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{"sheet":"Title","index":0,"n_rows":9,"n_cols":3,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
[null,null,"Calculation practice activities to accompany\nCHAPTER 12"]
[]
[null,null,"Social Statistics in Action: A Canadian Introduction"]
[null,null,"Andrea M. Noack"]
[]
[null,null,"Oxford University Press, 2018"]
[]
[null,null,"For more information, visit: "]
[null,null,"https://www.oupcanada.com/catalog/9780199015214.html"]

{"sheet":"Multiple Regression Predictions","index":1,"n_rows":21,"n_cols":5,"rows_kept":21,"cut":false,"hidden":false,"merged":[[12,4,12,5],[2,1,2,5],[0,1,0,5]]}
[null,"PRACTICE CALCULATING REGRESSION PREDICTIONS\n(MULTIPLE LINEAR REGRESSION)"]
[]
[null,"Use the constant and slope coefficients to find the predicted value on the dependent variable (y) \nfor a case with the values on the independent variables (x1, x2 and x3) specified in the yellow highlighted cells.  \nKeep two decimal places throughout your calculations.\nTo check your answer, click on the 'Show Answer' button."]
[]
[null,"Linear Regression Coefficients"]
[null,"Constant Coefficient (a):",18.93]
[null,"Slope Coefficient for Variable X1 (b1):",4.66]
[null,"Slope Coefficient for Variable X2 (b2):",-8.42]
[null,"Slope Coefficient for Variable X3 (b3):",9.75]
[]
[null,"The Case you are Making a Prediction for:"]
[null,"Value on Variable X1:",76]
[null,"Value on Variable X2:",36.159999999999997,null,"Need some help?"]
[null,"Value on Variable X3 (dummy variable):",0]
[null,"Predicted Value on Variable Y:","hidden"]
[]
[null,"REGRESSION PREDICTION CALCULATIONS"]
[null,"Predicted Value on Variable Y"]
[null,null,"= 18.93 + (4.66 x 76) + (-8.42 x 36.16) + (9.75 x 0)"]
[null,null,"= ? + ? + ? + ?"]
[null,null,"= ?"]

{"sheet":"Multiple Regress. Coefficients","index":2,"n_rows":45,"n_cols":5,"rows_kept":45,"cut":false,"hidden":false,"merged":[[0,1,0,5],[2,1,2,5],[20,4,20,5]]}
[null,"PRACTICE CALCULATING REGRESSION COEFFICIENTS \n(MULTIPLE LINEAR REGRESSION, TWO INDEPENDENT VARIABLES)"]
[]
[null,"Use the correlations and standard deviations in the yellow highlighted cells to calculate the partial slope coefficient \nfor each of the two independent variables. \nThen, use the partial slope coefficients and the variable means to calculate the constant coefficient. \nKeep four decimal places throughout your calculations.\nTo check your answers, click on the 'Show Slope Coefficients' and/or 'Show Constant Coefficient' buttons."]
[]
[null,"Means"]
[null,"Mean of Variable X1 (x-bar1):",25.6]
[null,"Mean of Variable X2 (x-bar2):",72.599999999999994]
[null,"Mean of Variable Y (y-bar):",187.47]
[]
[null,"Standard Deviations"]
[null,"Standard deviation of Variable X1 (sx₁):",14.31]
[null,"Standard deviation of Variable X2 (sx₂):",48.23]
[null,"Standard deviation of Variable Y (sy):",145.94999999999999]
[]
[null,"Correlations between Variables"]
[null,"Correlation between Variables X1 and X2 (rx₁,x₂):",0.34]
[null,"Correlation between Variables X1 and Y (rx₁,y):",0.5]
[null,"Correlation between Variables X2 and Y (rx₂,y):",0.27]
[]
[null,"Regression Coefficients"]
[null,"Partial slope coefficient for Variable X1:","hidden",null,"Need some help?"]
[null,"Partial slope coefficient for Variable X2:","hidden"]
[null,"Constant Coefficient:","hidden"]
[]
[null,"PARTIAL SLOPE COEFFICIENT FOR VARIABLE X1 CALCULATIONS"]
[null,"Partial Slope Coefficient (bx₁)"]
[null,null,"= {[0.5 - (0.34 x 0.27)] ÷ [1 - (0.34²)]} x (145.95 ÷ 14.31)"]
[null,null,"= [(? - ?) ÷ (? - ?)] x (? ÷ ?)"]
[null,null,"= (? ÷ ?) x (?)"]
[null,null,"= ? x ?"]
[null,null,"= ?"]
[]
[null,"PARTIAL SLOPE COEFFICIENT FOR VARIABLE X2 CALCULATIONS"]
[null,"Partial Slope Coefficient (bx₂)"]
[null,null,"= {[0.27 - (0.34 x 0.5)] ÷ [1 - (0.34²)]} x (145.95 ÷ 48.23)"]
[null,null,"= [(? - ?) ÷ (? - ?)] x (? ÷ ?)"]
[null,null,"= (? ÷ ?) x (?)"]
[null,null,"= ? x ?"]
[null,null,"= ?"]
[]
[null,"CONSTANT COEFFICIENT CALCULATIONS"]
[null,"Constant Coefficient"]
[null,null,"= 187.47 - (4.708 x 25.6) - (0.3423 x 72.6)"]
[null,null,"= ? - ? - ?"]
[null,null,"= ?"]

{"sheet":"Standardized Slope Coefficients","index":3,"n_rows":29,"n_cols":6,"rows_kept":29,"cut":false,"hidden":false,"merged":[[0,1,0,6],[2,1,2,6],[5,1,5,2],[6,1,6,2],[7,1,7,2],[15,1,15,2],[16,1,16,2],[4,1,4,2],[9,1,9,2],[14,1,14,2],[10,1,10,2],[11,1,11,2],[12,1,12,2]]}
[null,"PRACTICE CALCULATING STANDARDIZED SLOPE COEFFICIENTS\n(MULTIPLE LINEAR REGRESSION)"]
[]
[null,"Use the variable standard deviations to calculate standardized slope coefficients for the \ntwo unstandardized slope coefficients in the yellow highlighted cells.   \nKeep four decimal places throughout your calculations.\nTo check your answers, click on the 'Show Answers' button."]
[]
[null,"Standard Deviations"]
[null,"Standard deviation of Variable X1 (sx):",null,13.61]
[null,"Standard deviation of Variable X2 (sx):",null,57.51]
[null,"Standard deviation of Variable Y (sy):",null,127.83]
[]
[null,"Linear Regression Coefficients (Unstandardized)"]
[null,"Constant Coefficient (a):",null,64.62]
[null,"Slope Coefficient for Variable X1 (bx):",null,3.27]
[null,"Slope Coefficient for Variable X2 (bx):",null,0.33,null,"Need some help?"]
[]
[null,"Standardized Slope Coefficients"]
[null,"Standardized Slope Coefficient for Variable X1:",null,"hidden"]
[null,"Standardized Slope Coefficient for Variable X2:",null,"hidden"]
[]
[null,"STANDARDIZED SLOPE COEFFICIENT FOR VARIABLE X1 CALCULATIONS "]
[null,"Standardized Slope Coefficient (βx₁)"]
[null,null,"= 3.27 x (13.61 ÷ 127.83)"]
[null,null,"= ? x ?"]
[null,null,"= ?"]
[]
[null,"STANDARDIZED SLOPE COEFFICIENT FOR VARIABLE X2 CALCULATIONS "]
[null,"Standardized Slope Coefficient (βx₂)"]
[null,null,"= 0.33 x (57.51 ÷ 127.83)"]
[null,null,"= ? x ?"]
[null,null,"= ?"]

{"sheet":"Regression Predictions-A","index":4,"n_rows":21,"n_cols":6,"rows_kept":21,"cut":false,"hidden":true,"merged":[[0,1,0,3],[2,1,2,3]]}
[null,"PRACTICE CALCULATING REGRESSION PREDICTIONS\n(SIMPLE LINEAR REGRESSION)"]
[]
[]
[]
[null,"Linear Regression Coefficients"]
[{"$f":"RANDBETWEEN(100,5000)/100","v":32.81},"Constant Coefficient (a)",18.93]
[{"$f":"RANDBETWEEN(100,1000)/100","v":6.05},"Slope Coefficient for Variable X1 (b1)",4.66]
[{"$f":"(RANDBETWEEN(100,1000)/100)*-1","v":-2.5499999999999998},"Slope Coefficient for Variable X2 (b2)",-8.42]
[{"$f":"RANDBETWEEN(100,1000)/100","v":1.22},"Slope Coefficient for Variable X3 (b3)",9.75]
[]
[null,"The Case you are Making a Prediction for:"]
[{"$f":"RANDBETWEEN(16,80)","v":63},"Value on Variable X1",76]
[{"$f":"RANDBETWEEN(100,5000)/100","v":31.17},"Value on Variable X2",36.159999999999997]
[{"$f":"RANDBETWEEN(0,1)","v":0},"Value on Variable X3",0]
[null,"Predicted Value on Variable Y",{"$f":"D21","v":68.62}]
[]
[null,"REGRESSION PREDICTION CALCULATIONS"]
[null,"Predicted value on variable Y","FORMULA"]
[null,null,{"$f":"CONCATENATE(\"'= \",C6,\" + (\",C7,\" x \",C12,\") + (\",C8,\" x \",C13,\") + (\",C9,\" x \",C14,\")\")","v":"'= 18.93 + (4.66 x 76) + (-8.42 x 36.16) + (9.75 x 0)"}]
[null,null,{"$f":"CONCATENATE(\"'= \",C6,\" + (\",D20,\") + (\",E20,\") + (\",F20,\")\")","v":"'= 18.93 + (354.16) + (-304.47) + (0)"},{"$f":"ROUND(C12*C7,2)","v":354.16},{"$f":"ROUND(C8*C13,2)","v":-304.47000000000003},{"$f":"ROUND(C9*C14,2)","v":0}]
[null,null,{"$f":"CONCATENATE(\"'= \",D21)","v":"'= 68.62"},{"$f":"ROUND(C6+D20+E20+F20,2)","v":68.62}]

{"sheet":"Multiple Regression Coeff-A","index":5,"n_rows":106,"n_cols":14,"rows_kept":106,"cut":false,"hidden":true,"merged":[[0,1,0,5],[2,1,2,5],[19,4,19,5]]}
[null,"PRACTICE CALCULATING REGRESSION COEFFICIENTS \n(MULTIPLE LINEAR REGRESSION, TWO INDEPENDENT VARIABLES)"]
[]
[]
[]
[null,"Means"]
[null,"Mean of Variable X1 ",{"$f":"ROUND(AVERAGE($H$6:$H$106),2)","v":25.6},null,null,null,null,45,98,373,null,{"$f":"RANDBETWEEN(0,50)","v":34},{"$f":"IF(L6<25,RANDBETWEEN(0,100),RANDBETWEEN(0,200))","v":152},{"$f":"IF(L6>25,RANDBETWEEN(0,500),RANDBETWEEN(0,200))","v":280}]
[null,"Mean of Variable X2 ",{"$f":"ROUND(AVERAGE($I$6:$I$106),2)","v":72.599999999999994},null,null,null,null,14,27,35,null,{"$f":"RANDBETWEEN(0,50)","v":47},{"$f":"IF(L7<25,RANDBETWEEN(0,100),RANDBETWEEN(0,200))","v":86},{"$f":"IF(L7>25,RANDBETWEEN(0,500),RANDBETWEEN(0,200))","v":366}]
[null,"Mean of Variable Y",{"$f":"ROUND(AVERAGE($J$6:$J$106),2)","v":187.47},null,null,null,null,34,28,36,null,30,10,316]
[null,null,null,null,null,null,null,31,145,369,null,34,46,257]
[null,"Standard Deviations",null,null,null,null,null,50,15,321,null,18,80,186]
[null,"Standard deviation of Variable X1 ",{"$f":"ROUND(_xlfn.STDEV.S($H$6:$H$106),2)","v":14.31},null,null,null,null,10,46,155,null,11,48,109]
[null,"Standard deviation of Variable X2 ",{"$f":"ROUND(_xlfn.STDEV.S($I$6:$I$106),2)","v":48.23},null,null,null,null,27,107,452,null,30,11,399]
[null,"Standard deviation of Variable Y",{"$f":"ROUND(_xlfn.STDEV.S($J$6:$J$106),2)","v":145.94999999999999},null,null,null,null,9,75,190,null,41,161,253]
[null,null,null,null,null,null,null,45,65,497,null,36,100,64]
[null,"Correlations between Variables",null,null,null,null,null,32,62,329,null,21,73,34]
[null,"Correlation between Variables X1 and X2",{"$f":"ROUND(CORREL(H$6:H$106,I$6:I$106),2)","v":0.34},null,null,null,null,34,156,286,null,32,147,181]
[null,"Correlation between Variables X1 and Y",{"$f":"ROUND(CORREL(H$6:H$106,J$6:J$106),2)","v":0.5},null,null,null,null,42,119,470,null,28,74,108]
[null,"Correlation between Variables X2 and Y",{"$f":"ROUND(CORREL(I$6:I$106,J$6:J$106),2)","v":0.27},null,null,null,null,12,21,92,null,11,87,49]
[null,null,null,null,null,null,null,28,110,461,null,41,21,480]
[null,"Regression Coefficients",null,null,"Need some help?",null,null,47,40,370,null,31,3,100]
[null,"Partial slope coefficient for Variable X1",{"$f":"F31","v":4.7080000000000002},null,null,null,null,32,59,379,null,7,56,187]
[null,"Partial slope coefficient for Variable X2",{"$f":"F39","v":0.34229999999999999},null,null,null,null,41,192,0,null,43,58,221]
[null,"Constant Coefficient",{"$f":"F45","v":42.094200000000001},null,null,null,null,40,106,215,null,27,0,236]
[null,null,null,null,null,null,null,12,60,198,null,50,90,454]
[null,"PARTIAL SLOPE COEFFICIENT FOR VARIABLE X1 CALCULATIONS",null,null,null,null,null,31,146,479,null,48,103,7]
[null,"Partial Slope Coefficient (b1)",null,null,null,null,null,27,65,418,null,0,21,21]
[null,null,{"$f":"CONCATENATE(\"'= {[\",C17,\" - (\",C16,\" x \",C18,\")] ÷ [1 - (\",C16,F27,\")]} x (\",C13,\" ÷ \",C11,\")\")","v":"'= {[0.5 - (0.34 x 0.27)] ÷ [1 - (0.34²)]} x (145.95 ÷ 14.31)"},null,null,"²",null,35,163,169,null,25,167,87]
[null,null,{"$f":"CONCATENATE(\"'= [(\",C17,\" - \",F28,\") ÷ (1 - \",G28,\")] x (\",C13,\" ÷ \",C11,\")\")","v":"'= [(0.5 - 0.0918) ÷ (1 - 0.1156)] x (145.95 ÷ 14.31)"},null,null,{"$f":"ROUND(C16*C18,4)","v":9.1800000000000007E-2},{"$f":"ROUND(C16*C16,4)","v":0.11559999999999999},18,99,21,null,16,78,129]
[null,null,{"$f":"CONCATENATE(\"'= (\",F29,\" ÷ \",G29,\") x (\",G30,\")\")","v":"'= (0.4082 ÷ 0.8844) x (10.1992)"},null,null,{"$f":"ROUND(C17-F28,4)","v":0.40820000000000001},{"$f":"ROUND(1-G28,4)","v":0.88439999999999996},43,33,460,null,23,7,98]
[null,null,{"$f":"CONCATENATE(\"'= \",F30,\" x \",G30)","v":"'= 0.4616 x 10.1992"},null,null,{"$f":"ROUND(F29/G29,4)","v":0.46160000000000001},{"$f":"ROUND(C13/C11,4)","v":10.199199999999999},42,115,324,null,44,84,417]
[null,null,{"$f":"CONCATENATE(\"'= \",F31)","v":"'= 4.708"},null,null,{"$f":"ROUND(F30*G30,4)","v":4.7080000000000002},null,26,47,274,null,13,35,18]
[null,null,null,null,null,null,null,42,43,118,null,24,6,133]
[null,"PARTIAL SLOPE COEFFICIENT FOR VARIABLE X2 CALCULATIONS",null,null,null,null,null,32,103,73,null,13,26,183]
[null,"Partial Slope Coefficient (b2)",null,null,null,null,null,5,53,111,null,29,68,500]
[null,null,{"$f":"CONCATENATE(\"'= {[\",C18,\" - (\",C16,\" x \",C17,\")] ÷ [1 - (\",C16,F27,\")]} x (\",C13,\" ÷ \",C12,\")\")","v":"'= {[0.27 - (0.34 x 0.5)] ÷ [1 - (0.34²)]} x (145.95 ÷ 48.23)"},null,null,null,null,10,95,52,null,10,67,22]
[null,null,{"$f":"CONCATENATE(\"'= [(\",C18,\" - \",F36,\") ÷ (1 - \",G36,\")] x (\",C13,\" ÷ \",C12,\")\")","v":"'= [(0.27 - 0.17) ÷ (1 - 0.1156)] x (145.95 ÷ 48.23)"},null,null,{"$f":"ROUND(C16*C17,4)","v":0.17},{"$f":"ROUND(C16*C16,4)","v":0.11559999999999999},18,16,76,null,2,77,86]
[null,null,{"$f":"CONCATENATE(\"'= (\",F37,\" ÷ \",G37,\") x (\",G38,\")\")","v":"'= (0.1 ÷ 0.8844) x (3.0261)"},null,null,{"$f":"ROUND(C18-F36,4)","v":0.1},{"$f":"ROUND(1-G36,4)","v":0.88439999999999996},21,36,98,null,0,43,137]
[null,null,{"$f":"CONCATENATE(\"'= \",F38,\" x \",G38)","v":"'= 0.1131 x 3.0261"},null,null,{"$f":"ROUND(F37/G37,4)","v":0.11310000000000001},{"$f":"ROUND(C13/C12,4)","v":3.0261},16,93,30,null,31,55,41]
[null,null,{"$f":"CONCATENATE(\"'= \",F39)","v":"'= 0.3423"},null,null,{"$f":"ROUND(F38*G38,4)","v":0.34229999999999999},null,14,7,34,null,25,172,95]
[null,null,null,null,null,null,null,49,26,260,null,35,18,67]
[null,"CONSTANT COEFFICIENT",null,null,null,null,null,38,90,418,null,12,28,70]
[null,"Constant Coefficient",null,null,null,null,null,8,77,162,null,32,62,324]
[null,null,{"$f":"CONCATENATE(\"'= \",C8,\" - (\",F31,\" x \",C6,\") - (\",F39,\" x \",C7,\")\")","v":"'= 187.47 - (4.708 x 25.6) - (0.3423 x 72.6)"},null,null,null,null,47,105,118,null,28,121,448]
[null,null,{"$f":"CONCATENATE(\"'= \",C8,\" - (\",F44,\") - (\",G44,\")\")","v":"'= 187.47 - (120.5248) - (24.851)"},null,null,{"$f":"ROUND(F31*C6,4)","v":120.5248},{"$f":"ROUND(F39*C7,4)","v":24.850999999999999},0,5,154,null,42,89,373]
[null,null,{"$f":"CONCATENATE(\"'= \",F45)","v":"'= 42.0942"},null,null,{"$f":"ROUND(C8-F44-G44,4)","v":42.094200000000001},null,49,125,87,null,13,75,32]
[null,null,null,null,null,null,null,39,111,408,null,14,66,103]
[null,null,null,null,null,null,null,16,45,96,null,10,86,159]
[null,null,null,null,null,null,null,15,84,7,null,37,125,108]
[null,null,null,null,null,null,null,25,168,196,null,15,28,98]
[null,null,null,null,null,null,null,27,39,14,null,35,48,3]
[null,null,null,null,null,null,null,20,80,180,null,44,37,179]
[null,null,null,null,null,null,null,26,50,471,null,21,26,88]
[null,null,null,null,null,null,null,29,173,472,null,7,24,143]
[null,null,null,null,null,null,null,6,16,50,null,15,54,137]
[null,null,null,null,null,null,null,45,129,435,null,27,134,274]
[null,null,null,null,null,null,null,39,103,120,null,44,89,357]
[null,null,null,null,null,null,null,29,42,361,null,35,44,35]
[null,null,null,null,null,null,null,1,79,192,null,25,139,187]
[null,null,null,null,null,null,null,17,0,183,null,24,74,24]
[null,null,null,null,null,null,null,26,88,204,null,23,10,84]
[null,null,null,null,null,null,null,10,52,24,null,16,92,49]
[null,null,null,null,null,null,null,7,20,81,null,22,69,87]
[null,null,null,null,null,null,null,37,6,184,null,17,19,94]
[null,null,null,null,null,null,null,10,82,9,null,37,114,170]
[null,null,null,null,null,null,null,46,145,344,null,48,15,377]
[null,null,null,null,null,null,null,40,135,162,null,2,84,28]
[null,null,null,null,null,null,null,37,47,50,null,0,17,10]
[null,null,null,null,null,null,null,3,79,19,null,26,159,99]
[null,null,null,null,null,null,null,20,56,132,null,44,185,49]
[null,null,null,null,null,null,null,21,60,54,null,39,95,457]
[null,null,null,null,null,null,null,9,18,67,null,{"$f":"RANDBETWEEN(0,50)","v":14},{"$f":"IF(L71<25,RANDBETWEEN(0,100),RANDBETWEEN(0,200))","v":21},{"$f":"IF(L71>25,RANDBETWEEN(0,500),RANDBETWEEN(0,200))","v":53}]
[null,null,null,null,null,null,null,9,36,26,null,9,84,140]
[null,null,null,null,null,null,null,31,82,195,null,24,96,99]
[null,null,null,null,null,null,null,12,38,151,null,14,21,14]
[null,null,null,null,null,null,null,37,27,234,null,49,85,147]
[null,null,null,null,null,null,null,5,56,160,null,47,123,116]
[null,null,null,null,null,null,null,2,91,159,null,6,45,17]
[null,null,null,null,null,null,null,12,92,34,null,20,16,25]
[null,null,null,null,null,null,null,34,77,482,null,12,33,155]
[null,null,null,null,null,null,null,18,13,99,null,48,142,364]
[null,null,null,null,null,null,null,9,54,116,null,28,53,388]
[null,null,null,null,null,null,null,24,50,37,null,3,21,164]
[null,null,null,null,null,null,null,24,100,155,null,17,11,134]
[null,null,null,null,null,null,null,12,24,57,null,43,15,180]
[null,null,null,null,null,null,null,48,0,136,null,2,92,98]
[null,null,null,null,null,null,null,40,25,101,null,28,183,419]
[null,null,null,null,null,null,null,15,56,41,null,6,56,53]
[null,null,null,null,null,null,null,36,184,73,null,37,18,151]
[null,null,null,null,null,null,null,42,182,364,null,48,102,412]
[null,null,null,null,null,null,null,18,20,12,null,8,13,79]
[null,null,null,null,null,null,null,32,104,224,null,21,58,100]
[null,null,null,null,null,null,null,19,76,77,null,39,128,221]
[null,null,null,null,null,null,null,9,97,11,null,7,80,39]
[null,null,null,null,null,null,null,11,4,139,null,23,77,116]
[null,null,null,null,null,null,null,10,54,183,null,3,40,143]
[null,null,null,null,null,null,null,40,18,49,null,13,65,14]
[null,null,null,null,null,null,null,50,107,188,null,5,77,80]
[null,null,null,null,null,null,null,27,93,68,null,36,127,251]
[null,null,null,null,null,null,null,2,56,91,null,6,83,13]
[null,null,null,null,null,null,null,32,169,104,null,13,44,198]
[null,null,null,null,null,null,null,47,15,421,null,3,77,170]
[null,null,null,null,null,null,null,28,90,145,null,7,86,121]
[null,null,null,null,null,null,null,11,58,197,null,40,43,160]
[null,null,null,null,null,null,null,23,24,166,null,38,111,165]
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{"sheet":"Standardized Slope Coeff-A","index":6,"n_rows":110,"n_cols":12,"rows_kept":110,"cut":false,"hidden":true,"merged":[[7,1,7,2],[0,1,0,6],[2,1,2,6],[4,1,4,2],[5,1,5,2],[6,1,6,2],[15,1,15,2],[16,1,16,2],[9,1,9,2],[10,1,10,2],[11,1,11,2],[12,1,12,2],[14,1,14,2]]}
[null,"PRACTICE CALCULATING STANDARDIZED SLOPE COEFFICIENTS\n(MULTIPLE LINEAR REGRESSION)"]
[]
[]
[null,null,null,null,null,{"$f":"CORREL(F10:F110, H10:H110)","v":0.39360203032594565},{"$f":"CORREL(G10:G110, H10:H110)","v":0.25522323314275253},{"$f":"CORREL(G10:G110, F10:F110)","v":0.30058730464733702}]
[null,"Standard Deviations"]
[null,"Standard deviation of Variable X1 ",null,{"$f":"ROUND(E6,2)","v":13.61},{"$f":"_xlfn.STDEV.S(F10:F110)","v":13.607671103876928},{"$f":"F4-(H4*G4)","v":0.3168851665921868},{"$f":"1-(H4*H4)","v":0.90964727228484898},{"$f":"F6/G6","v":0.34836048680301729},{"$f":"D8/D6","v":9.3923585598824388},null,{"$f":"H6*I6","v":3.2719266001491327}]
[null,"Standard deviation of Variable X2 ",null,{"$f":"ROUND(E7,2)","v":57.51},{"$f":"_xlfn.STDEV.S(G10:G110)","v":57.511552003587816},{"$f":"G4-(H4*F4)","v":0.13691145974335711},null,{"$f":"F7/G6","v":0.15051049336899935},{"$f":"D8/D7","v":2.2227438706311946},null,{"$f":"H7*I7","v":0.3345462766016204}]
[null,"Standard deviation of Variable Y",null,{"$f":"ROUND(E8,2)","v":127.83},{"$f":"_xlfn.STDEV.S(H10:H110)","v":127.82705054676474},{"$f":"AVERAGE(F10:F110)","v":28.653465346534652},{"$f":"AVERAGE(G10:G110)","v":75.683168316831683},{"$f":"AVERAGE(H10:H110)","v":183.69306930693068},{"$f":"H8-(F8*K6)-(G8*K7)","v":64.621511691342789}]
[null,null,null,null,null,"X1","X2","Y"]
[null,"Linear Regression Coefficients (Unstandardized)",null,null,null,9,82,172,null,{"$f":"RANDBETWEEN(0,50)","v":29},{"$f":"IF(J10<25,RANDBETWEEN(0,100),RANDBETWEEN(0,200))","v":191},{"$f":"IF(J10>25,RANDBETWEEN(0,500),RANDBETWEEN(0,200))","v":331}]
[null,"Constant Coefficient (a)",null,{"$f":"ROUND(I8,2)","v":64.62},null,12,60,196,null,{"$f":"RANDBETWEEN(0,50)","v":1},{"$f":"IF(J11<25,RANDBETWEEN(0,100),RANDBETWEEN(0,200))","v":75},{"$f":"IF(J11>25,RANDBETWEEN(0,500),RANDBETWEEN(0,200))","v":39}]
[null,"Slope Coefficient for Variable X1 (b1)",null,{"$f":"ROUND(K6,2)","v":3.27},null,22,29,196,null,14,56,83]
[null,"Slope Coefficient for Variable X2 (b2)",null,{"$f":"ROUND(K7,2)","v":0.33},null,24,37,95,null,7,40,185]
[null,null,null,null,null,31,42,343,null,32,79,340]
[null,"Standardized Slope Coefficients",null,null,null,2,87,88,null,40,134,497]
[null,"Standardized Slope Coefficient for Variable X1 (βx1)",null,{"$f":"D23","v":0.3483},null,33,179,373,null,10,87,44]
[null,"Standardized Slope Coefficient for Variable X2 (βx2)",null,{"$f":"D29","v":0.14849999999999999},null,32,186,219,null,43,58,71]
[null,null,null,null,null,10,13,92,null,43,13,421]
[null,"STANDARDIZED SLOPE COEFFICIENT FOR VARIABLE X1 CALCULATIONS ",null,null,null,45,0,270,null,14,25,176]
[null,"Standardized Slope Coefficient (βx1)",null,null,null,35,197,494,null,43,101,95]
[null,null,{"$f":"CONCATENATE(\"'= \",D12,\" x (\",D6,\" ÷ \",D8,\")\")","v":"'= 3.27 x (13.61 ÷ 127.83)"},null,null,28,135,168,null,17,50,168]
[null,null,{"$f":"CONCATENATE(\"'= \",D12,\" x \",D22)","v":"'= 3.27 x 0.1065"},{"$f":"ROUND(D6/D8,4)","v":0.1065},null,5,97,129,null,33,24,493]
[null,null,{"$f":"CONCATENATE(\"'= \",D23)","v":"'= 0.3483"},{"$f":"ROUND(D12*D22,4)","v":0.3483},null,50,166,300,null,26,28,307]
[null,null,null,null,null,18,81,111,null,45,40,201]
[null,"STANDARDIZED SLOPE COEFFICIENT FOR VARIABLE X2 CALCULATIONS ",null,null,null,28,118,60,null,12,29,61]
[null,"Standardized Slope Coefficient (βx2)",null,null,null,35,169,90,null,44,7,52]
[null,null,{"$f":"CONCATENATE(\"'= \",D13,\" x (\",D7,\" ÷ \",D8,\")\")","v":"'= 0.33 x (57.51 ÷ 127.83)"},null,null,21,49,20,null,36,165,35]
[null,null,{"$f":"CONCATENATE(\"'= \",D13,\" x \",D28)","v":"'= 0.33 x 0.4499"},{"$f":"ROUND(D7/D8,4)","v":0.44990000000000002},null,47,64,160,null,7,86,112]
[null,null,{"$f":"CONCATENATE(\"'= \",D29)","v":"'= 0.1485"},{"$f":"ROUND(D13*D28,4)","v":0.14849999999999999},null,4,30,151,null,23,31,45]
[null,null,null,null,null,21,6,6,null,48,45,83]
[null,null,null,null,null,34,100,400,null,35,47,391]
[null,null,null,null,null,36,176,184,null,2,61,123]
[null,null,null,null,null,39,187,315,null,27,0,424]
[null,null,null,null,null,20,79,122,null,7,43,78]
[null,null,null,null,null,27,170,255,null,10,61,139]
[null,null,null,null,null,46,106,328,null,21,32,52]
[null,null,null,null,null,29,147,443,null,49,28,289]
[null,null,null,null,null,34,66,91,null,0,93,65]
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