\left(A\\right)\\cdot E\\left(B\\right)}{\\sqrt{E\\left(A^{2}\\right)-E\\left(A\\right)^{2}}\\cdot\\sqrt{E\\left(B^{2}\\right)-E\\left(B\\right)^{2}}}","labelSize":"medium"},{"type":"expression","id":"7","color":"#2d70b3","latex":"\\frac{\\frac{\\operatorname{total}\\left(AB\\right)}{\\operatorname{length}\\left(A\\right)}-\\frac{\\operatorname{total}\\left(A\\right)}{\\operatorname{length}\\left(A\\right)}\\cdot\\frac{\\operatorname{total}\\left(B\\right)}{\\operatorname{length}\\left(B\\right)}}{\\sqrt{\\frac{\\operatorname{total}\\left(A\\right)}{\\operatorname{length}\\left(A\\right)}-\\left(\\frac{\\operatorname{total}\\left(A\\right)}{\\operatorname{length}\\left(A\\right)}\\right)^{2}}\\cdot\\sqrt{\\frac{\\operatorname{total}\\left(B\\right)}{\\operatorname{length}\\left(B\\right)}-\\left(\\frac{\\operatorname{total}\\left(B\\right)}{\\operatorname{length}\\left(B\\right)}\\right)^{2}}}"},{"type":"expression","id":"14","color":"#2d70b3","latex":"\\frac{\\frac{1}{\\operatorname{length}\\left(A\\right)}\\cdot\\left(\\operatorname{total}\\left(AB\\right)-\\frac{\\operatorname{total}\\left(A\\right)\\operatorname{total}\\left(B\\right)}{\\operatorname{length}\\left(A\\right)}\\right)}{\\sqrt{\\frac{\\operatorname{total}\\left(A\\right)}{\\operatorname{length}\\left(A\\right)}\\cdot\\left(1-\\frac{\\operatorname{total}\\left(A\\right)}{\\operatorname{length}\\left(A\\right)}\\right)}\\cdot\\sqrt{\\frac{\\operatorname{total}\\left(B\\right)}{\\operatorname{length}\\left(B\\right)}\\cdot\\left(1-\\frac{\\operatorname{total}\\left(B\\right)}{\\operatorname{length}\\left(B\\right)}\\right)}}"},{"type":"expression","id":"15","color":"#000000","latex":"\\left(1,1\\right)","pointOpacity":"1","pointSize":"E\\left(\\left(1-A\\right)\\left(1-B\\right)\\right)"},{"type":"expression","id":"23","color":"#000000","latex":"\\left(2,1\\right)","pointOpacity":"1","pointSize":"100E\\left(A\\left(1-B\\right)\\right)"},{"type":"expression","id":"22","color":"#000000","latex":"\\left(1,2\\right)","pointOpacity":"1","pointSize":"100E\\left(\\left(1-A\\right)B\\right)"},{"type":"expression","id":"21","color":"#000000","latex":"\\left(2,2\\right)","pointOpacity":"1","pointSize":"100E\\left(AB\\right)"}]}}