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[null,"      The Correlation Coefficient "]
[null,"    and the Sum of the Squares"]
[]
["          This DIGMath program lets you explore the"]
[null,"           the correlation coefficient and"]
[null,"                 the Sum of the Squares"]
[null,"  to see how both measure how well a line "]
[null,"         captures the trend in a set of data"]
[]
[]
[null,"The scatterplot is based on a fixed set of data in blue."]
[null,"The associated regression line is also shown."]
[null,"The second set of data in red is generated by either squeezing"]
[null,"    the original data values together vertically about the regression line",null,null,null,null,null,null,null,null,null,"For the original data, "]
[null,"   or stretching the original data values vertically about the regression line.",null,null,null,null,null,null,null,null,null,"   the correlation coefficient r =",null,null,null,{"$f":"Sheet2!J10","v":0.82857142857142851}]
[null,"In either case, the new data set has the same regression line.",null,null,null,null,null,null,null,null,null,"  and the sum of the squares =",null,null,null,{"$f":"Sheet2!E8","v":21.942857309999997}]
[]
[]
[null,"Enter the factor by which the data points are squeezed or stretched:",null,null,null,null,null,null,null,null,null,"For the transformed data, ",null,null,null,null,null,null,null," "]
[null,"    the multiple is between 0 and 2.0 ",null,null,{"$f":"G20/10","v":1.7},null,17,null,null,null,null,"   the correlation coefficient r =",null,null,null,{"$f":"Sheet2!J11","v":0.65659950289928404}]
[null,null,null,null,null,null,null,null,null,null,null,"  and the sum of the squares =",null,null,null,{"$f":"Sheet2!H8","v":63.414857625899998}]
[]
[null,"Notice that as the points are squeezed closer to the regression line,",null,null,null,null,null,null,null,null,null,"Based on n = 6 data points,"]
[null,"   the value of the correlation coefficient gets closer to 1",null,null,null,null,null,null,null,null,null,"   the critical value for the correlation coefficient is r = 0.811"]
[null,"   and the value of the sum of the squares gets smaller."]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(P20 <0.811,\"   There is no significant correlation between the transformed data\",\"\")","v":"   There is no significant correlation between the transformed data"}]
[null,"As the points are stretched further from the regression line,",null,null,null,null,null,null,null,null,null,{"$f":"IF(P20>=0.811,\"  There is a significant level of correlation.\",\"\")","v":""}]
[null,"   the value of the correlation coefficient gets closer to 0"]
[null,"   and the value of the sum of the squares gets larger."]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[null,null,"   Item 4"]
[]
[]
[]
[]
[]
[]
["Created by:  Sheldon P. Gordon"]
["                     Farmingdale StateCollege"]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

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["x","y","yL","y -yL","(y -yL)2","New y","y -yL","(y -yL)2"]
[1,9,{"$f":"1.6571*A2+6.2","v":7.8571},{"$f":"B2-C2","v":1.1429},{"$f":"D2^2","v":1.3062204100000001},{"$f":"C2+n*D2","v":9.8000299999999996},{"$f":"F2-C2","v":1.9429299999999996},{"$f":"G2^2","v":3.7749769848999986}]
[2,7,9.5142000000000007,-2.5142000000000007,6.3212016400000035,5.2400599999999997,-4.2741400000000009,18.268272739600008]
[3,13,11.1713,1.8286999999999995,3.3441436899999983,14.28009,3.1087899999999991,9.6645752640999945]
[4,11,12.8284,-1.8284000000000002,3.3430465600000008,9.7201199999999996,-3.1082800000000006,9.6614045584000046]
[5,17,14.485500000000002,2.5144999999999982,6.3227102499999912,18.760149999999999,4.2746499999999976,18.27263262249998]
[6,15,16.142600000000002,-1.1426000000000016,1.3055347600000038,14.20018,-1.942420000000002,3.7729954564000079]
[null,null,null,null,{"$f":"SUM(E2:E7)","v":21.942857309999997},null,null,{"$f":"SUM(H2:H7)","v":63.414857625899998}]
[null,null,null,null,null,null,null,null,"y = 1.6571x + 6.2"]
[null,null,null,null,null,null,null,null,"r0 =",{"$f":"CORREL(A2:A7,B2:B7)","v":0.82857142857142851}]
[null,null,null,null,null,null,null,null,"r =",{"$f":"CORREL(A2:A7,F2:F7)","v":0.65659950289928404}]

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