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{"sheet":"45","index":1,"n_rows":39,"n_cols":9,"rows_kept":39,"cut":false,"hidden":false,"merged":[]}
["Count",{"$f":"COUNT(B9:B13)","v":5},{"$f":"COUNT(C9:C13)","v":5}]
["Count -1",{"$f":"B1-1","v":4},4]
["Mean",{"$f":"AVERAGE(B9:B13)","v":8},{"$f":"AVERAGE(C9:C13)","v":46}]
["SD",{"$f":"_xlfn.STDEV.S(B9:B13)","v":5.4313902456001077},{"$f":"_xlfn.STDEV.S(C9:C13)","v":11.401754250991379}]
["Covariance",{"$f":"_xlfn.COVARIANCE.S(C9:C13,B9:B13)","v":-60}]
["Coefficient of Correlation",{"$f":"CORREL(C9:C13,B9:B13)","v":-0.96887682119787466},{"$f":"B6=H21","v":true}]
[]
[null,"xi","yi","xi - Xbar","(xi - Xbar)^2","yi - Ybar","(yi - Ybar)^2","(xi - Xbar)*(yi - Ybar)"]
[null,4,50,{"$f":"B9-$B$3","v":-4},{"$f":"D9^2","v":16},{"$f":"C9-$C$3","v":4},{"$f":"F9^2","v":16},{"$f":"D9*F9","v":-16}]
[null,6,50,{"$f":"B10-$B$3","v":-2},{"$f":"D10^2","v":4},{"$f":"C10-$C$3","v":4},{"$f":"F10^2","v":16},-8]
[null,11,40,{"$f":"B11-$B$3","v":3},9,{"$f":"C11-$C$3","v":-6},36,-18]
[null,3,60,{"$f":"B12-$B$3","v":-5},25,{"$f":"C12-$C$3","v":14},196,-70]
[null,16,30,{"$f":"B13-$B$3","v":8},64,{"$f":"C13-$C$3","v":-16},256,-128]
[]
[null,null,null,null,null,null,"Variancex",{"$f":"SUM(E9:E13)/$C$2","v":29.5}]
[null,null,null,null,null,null,"SDx",{"$f":"H15^(1/2)","v":5.4313902456001077}]
[null,null,null,null,null,null,"Variancey",{"$f":"SUM(G9:G13)/$C$2","v":130}]
[null,null,null,null,null,null,"SDy",{"$f":"H17^(1/2)","v":11.401754250991379}]
[null,null,null,null,null,null,"Total (xi - Xbar)*(yi - Ybar)",{"$f":"SUM(H9:H13)","v":-240}]
[null,null,null,null,null,null,"Covariance",{"$f":"H19/B2","v":-60}," Tells us there is a negative relationship, but because of the units we must go one step further and calculation rxy"]
[null,null,null,null,null,null,"Coefficient of Correlation",{"$f":"H20/(H16*H18)","v":-0.96887682119787455},"tells us that there is a strong negative relationship between the two variables. As x increated, y decreases"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,"Xbar","y","x","Yabr"]
[null,null,{"$f":"$B$3","v":8},20,0,{"$f":"$C$3","v":46}]
[null,null,8,70,20,46]

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["Xbar",{"$f":"AVERAGE(B8:B34)","v":6.8148148148148138E-2},6.3307407407407409E-2,null,null,null,null,null,null,"Xbar",{"$f":"AVERAGE(K8:K34)","v":6.8148148148148149},6.3307407407407412]
["SD",{"$f":"_xlfn.STDEV.S(B8:B34)","v":9.9564579108765705E-3},2.2365786473057543E-2,null,null,null,null,null,null,"SD",{"$f":"_xlfn.STDEV.S(K8:K34)","v":0.99564579108765083},2.2365786473057563]
["n",{"$f":"COUNT(B8:B34)","v":27}]
["n-1",{"$f":"B3-1","v":26}]
[]
[null,"x","y","(x-Xbar)*(y-Ybar)","(x-Xbar)^2","(y - Ybar)^2",null,null,null,null,"x","y"]
["Metro Area","Jobless Rate","Delinquent Loans","Deviation in x * Deviation in y","x Deviation Squared","y Deviation Squared",null,"Correlation Coefficient",null,"Metro Area","Jobless Rate (%)","Delinquent Loans (%)",null,"Correlation Coefficient"]
["Atlanta",7.0999999999999994E-2,7.0199999999999999E-2,{"$f":"(B8-$B$1)*(C8-$C$1)","v":1.9656652949245558E-5},{"$f":"(B8-B$1)^2","v":8.1330589849108564E-6},{"$f":"(C8-C$1)^2","v":4.7507832647462227E-5},"a",{"$f":"CORREL(C8:C34,B8:B34)","v":0.44132393135015574},{"$f":"H8=D38","v":true},"Atlanta",7.1,7.02,null,{"$f":"CORREL(L8:L34,K8:K34)","v":0.4413239313501558}]
["Boston",5.2000000000000005E-2,5.3099999999999994E-2,{"$f":"(B9-$B$1)*(C9-$C$1)","v":1.6483072702331959E-4},{"$f":"(B9-B$1)^2","v":2.6076268861454E-4},1.0419116598079576E-4,null,null,null,"Boston",5.2,5.31]
["Charlotte",7.8E-2,5.3800000000000001E-2,-9.3665569272976786E-5,9.7058984910836961E-5,9.0390795610425273E-5,null,"From our",null,"Charlotte",7.8,5.38]
["Chicago",7.8E-2,5.4000000000000006E-2,-9.1695198902606363E-5,9.7058984910836961E-5,8.6627832647462192E-5,null,"sample data,",null,"Chicago",7.8,5.4]
["Dallas",5.7999999999999996E-2,0.05,1.3504554183813434E-4,1.0298491083676257E-4,1.7708709190672153E-4,null,"there does not",null,"Dallas",5.8,5]
["Denver",5.7999999999999996E-2,4.07E-2,2.2942331961591211E-4,1.0298491083676257E-4,5.1109486968449935E-4,null,"seem to be a",null,"Denver",5.8,4.07]
["Detroit",9.3000000000000013E-2,6.5299999999999997E-2,4.9519615912208426E-5,6.1761454046639348E-4,3.970425240054849E-6,null,"strong",null,"Detroit",9.3000000000000007,6.53]
["Houston",5.7000000000000002E-2,5.57E-2,8.4808504801097331E-5,1.2428120713305871E-4,5.7872647462277129E-5,null,"correlation",null,"Houston",5.7,5.57]
["Jacksonville",7.2999999999999995E-2,6.9900000000000004E-2,3.1986282578875218E-5,2.3540466392318295E-5,4.3462277091906743E-5,null,"between",null,"Jacksonville",7.3,6.99]
["Las Vegas",7.5999999999999998E-2,0.11119999999999999,3.7604554183813473E-4,6.1651577503429487E-5,2.2937004252400542E-3,null,"jobless rate",null,"Las Vegas",7.6,11.12]
["Los Angeles",8.199999999999999E-2,7.5600000000000001E-2,1.7027517146776404E-4,1.9187379972565157E-4,1.5110783264746225E-4,null,"and delinquent",null,"Los Angeles",8.1999999999999993,7.56]
["Miami",7.0999999999999994E-2,0.1211,1.6481591220850501E-4,8.1330589849108564E-6,3.3399837585733881E-3,null,"loans.",null,"Miami",7.1,12.11]
["Minneapolis",6.3E-2,4.3899999999999995E-2,9.9912208504800937E-5,2.6503429355281102E-5,3.7664746227709218E-4,null,"However, there",null,"Minneapolis",6.3,4.3899999999999997]
["Nashville",6.6000000000000003E-2,4.7800000000000002E-2,3.3312208504800897E-5,4.6145404663922623E-6,2.4047968449931412E-4,null,"is a modest",null,"Nashville",6.6,4.78]
["New York",6.2E-2,5.7800000000000004E-2,3.3860356652949183E-5,3.7799725651577389E-5,3.0331536351165956E-5,null,"positive",null,"New York",6.2,5.78]
["Orange County",6.3E-2,6.08E-2,1.2908504801097379E-5,2.6503429355281102E-5,6.2870919067215471E-6,null,"relationship so",null,"Orange County",6.3,6.08]
["Orlando",7.0000000000000007E-2,0.10050000000000001,6.8875171467764677E-5,3.4293552812071945E-6,1.3832889437585738E-3,null,"that you would",null,"Orlando",7,10.050000000000001]
["Philadelphia",6.2E-2,4.7500000000000001E-2,9.7186282578875027E-5,3.7799725651577389E-5,2.4987412894375864E-4,null,"expect to have",null,"Philadelphia",6.2,4.75]
["Phoenix",5.5E-2,7.22E-2,-1.1692112482853213E-4,1.728737997256513E-4,7.9078203017832611E-5,null,"delinquent",null,"Phoenix",5.5,7.22]
["Portland",6.5000000000000002E-2,3.7900000000000003E-2,7.9986282578874867E-5,9.9108367626885389E-6,6.4553635116598078E-4,null,"loans go up if",null,"Portland",6.5,3.79]
["Raleigh",0.06,3.6200000000000003E-2,2.2087517146776383E-4,6.6392318244169973E-5,7.3481153635116588E-4,null,"the jobless rate",null,"Raleigh",6,3.62]
["Sacramento",8.3000000000000004E-2,9.2399999999999996E-2,4.3207887517146808E-4,2.205775034293557E-4,8.4637894375857309E-4,null,"went up.",null,"Sacramento",8.3000000000000007,9.24]
["St. Louis",7.4999999999999997E-2,4.4000000000000004E-2,-1.3229149519890273E-4,4.6947873799725748E-5,3.7277598079561036E-4,null,null,null,"St. Louis",7.5,4.4000000000000004]
["San  Diego",7.0999999999999994E-2,6.9099999999999995E-2,1.6519615912208505E-5,8.1330589849108564E-6,3.3554128943758487E-5,null,"b",null,"San  Diego",7.1,6.91]
["San Francisco",6.8000000000000005E-2,5.57E-2,1.1270233196158001E-6,2.1947873799721275E-8,5.7872647462277129E-5,null,null,null,"San Francisco",6.8,5.57]
["Seattle",5.5E-2,3.8699999999999998E-2,3.2354183813443051E-4,1.728737997256513E-4,6.0552449931412908E-4,null,null,null,"Seattle",5.5,3.87]
["Tampa",7.4999999999999997E-2,8.4199999999999997E-2,1.4315294924554194E-4,4.6947873799725748E-5,4.3650042524005469E-4,null,null,null,"Tampa",7.5,8.42]
[]
[null,null,"Total",{"$f":"SUM(D8:D34)","v":2.5551703703703696E-3},2.5774074074074067E-3,1.300593851851852E-2]
[null,null,"Covariance",{"$f":"D36/$B$4","v":9.8275783475783453E-5},9.9131054131054101E-5,5.0022840455840459E-4]
[null,null,"Coefficient of Correlation",{"$f":"D37/PRODUCT(E40:F40)","v":0.44132393135015591},null,null,null,null,null,"Xbar","y","x","Yabr"]
[null,null,null,null,null,null,null,null,null,{"$f":"$B$1","v":6.8148148148148138E-2},0,0,{"$f":"$C$1","v":6.3307407407407409E-2}]
[null,null,null,"SD",{"$f":"SQRT(E37)","v":9.9564579108764421E-3},{"$f":"SQRT(F37)","v":2.236578647305756E-2},null,null,null,{"$f":"$B$1","v":6.8148148148148138E-2},0.14000000000000001,0.1,6.3307407407407409E-2]

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["Daily % increase/decrease from 9 days over last three months"]
[]
["Mean",{"$f":"AVERAGE(B10:B18)","v":1.6000000000000001E-3},{"$f":"AVERAGE(C10:C18)","v":1.2999999999999999E-3}]
["Count = n",{"$f":"COUNT(B10:B18)","v":9}]
["n-1",{"$f":"B4-1","v":8}]
["SD",{"$f":"_xlfn.STDEV.S(B10:B18)","v":6.1200490194115277E-3},5.574495492867493E-3,null,null,null,null,"a"]
[]
[null,"x","y","(x-Xbar)*(y-Ybar)"]
[null,"DJIA","S&P 500","Deviation in x * Deviation in y"]
[null,2E-3,2.3999999999999998E-3,{"$f":"(B10-$B$3)*(C10-$C$3)","v":4.3999999999999992E-7}]
[null,8.199999999999999E-3,1.9E-3,3.9600000000000002E-6]
[null,-9.8999999999999991E-3,-9.1000000000000004E-3,1.1959999999999999E-4]
[null,4.0000000000000002E-4,8.0000000000000004E-4,5.9999999999999997E-7]
[null,-2.3999999999999998E-3,-3.3E-3,1.84E-5]
[null,1.01E-2,8.6999999999999994E-3,6.2899999999999984E-5]
[null,3.0000000000000001E-3,3.5999999999999999E-3,3.2200000000000001E-6]
[null,5.5000000000000005E-3,8.3000000000000001E-3,2.7300000000000006E-5]
[null,-2.5000000000000001E-3,-1.6000000000000001E-3,1.189E-5]
[]
[null,null,null,{"$f":"SUM(D10:D18)","v":2.4831000000000001E-4}]
[null,null,"Covariance",{"$f":"D20/B5","v":3.1038750000000002E-5}]
[null,"b","Coefficient of Correlation",{"$f":"D21/PRODUCT(B6:C6)","v":0.90979543539336993}]
[]
[null,"c","The DJIA and the S & P 500 are atrongly correlated. When one goes up, the other tends to go up; and when one goes down, the other tends to go down."]
[null,null,"The general movement of the market can be ascertained by looking at one or the other."]
[]
[null,"Check"]
[null,null,"Covariance",{"$f":"_xlfn.COVARIANCE.S(C10:C18,B10:B18)","v":3.1038750000000002E-5},{"$f":"D28=D21","v":true}]
[null,null,"Coefficient of Correlation",{"$f":"CORREL(C10:C18,B10:B18)","v":0.90979543539337004},{"$f":"D29=D22","v":true}]

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["a",null,null,null,null,null,null,null,"Xbar","y","x","Yabr"]
[null,null,null,null,null,null,null,null,{"$f":"$B$16","v":3},0,0,{"$f":"$C$16","v":8}]
[null,null,null,null,null,null,null,null,3,15,6,8]
[]
[]
[]
[]
[]
[]
[]
[]
["b","The relationship is direct or positive: as x increases, y increases"]
["c","See chart"]
["d"]
[]
["Mean",{"$f":"AVERAGE(B22:B26)","v":3},8]
["SD",{"$f":"_xlfn.STDEV.S(B22:B26)","v":1.5811388300841898},4.4721359549995796]
["Count",{"$f":"COUNT(B22:B26)","v":5}]
["Count - 1",{"$f":"B18-1","v":4}]
[]
[null,"xi","yi","(xi - Xbar)","(yi - Ybar)",{"$f":"D21&\"*\"&E21","v":"(xi - Xbar)*(yi - Ybar)"},{"$f":"D21&\"^2\"","v":"(xi - Xbar)^2"}]
[null,1,3,{"$f":"(B22-B$16)","v":-2},-5,{"$f":"E22*D22","v":10},{"$f":"D22^2","v":4}]
[null,2,7,-1,-1,1,1]
[null,3,5,0,-3,0,0]
[null,4,11,1,3,3,1]
[null,5,14,2,6,12,4]
[null,null,null,null,null,{"$f":"SUM(F22:F26)","v":26},{"$f":"SUM(G22:G26)","v":10}]
[]
[]
[null,null,null,"Slope","b1",{"$f":"F27/G27","v":2.6}]
[null,null,null,"Intercept","B0",{"$f":"C16-B16*F30","v":0.19999999999999929}]
[]
[null,null,null,"Slope","b1",{"$f":"SLOPE($C$22:$C$26,$B$22:$B$26)","v":2.6}]
[null,null,null,"Intercept","B0",{"$f":"INTERCEPT($C$22:$C$26,$B$22:$B$26)","v":0.19999999999999929}]
[]
[null,null,"d","Equation:","Predicted y =",{"$f":"ROUND(F31,1)&\" + \"&F30&\"*xi\"","v":"0.2 + 2.6*xi"}]
[null,null,null,null,"x",4]
[null,null,"e",null,"Predicted y =",{"$f":"F31+F30*F37","v":10.6}]
[]
["#15:"]
[null,null,null,"Covariance","Sxy",{"$f":"F27/B19","v":6.5}]
[]
[null,null,null,"Covariance","Sxy",{"$f":"_xlfn.COVARIANCE.S(C22:C26,B22:B26)","v":6.5}]
[]
["(Strength and Direction of Relationship)",null,null,"Coefficient of Correlation","rxy",{"$f":"F43/PRODUCT(B17:C17)","v":0.91923881554251163}]
[]
[null,null,null,"Coefficient of Correlation","rxy",{"$f":"PEARSON(C22:C26,B22:B26)","v":0.91923881554251174}]
[]
["% of variability in y that can be explained by the linear relationship",null,null,"Coefficient of Determination","r2",{"$f":"F47^2","v":0.84499999999999997}]
[]
[null,{"$f":"B21","v":"xi"},"yi","Ypredicted ","(yi - Yabr)^2","(yi - Ypredicted)^2"]
[null,1,3,{"$f":"$F$31+$F$30*B52","v":2.7999999999999994},{"$f":"(C52-$C$16)^2","v":25},{"$f":"(C52-D52)^2","v":4.0000000000000251E-2},{"$f":"(D52-$C$16)^2","v":27.04000000000001}]
[null,2,7,{"$f":"$F$31+$F$30*B53","v":5.3999999999999995},{"$f":"(C53-$C$16)^2","v":1},{"$f":"(C53-D53)^2","v":2.5600000000000018},{"$f":"(D53-$C$16)^2","v":6.7600000000000025}]
[null,3,5,8,{"$f":"(C54-$C$16)^2","v":9},9,0]
[null,4,11,10.6,{"$f":"(C55-$C$16)^2","v":9},0.16000000000000028,6.759999999999998]
[null,5,14,13.2,{"$f":"(C56-$C$16)^2","v":36},0.64000000000000112,27.039999999999992]
[null,"a","SST",null,{"$f":"SUM(E52:E56)","v":80}]
[null,null,null,null,"SSE",{"$f":"SUM(F52:F56)","v":12.400000000000002}]
[null,null,null,null,null,"SSR",{"$f":"SUM(G52:G56)","v":67.599999999999994}]
[]
[null,null,null,"b","Coefficient of Determination","r2",{"$f":"G59/E57","v":0.84499999999999997},"This is a good fit. When SSE is zero, the predicted and"]
[null,null,null,"c","Coefficient of Correlation","r",{"$f":"SQRT(G61)","v":0.91923881554251174},"observed values are equal and thus SSR/SST would equal 1, a"]
[null,null,null,null,null,null,null,"perfect Fit. So since r^2 is .845, this is a good fit."]

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[null,"Xbar","Ybar"]
["Mean",{"$f":"AVERAGE(A19:A28)","v":87.4},{"$f":"AVERAGE(B19:B28)","v":6.6399999999999988},null,"Xbar",null,null,"Ybar"]
[null,"n -1"]
["n -1",{"$f":"COUNT(A19:A28)-1","v":9}]
[null,"Sample SD x","Sample SD y"]
["Sample SD",{"$f":"_xlfn.STDEV.S(A19:A28)","v":23.926740038895566},{"$f":"_xlfn.STDEV.S(B19:B28)","v":0.79749608149508655},null,{"$f":"$B$2","v":87.4},0,0,{"$f":"$C$2","v":6.6399999999999988}]
["Sample Covariance",{"$f":"_xlfn.COVARIANCE.S(B19:B28,A19:A28)","v":-15.073333333333336},null,null,87.4,{"$f":"ROUNDUP(MAX(B19:B28),0)","v":8},{"$f":"CEILING(MAX(A19:A28),5)","v":140},6.6399999999999988]
["Coefficient of Correlation",{"$f":"PEARSON(B19:B28,A19:A28)","v":-0.78994565455478216}]
["Coefficient of Determination",{"$f":"RSQ(B19:B28,A19:A28)","v":0.62401413714998322}]
["Slope",{"$f":"SLOPE(B19:B28,A19:A28)","v":-2.6329477525036882E-2}]
["Intercept",{"$f":"INTERCEPT(B19:B28,A19:A28)","v":8.9411963356882218}]
[]
["a"]
["b","Relationship is negative (inverse), as miles increase, price decreases",null,null,null,null,null,null,null,null,null,"Variation ",null,"Variation "]
[null,null,null,null,null,null,null,null,null,null,null,"Not Explained",null,"Explained"]
[null,null,null,null,null,null,null,null,null,null,null,"by Model",null,"by Model"]
["x","y","x Deviation","y Deviation",{"$f":"C17&\"^2\"","v":"x Deviation^2"},"y Deviation^2","Mult Deviations","Predicted y values",null,null,"Residual","Residual Squared"]
["Miles (1000s)","Price ($1000s)","(x - Xbar)","(y - Ybar)","(x - Xbar)^2","(y - Ybar)^2",{"$f":"C18&\"*\"&D18","v":"(x - Xbar)*(y - Ybar)"},{"$f":"\"y Predicted = \"&ROUND(G33,2)&\" + \"&ROUND(G32,3)&\"*x\"","v":"y Predicted = 8.94 + -0.026*x"},null,null,"y -\ny Predicted",{"$f":"\"(\"&K18&\")^2\"","v":"(y -\ny Predicted)^2"},null,"(y Predicted - Ybar)"]
[57,7,{"$f":"A19-B$2","v":-30.400000000000006},{"$f":"B19-C$2","v":0.36000000000000121},{"$f":"C19^2","v":924.16000000000031},{"$f":"D19^2","v":0.12960000000000088},{"$f":"C19*D19","v":-10.944000000000038},{"$f":"$G$33+A19*$G$32","v":7.4404161167611198},null,null,{"$f":"B19-H19","v":-0.4404161167611198},{"$f":"K19^2","v":0.19396635590294431},null,{"$f":"(H19-$C$2)^2","v":0.64066595997095255}]
[59,7.5,-28.400000000000006,0.86000000000000121,806.56000000000029,0.73960000000000203,-24.424000000000039,7.387757161711046,null,null,0.11224283828895398,1.2598454747160275E-2,null,0.55914077289016118]
[66,6.6,-21.400000000000006,-3.9999999999999147E-2,457.96000000000026,1.5999999999999318E-3,0.855999999999982,7.2034508190357878,null,null,-0.60345081903578812,0.36415289099496351,null,0.31747682547210143]
[87,7.2,-0.40000000000000568,0.56000000000000139,0.16000000000000456,0.31360000000000154,-0.22400000000000372,6.650531791010013,null,null,0.54946820898998716,0.30191531269066418,null,1.1091862187861643E-4]
[87,7.2,-0.40000000000000568,0.56000000000000139,0.16000000000000456,0.31360000000000154,-0.22400000000000372,6.650531791010013,null,null,0.54946820898998716,0.30191531269066418,null,1.1091862187861643E-4]
[90,7,2.5999999999999943,0.36000000000000121,6.7599999999999705,0.12960000000000088,0.93600000000000105,6.5715433584349023,null,null,0.42845664156509766,0.18357509370124259,null,4.6863117743720919E-3]
[90,7,2.5999999999999943,0.36000000000000121,6.7599999999999705,0.12960000000000088,0.93600000000000105,6.5715433584349023,null,null,0.42845664156509766,0.18357509370124259,null,4.6863117743720919E-3]
[94,6.4,6.5999999999999943,-0.23999999999999844,43.559999999999924,5.7599999999999249E-2,-1.5839999999999883,6.4662254483347548,null,null,-6.6225448334754411E-2,4.3858100071392254E-3,null,3.0197594806456566E-2]
[106,5.4,18.599999999999994,-1.2399999999999984,345.95999999999981,1.5375999999999961,-23.063999999999965,6.1502717180343121,null,null,-0.7502717180343117,0.56290765088215766,null,0.23983379015706319]
[138,5.0999999999999996,50.599999999999994,-1.5399999999999991,2560.3599999999992,2.3715999999999973,-77.92399999999995,5.3077284372331324,null,null,-0.20772843723313272,4.3151103635319564E-2,null,1.7749475169572686]
[null,null,null,"Total / SST",{"$f":"SUM(E19:E28)","v":5152.3999999999996},{"$f":"SUM(F19:F28)","v":5.7240000000000002},-135.66000000000003,null,null,null,"SSE",{"$f":"SUM(L19:L28)","v":2.1521430789534977},"SSR",{"$f":"SUM(N19:N28)","v":3.5718569210465048}]
[null,null,null,"SD",{"$f":"SQRT(E29/$B$4)","v":23.926740038895581},{"$f":"SQRT(F29/$B$4)","v":0.79749608149507545},null,null,null,null,"Measure of how clustered the"]
[null,null,null,null,null,null,null,null,null,null,"observations are around",null,null,"Check r^2:"]
[null,null,null,null,"c","Slope",{"$f":"G29/E29","v":-2.6329477525036882E-2},null,null,null,"Regression Line (Not",null,null,{"$f":"N29/F29","v":0.62401413714998333}]
[null,null,null,null,null,"Intercept",{"$f":"C2-B2*G32","v":8.9411963356882218},null,null,null,"Explained Part)"]
[null,null,null,null,"d","For every one unit of increares in x (1000s miles), y decreases by -0.026 ($1000)."]
[null,null,null,null,null,"For evey 1 mile increase, the model predicts that the price will drop by 2.6 cents",null,null,null,null,"Covariance",{"$f":"G29/B4","v":-15.073333333333336},"Strength of Relationship"]
[null,null,null,null,null,"For every100 miles on the car, the estimated price will drop by $26.",null,null,null,null,"Coefficient of Correlation",{"$f":"L35/PRODUCT(E30:F30)","v":-0.78994565455478216},"Strength and Direction of Relationship (between -1 and 1)"]
[null,null,null,null,"e",null,null,null,null,null,"Coefficient of Determination",{"$f":"L36^2","v":0.62401413714998322},"Goodness of fit of model: % of variation in y values that model can explain"]
[null,null,null,null,"x",100,null,null,null,null,null,null,"(Between 0 and 1)"]
[null,null,null,null,"Predicted y",{"$f":"G33+G32*F38","v":6.3082485831845334},null,null,null,null,null,null,"Coefficient of Determination = How well does the"]
[null,null,null,null,null,{"$f":"F39*1000","v":6308.2485831845333},null,null,null,null,null,null,"estimated regression line fit the data? = Measure of the goodness of fit for"]
[null,null,null,null,null,null,null,null,null,null,null,null,"the estimated regression line = A number between 0 and +1. Can be used"]
[null,null,null,null,null,null,null,null,null,null,null,null,"your nonlinear relationships as well as linear."]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"SST How well observations clustered around Y bar"]

{"sheet":"5,22","index":7,"n_rows":68,"n_cols":9,"rows_kept":68,"cut":false,"hidden":false,"merged":[[35,7,37,8],[39,7,40,8]]}
["Mean",{"$f":"AVERAGE(B7:B14)","v":1875},74]
["Sample Size",{"$f":"COUNT(B7:B14)","v":8},8]
["Sample Size - 1",{"$f":"B2-1","v":7},7," <<== Only 1 Independent Variable"]
[null,null,null,"Standard Deviation Calculation",null,null,null,null,"Covariance, Coefficient of Correlation, Coefficient of Determination"]
[null,"x","f(x) = y","x Deviation","y Deviation",{"$f":"D5&\"^2\"","v":"x Deviation^2"},"y Deviation^2",null,"Deviations Multiplied"]
["Brand and Model","Price","Rating","(x - Xbar)","(y - Ybar)","(x - Xbar)^2","(y - Ybar)^2",null,{"$f":"D6&\" * \"&E6","v":"(x - Xbar) * (y - Ybar)"}]
["Precor 5.31",3700,87,{"$f":"B7-B$1","v":1825},13,{"$f":"D7^2","v":3330625},169,null,{"$f":"D7*E7","v":23725}]
["Keys Fitness CG2",2500,84,625,10,390625,100,null,6250]
["Octane Fitness Q37e",2800,82,925,8,855625,64,null,7400]
["LifeFitness X1 Basic",1900,74,25,0,625,0,null,0]
["NordicTrack AudioStrider 990",1000,73,-875,-1,765625,1,null,875]
["Schwinn 430",800,69,-1075,-5,1155625,25,null,5375]
["Vision Fitness X6100",1700,68,-175,-6,30625,36,null,1050]
["ProForm XP 520 Razor",600,55,-1275,-19,1625625,361,null,24225]
[null,null,"Total",{"$f":"SUM(D7:D14)","v":0},0,{"$f":"SUM(F7:F14)","v":8155000},756,"Total",{"$f":"SUM(I7:I14)","v":68900}]
[null,null,null,null,"Sample Standard Deviation",{"$f":"SQRT(F15/B3)","v":1079.3516572461451},{"$f":"SQRT(G15/C3)","v":10.392304845413264},"Covariance",{"$f":"I15/B3","v":9842.8571428571431}]
[null,null,null,null,"Check:",{"$f":"_xlfn.STDEV.S(B7:B14)","v":1079.3516572461451},{"$f":"_xlfn.STDEV.S(C7:C14)","v":10.392304845413264},"Covariance",{"$f":"_xlfn.COVARIANCE.S(C7:C14,B7:B14)","v":9842.8571428571431}]
[null,null,null,null,null,null,null,null,"Q1 and Q3 Majority, so positive relationship"]
["a",null,null,null,null,null,null,"Coefficient of Correlation",{"$f":"I16/PRODUCT(F16:G16)","v":0.87749841658380712}]
[null,"X bar",null,null,"Y bar",null,null,"Coefficient of Correlation",{"$f":"PEARSON(C7:C14,B7:B14)","v":0.87749841658380701}]
[null,{"$f":"$B$1","v":1875},0,0,{"$f":"$C$1","v":74},null,null,null,"Strong positive Correlation (not causation)"]
[null,{"$f":"$B$1","v":1875},{"$f":"MAX(C7:C14)","v":87},{"$f":"MAX(B7:B14)","v":3700},{"$f":"$C$1","v":74},null,null,"Slope",{"$f":"I15/F15","v":8.4488044144696503E-3}]
[null,null,null,null,null,null,null,null,"For every $1 in Price increase, we see 8/10 of a point"]
[null,null,null,null,null,null,null,null,"increase in Rating"]
[null,null,null,null,null,null,null,"Check:",{"$f":"SLOPE(C7:C14,B7:B14)","v":8.4488044144696503E-3}]
[]
[null,null,null,null,null,null,null,"Intercept",{"$f":"C1-B1*I22","v":58.158491722869407}]
[null,null,null,null,null,null,null,null,"Estimated Line Crosses at 58 rating"]
[null,null,null,null,null,null,null,"Check:",{"$f":"INTERCEPT(C7:C14,B7:B14)","v":58.158491722869407}]
[]
[null,null,null,null,null,null,"c","Equation:",{"$f":"\"Predicted y = \"&ROUND(I29,3)&\" + \"&ROUND(I25,4)&\" * x\"","v":"Predicted y = 58.158 + 0.0084 * x"}]
[]
[null,null,null,null,null,null,null,"x =",1500]
[null,null,null,null,null,null,"d",{"$f":"\"F( \"&DOLLAR(I33,0)&\" ) =\"","v":"F( $1,500 ) ="},{"$f":"I29+I25*I33","v":70.83169834457388}]
[]
[null,null,null,null,null,null,null,{"$f":"\"At \"&DOLLAR(I33)&\" Price (Predictor Variable), the Estimates Simple Linear Regression Equarion predictes that the Rating would be \"&ROUND(I34,2)","v":"At $1,500.00 Price (Predictor Variable), the Estimates Simple Linear Regression Equarion predictes that the Rating would be 70.83"}]
[]
[]
[]
[null,null,null,null,null,null,"b","Given the strong positive liner relationship between Price and Rating, the Quality sign seems reasonable"]
[]
[]
["#22:"]
[]
["Coefficient of Determination"]
["Observed x","Observed y","Predicted y","Residuals","Residuals Squared","Error from Using Ybar to Estimate Rating: y Deviation","Squared Deviation"]
[{"$f":"B6","v":"Price"},"Rating",{"$f":"I31","v":"Predicted y = 58.158 + 0.0084 * x"},"(yi - Predicted y)",{"$f":"D47&\"^2\"","v":"(yi - Predicted y)^2"},"(yi - Ybar)",{"$f":"F47&\"^2\"","v":"(yi - Ybar)^2"}]
[3700,87,{"$f":"$I$27+$I$22*A48","v":89.419068056407113},{"$f":"B48-C48","v":-2.419068056407113},{"$f":"D48^2","v":5.8518902615292872},{"$f":"B48-$C$1","v":13},{"$f":"F48^2","v":169}]
[2500,84,79.280502759043529,4.7194972409564713,22.273654207395744,10,100]
[2800,82,81.815144083384425,0.18485591661557521,3.4171709907784495E-2,8,64]
[1900,74,74.211220110361751,-0.21122011036175081,4.4613935021230192E-2,0,0]
[1000,73,66.607296137339063,6.3927038626609374,40.866662675680068,-1,1]
[800,69,64.917535254445127,4.0824647455548728,16.666518398698411,-5,25]
[1700,68,72.521459227467815,-4.5214592274678154,20.443593545653854,-6,36]
[600,55,63.227774371551199,-8.2277743715511988,67.696271109154722,-19,361]
[null,null,null,"SSE",{"$f":"SUM(E48:E55)","v":173.87737584304111},{"$f":"SUM(F48:F55)","v":0}]
[null,null,null,null,null,"SST",{"$f":"SUM(G48:G55)","v":756}]
[null,null,null,null,"a","SSR",{"$f":"G57-E56","v":582.12262415695886}]
[null,null,null,null,"r^2","Coefficient of Determination",{"$f":"G58/G57","v":0.77000347110708844},"SSR/SST"]
[null,null,null,null,"r^2","Coefficient of Determination",{"$f":"RSQ(B48:B55,A48:A55)","v":0.77000347110708867},"RSQ function"]
[null,null,null,null,"r^2","Coefficient of Determination",{"$f":"I19^2","v":0.77000347110708867},"(Coefficient of Correlation)^2"]
[]
[null,null,null,null,"b","Yes, .77 is a reasonable fit. 77% of the variability has been explained"]
[null,null,null,null,null,"by the Regression Line."]
[]
[null,null,null,null,"c"]
[null,null,null,null,"r",{"$f":"SQRT(G61)","v":0.87749841658380712}]
[null,null,null,null,null,"Strong, positive relationship"]

{"sheet":"7,19","index":8,"n_rows":60,"n_cols":12,"rows_kept":60,"cut":false,"hidden":false,"merged":[]}
[]
[null,null,null,null,null,null,null,null,"07:00:00"]
[]
[]
[]
[null,"Xbar",null,null,"Ybar"]
[null,{"$f":"$B$26","v":7},0,0,{"$f":"$C$26","v":108}]
[null,{"$f":"$B$26","v":7},{"$f":"MAX(C29:C38)","v":136},{"$f":"MAX(B29:B38)","v":13},108]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["n",{"$f":"COUNT(B29:B38)","v":10},null,null,null,null,null,"Multiply to get","7 b"]
["n -1",{"$f":"B23-1","v":9},null,"Partaicular x","Partaicular y","Used To Calc:","Used To Calc:","preponderance of signs for","What model predicts","Errors in Model","Used To Calc:","Used To Calc:"]
[null,"Xbar","Ybar","minus","minus","1) x Sample SD","1) y Sample SD","Relationship",null,"as compared to","1) SSE","1) SSR"]
["Mean",{"$f":"AVERAGE(B29:B38)","v":7},108,"Mean","Mean","2) Slope","2) SST","Cov, Corr, Slope",null,"Observed y"]
[null,"x","Observed y","(x Deviation)","(y Deviation)",{"$f":"D27&\"^2\"","v":"(x Deviation)^2"},"(y Deviation)^2",{"$f":"D27&\"*\"&E27","v":"(x Deviation)*(y Deviation)"},"Predicted y","Residuals","Residuals^2","Regression Error"]
[null,"Years Worked","Annual Sales ($1000)","(x - Xbar)","(y - Ybar)",{"$f":"D28&\"^2\"","v":"(x - Xbar)^2"},{"$f":"E28&\"^2\"","v":"(y - Ybar)^2"},{"$f":"D28&\"*\"&E28","v":"(x - Xbar)*(y - Ybar)"},"Predicted y = B0 + b1*x1","(y1 - Predicted y)",{"$f":"J28&\"^2\"","v":"(y1 - Predicted y)^2"},"(Predicted y - Ybar)^2"]
[null,1,80,{"$f":"B29-B$26","v":-6},{"$f":"C29-C$26","v":-28},{"$f":"D29^2","v":36},{"$f":"E29^2","v":784},{"$f":"D29*E29","v":168},{"$f":"$H$55+$H$53*B29","v":84},{"$f":"C29-I29","v":-4},{"$f":"J29^2","v":16},{"$f":"(I29-$C$26)^2","v":576}]
[null,3,97,-4,-11,16,121,44,92,5,25,256]
[null,4,92,-3,-16,9,256,48,96,-4,16,144]
[null,4,102,-3,-6,9,36,18,96,6,36,144]
[null,6,103,-1,-5,1,25,5,104,-1,1,16]
[null,8,111,1,3,1,9,3,112,-1,1,16]
[null,10,119,3,11,9,121,33,120,-1,1,144]
[null,10,123,3,15,9,225,45,120,3,9,144]
[null,11,117,4,9,16,81,36,124,-7,49,256]
[null,13,136,6,28,36,784,168,132,4,16,576]
[null,null,null,{"$f":"SUM(D29:D38)","v":0},0,null,null,null,null,null,null,{"$f":"SUM(L29:L38)","v":2272}]
[null,null,null,null,"Σ(x - Xbar)^2",{"$f":"SUM(F29:F38)","v":142},null,null,"19 a","SSE = Σ(y - y Predicted)^2",{"$f":"SUM(K29:K38)","v":170},"How Well observations cluster around Estimated Line (not explained part)"]
[null,null,null,null,null,"Σ(y - Ybar)^2",{"$f":"SUM(G29:G38)","v":2442},null,null,"SST = Σ(y - Ybar)^2",{"$f":"G41","v":2442},"How well observations cluster around Ybar Line (Total Deviation)"]
[null,null,null,null,null,null,"Σ(x - Xbar)*(y - Ybar)",{"$f":"SUM(H29:H38)","v":568},null,"SSR",{"$f":"K41-K40","v":2272},"Explained Part of the variation"]
[null,null,null,null,null,null,null,null,"19 b","r^2 = Coefficient of Determination",{"$f":"K42/K41","v":0.93038493038493042},"Goodness of fit for model is high. Between 0 and 1. At SSE = 0,"]
[null,null,null,null,"Sample SD x",{"$f":"SQRT(F40/B24)","v":3.9721250959376619},"SQRT((Σ(x - Xbar)^2)/(n-1)","How Clustered are the data points around Mean",null,null,null,"Particular and Predicted are the same and model preditcs perfectly."]
[null,null,null,null,"Check:",{"$f":"_xlfn.STDEV.S(B29:B38)","v":3.9721250959376619},null,null,null,null,null,"The closer this is to 1, the better the fit. So this is a good fit."]
[null,null,null,null,null,"Sample SD y",{"$f":"SQRT(G41/B24)","v":16.472198800807782},"SQRT((Σ(y - Ybar)^2)/(n-1)","How Clustered are the data points around Mean",null,null,"93% of the variability in y is explained by the Regression Line."]
[null,null,null,null,null,"Check:",{"$f":"_xlfn.STDEV.S(C29:C38)","v":16.472198800807782},null,"19 c","r = Coefficient of Correlation",{"$f":"SQRT(K43)","v":0.96456463255964886},"Strength and direction of linear relationship (between -1 and 1)"]
[null,null,null,null,null,null,null,null,null,"Check:",{"$f":"RSQ(C29:C38,B29:B38)","v":0.93038493038493064}]
[null,null,null,null,null,null,"Covariance",{"$f":"H42/B24","v":63.111111111111114},"(Σ(x - Xbar)*(y - Ybar)/(n-1)","Measures strength of relationship, but problem with units"]
[null,null,null,null,null,null,"Check:",{"$f":"_xlfn.COVARIANCE.S(C29:C38,B29:B38)","v":63.111111111111114}]
[null,null,null,null,null,null,"Coefficient of Correlation",{"$f":"H49/PRODUCT(F44,G46)","v":0.96456463255964897},"(Σ(x - Xbar)*(y - Ybar)/(n-1)/(SDx*Sdy)",null,"Measures Strength and Direction of relationship (-1 to 1)"]
[null,null,null,null,null,null,"Check:",{"$f":"PEARSON(C29:C38,B29:B38)","v":0.96456463255964886}]
[null,null,null,null,null,null,"Slope",{"$f":"H42/F40","v":4},"b1 = (Σ(x - Xbar)*(y - Ybar)/(n-1)/(Σ(x - Xbar)^2)",null,"For every 1 unit of x, how does y move?"]
[null,null,null,null,null,null,"Check:",{"$f":"SLOPE(C29:C38,B29:B38)","v":4}]
[null,null,null,null,null,null,"Intercept",{"$f":"C26-B26*H53","v":80},"b0 = Ybar  - Xbar*b1",null,"Where Estimated Regression Line Crosses y-axis"]
[null,null,null,null,null,null,"Check:",{"$f":"INTERCEPT(C29:C38,B29:B38)","v":80}]
[]
[null,null,null,null,null,null,"7 c"]
[null,null,null,null,null,null,"x",9,"years"]
[null,null,null,null,null,null,"Predicted y",{"$f":"H55+H59*H53","v":116},"Annual Sales ($1000)"]