- =6$ &GSP! ?N  xl\"lx $lx4vxl  A (m ^@p<< Negative Areasasp 8 =!aC Ps8reas ^@p<< Negative Areasasp 8 =!aC Ps.,> ^@p<< Positive Areasasp 8 =!aC PseQs ^@p<< Positive Areasasp 8 =!aC Ps8F=KU A^@p<<BC8= B^@p<<CCBG p1^@p<<CC| p2^@p<<CCg&+B P p3^@p<<CVCsx F p4^@p<<BCxBgN p5^@p<<C{Cl/ /+ p6^@p<<CVCG3@^  p6^@p<<I h Utu./VThe six data points determine a mean point. Drag the points around to see the effect of their position on the mean. Each data point is used to construct a rectangle with the mean as its other corner. The (signed and normalized) sum of the areas of the rectangles is the correlation coefficient (r). 1) Move the data points so that r = 1. 2) Move the data points so that r = -1. 3) Find three ways to produce a correlation coefficient (r) of zero.at ojɜP floz'g s 3rEk  p6^@p<<  !<GBill Finzer From an idea by Gail Burrill and Dick Schaeffer March, 199393k3Y0k@ɜP0ɜP20v p6^@p<< %Correlation Coefficient Visualization0kdUUU`T@kNt0k7='BgBg j6^@p<<BCCC?E'K m6^@p<<BCBD1@?~' n6^@p<<CCCD3?' p6^@p<<CCgCD?' q6^@p<<CVCCVD,? r'x^  r6^@p<<BCxBD ? ' s6^@p<<C{ClC{D? ' t6^@p<<CVCGCVD? 8= K6^@p<<CC8= L6^@p<<CC8= M6^@p<<CVC8s=x N6^@p<<BC8= P6^@p<<C{C8= Q6^@p<<CVCAG' u6^@p<<CCÅC?' v6^@p<<CCgwCg?%+'C w6^@p<<CVC5C? ' x6^@p<<BCxËCx? 'ntly y6^@p<<C{ClCl? 'hat  z6^@p<<CVCG5CG? BFGK( A^@p<<BCBFGK R^@p<<BCFK S^@p<<BCg&F+K T^@p<<BC FK U^@p<<BCx!FK V^@p<<BCl"FK W^@p<<BCG#FKp A@p<<BCq$8= A@p<<CC%FKne y AՀp<<BC_+ 8= AՀp<<CMC,&FKto d A՛p<<BC- 8Y=^ A՛p<<CC.' MFRK for Ap<<BB/ 8=Us Ap<<CC0( FK_ A<<B1 89=> A<<DC2) FK>* A<<BC38=p A<<D2@C4* 'ble  red< <BCáCi9m 58=>* A<<C2VC6' | blue<<C2VCC2VD1@,%8~' dlue<<CCCŽ?7'UU flue<<CCgC$?7' hlue<<CVCCV?7 r'x klue<<BCxB?7 'mh k1ue<<C{ClC{?7 ' n1ue<<CVCGCVD?7 AG' r1ue<<CCÅC?7' t1ue<<CCgwCg?7%+'W v1ue<<CVC5C?7 'O x1ue<<BCxËCx?7 ']B z1ue<<C{ClCl?7 ' b1ue<<CVCG5CG?7 < (meanX, meanY)<<C2VC79@m$ B1eanX, meanY)<<CC7:AG'm  e1eanX, meanY)<<CCÅC?9C D1eanX, meanY)<<CC;7'veme g1eanX, meanY)<<CCgwCg?9( F1eanX, meanY)<<CVC<7%+' j1eanX, meanY)<<CVC5C?9 sx H1eanX, meanY)<<BC=7'U j1eanX, meanY)<<BCxËCx?9 j K1eanX, meanY)<<C{C>7' m1eanX, meanY)<<C{ClCl?9  M1eanX, meanY)<<CVC?7'^,, p1eanX, meanY)<<CVCG5CG?9 ~'@ d1eanX, meanY)<<CCCD3?9'@g f1eanX, meanY)<<CCgCD?9'3 h1eanX, meanY)<<CVCCVD,?9 r'xo0@ k1eanX, meanY)<<BCxBD ?9 '@ k2eanX, meanY)<<C{ClC{D?9 'Jn n2eanX, meanY)<<CVCGCVD?9 H red unitmeanY)< <CzVCFH blue uniteanY)< <C2VC7FBG C1ue uniteanY)<<C2VC9H E1ue uniteanY)<<C2VCgJ9&+H G1ue uniteanY)<<C2VCL9 J1ue uniteanY)<<C2VCxN9@o  L1ue uniteanY)<<C2VClP9mT@ N1ue uniteanY)<<C2VCGR9=E*e 11ue uniteanY)<<CCB?5%F?5%FG{ 21ue uniteanY)<<CCAUX?5%F?5%FI)  31ue uniteanY)<<CVCB!UT?5%F?5%FK m~ 41ue uniteanY)<<BC@U`?5%F?5%FM  51ue uniteanY)<<C{CAUX?5%F?5%FO 9 61ue uniteanY)<<CVCBb?5%F?5%FQ ;Q 21ue uniteanY)<<  %1Ratio((meanX, meanY)B1/(meanX, meanY)red unit) = @+0 -@xz@@'$-0.690 x@ FYG;(Tffff 31ue uniteanY)<<  ^Ѐ2Ratio((meanX, meanY)C1/(meanX, meanY)blue unit) = @+0 -@xz@@'$-0.950 x@ FZ[Em E21ue uniteanY)< <CCC2VCC2VCCCGF[6;BQ 51ue uniteanY)<<  hK1Ratio((meanX, meanY)D1/(meanX, meanY)red unit) = @+0 -@xz@@'$-0.430 x@ FYIC;ONCu 61ue uniteanY)<<  ? 2Ratio((meanX, meanY)E1/(meanX, meanY)blue unit) = @+0 -@xz@@'$0.3430 x@ FZ\Nu + g @#31ue uniteanY)<<CCC2VCC2VCgCCgIF\B;NK8 81ue uniteanY)<<  ?B_ 1Ratio((meanX, meanY)F1/(meanX, meanY)red unit) = @+0 -@xz@@'$0.4930 x@ FYKO;[T 91ue uniteanY)<<  `2Ratio((meanX, meanY)G1/(meanX, meanY)blue unit) = @+0 -@xz@@'$-0.560 x@ FZ])( 41ue uniteanY)<<CVCC2VCC2VCCVCKF] \<hRmH 11ue uniteanY)<<  {B@1Ratio((meanX, meanY)H1/(meanX, meanY)red unit) = @+0 -@xz@@'$-0.860 x@ FYMi<uP 12ue uniteanY)<<  ?B`2Ratio((meanX, meanY)J1/(meanX, meanY)blue unit) = @+0 -@xz@@'$0.1160 x@ FZ^u4 ((52ue uniteanY)<<BCC2VCC2VCxBCxMF^ [<gM 14ue uniteanY)<<  ? {`1Ratio((meanX, meanY)K1/(meanX, meanY)red unit) = @+0 -@xz@@'$1.0060 x@ FYOh<tOo( 15ue uniteanY)<<  ?{B2Ratio((meanX, meanY)L1/(meanX, meanY)blue unit) = @+0 -@xz@@'$0.2760 x@ FZ_ Y65ue uniteanY)<<C{CC2VCC2VClC{ClOF_ u<O 17ue uniteanY)<<  ?B_ 1Ratio((meanX, meanY)M1/(meanX, meanY)red unit) = @+0 -@xz@@'$0.4960 x@ FYQ<P 18ue uniteanY)<<  ?/h2Ratio((meanX, meanY)N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$0.7960 x@ FZ` 78ue uniteanY)<<CVCC2VCC2VCGCVCGQF`  P1ue uniteanY)< <CEUVC7a R1ue uniteanY)< <C,C7b$ T1ue uniteanY)< <C~UVC7c{ V1ue uniteanY)< <BUXC7d  X1ue uniteanY)< <CUVC7e o @ Z1ue uniteanY)< <CUVC7fw@ 71ue uniteanY)<<C2VCBGUX?5%F?5%F[ 81ue uniteanY)<<C2VCgA?5%F?5%F\L 91ue uniteanY)<<C2VCB ?5%F?5%F] u7 10ue uniteanY)<<C2VCxBwUX?5%F?5%F^ k5 11ue uniteanY)<<C2VClBUT?5%F?5%F_  12ue uniteanY)<<C2VCGB ?5%F?5%F` );5, 42ue uniteanY)<<  ?-c area 1 = anX, meanY)N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$0.6660 x@ gh5;A 72ue uniteanY)<<  vT area 2 = anX, meanY)N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$-0.150 x@ jkB<N 10ue uniteanY)<<  тA` area 3 = anX, meanY)N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$-0.270 x@ mnN<Z 13ue uniteanY)<<  ij area 4 = anX, meanY)N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$-0.090 x@ pqZ<fu 16ue uniteanY)<<  ?х area 5 = anX, meanY)N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$0.2790 x@ stf<r 19ue uniteanY)<<  ?ؚ)u area 6 = anX, meanY)N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$0.3890 x@ vw>LQ Show RectsanY)<< xruoliPMc Hide RectsanY)<< xruoli'nge  q1de RectsanY)<<CEUUCCEUU UU?7y' s1de RectsanY)<<C,CC, UU?7z' u1de RectsanY)<<C~UUCC~UU UU?7{z'@ w1de RectsanY)<<BUZCBUZ UU?7| '0 y1de RectsanY)<<CUVCCUV UU?7} ' a1de RectsanY)<<CUVCCUV UU?7~ B2de RectsanY)< <C2VCU9 D2de RectsanY)< <C2VCH*9@^ F2de RectsanY)< <C2VCj9@oT H2de RectsanY)< <C2VC:*9 K2de RectsanY)< <C2VC#V9N2 M2de RectsanY)< <C2VC#V9o 20de RectsanY)<<  ?鴬Y0sum of areas = eanY)N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$0.8090 x@  BG Q1de RectsanY)<<CEUUC@@ S1de RectsanY)<<C,CgA&+t) = U1de RectsanY)<<C~UUCB{ W1de RectsanY)<<BUZCxC mC@ Y1de RectsanY)<<CUVClD ww A2de RectsanY)<<CUVCGE'$ c1de RectsanY)<<C2VCUX*CU?9'x e1de RectsanY)<<C2VCH*X*CH*?9'] g1de RectsanY)<<C2VCjX*Cj?9'% j1de RectsanY)<<C2VC:*X*C:*?9'@p j2de RectsanY)<<C2VC#VX*C#V?9'YO/ m2de RectsanY)<<C2VC#VX*C#V?9Etor 5->p682de RectsanY)<<CCCEUVCCEUUCCCGy 92de RectsanY)<<CCC,CC,CgCCgIz)ox@ @oP10de RectsanY)<<CVCC~UVCC~UUCCVCK{ u~ '11de RectsanY)<<BCBUXCBUZCxBCxM| C Cw@12de RectsanY)<<C{CCUVCCUVClC{ClO}  13de RectsanY)<<CVCCUVCCUVCGCVCGQ~  C2de RectsanY)<<CCUS@^| E2de RectsanY)<<CCH*T G2de RectsanY)<<CVCjUsx J2de RectsanY)<<BC:*V P0, L2de RectsanY)<<C{C#VWd< N2de RectsanY)<<CVC#VXw 21de RectsanY)<< @RArea(Polygon 8) = Y)N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$5.08 square cm x@ )w 22de RectsanY)<< ?/ugArea(Polygon 9) = Y)N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$0.66 square cm x@ *6}((88 23de RectsanY)<< ?R c@Area(Polygon 10) = )N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$1.77 square cm x@ 7C} 24de RectsanY)<< ?_JpArea(Polygon 11) = )N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$0.06 square cm x@ DP} 25de RectsanY)<< ?f"Area(Polygon 12) = )N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$0.42 square cm x@ Q]} 26de RectsanY)<< @ Area(Polygon 13) = )N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$3.49 square cm x@ E n14de RectsanY)<<C2VCC2VCUCCUCC[_4 @^415de RectsanY)<<C2VCgC2VCH*CCH*CCg\)@ @m816de RectsanY)<<C2VCC2VCjCVCjCVC] u @^ @17de RectsanY)<<C2VCxC2VC:*BC:*BCx^  m /#18de RectsanY)<<C2VClC2VC#VC{C#VC{Cl_ Hn H.19de RectsanY)<<C2VCGC2VC#VCVC#VCVCG` p 27de RectsanY)<<  ?Aǣ|sy = Polygon 13) = )N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$1.52 square cm x@ 5!{ 28de RectsanY)<< @6DArea(Polygon 14) = )N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$2.70 square cm x@ ".{" 29de RectsanY)<< ?GArea(Polygon 15) = )N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$1.03 square cm x@ /;{o 30de RectsanY)<< ?\Area(Polygon 16) = )N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$1.35 square cm x@ <H{g* 31de RectsanY)<< @6}y'Area(Polygon 17) = )N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$4.16 square cm x@ IU{gv 32de RectsanY)<< @]Area(Polygon 18) = )N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$5.67 square cm x@ Vb{( 33de RectsanY)<< ?\Area(Polygon 19) = )N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$1.35 square cm x@ p, 34de RectsanY)<<  ?p8csx = Polygon 19) = )N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$1.80 square cm x@ 5p, 35de RectsanY)<<  ?yzur = Polygon 19) = )N1/(meanX, meanY)blue unit) = @+0 -@xz@@'$0.06 square cm x@ YZ