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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 11"]
[]
[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":"Regression Predictions","index":1,"n_rows":19,"n_cols":3,"rows_kept":19,"cut":false,"hidden":false,"merged":[[2,1,2,4],[0,1,0,4]]}
[null,"PRACTICE CALCULATING REGRESSION PREDICTIONS\n(SIMPLE LINEAR REGRESSION)"]
[]
[null,"Use the slope and the constant coefficient to calculate the predicted value on the dependent variable (y), \nfor a case with the value on the independent variable (x) specified in the yellow highlighted cell.  \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):",16.41]
[null,"Slope Coefficient (b):",8.9700000000000006]
[]
[null,"The Case you are Making a Prediction for:"]
[null,"Value on Variable X:",31.37]
[null,"Predicted Value on Variable Y:","hidden"]
[]
[null,"Need some help?"]
[]
[null,"REGRESSION PREDICTION CALCULATIONS"]
[null,"Predicted value on variable Y"]
[null,null,"= 16.41 + (8.97 x 31.37)"]
[null,null,"= ? + ?"]
[null,null,"= ?"]

{"sheet":"Slope & Constant Coefficients","index":2,"n_rows":55,"n_cols":11,"rows_kept":55,"cut":false,"hidden":false,"merged":[[0,1,0,11],[2,1,2,11],[5,1,6,1],[5,2,6,2],[5,3,6,3],[5,5,5,7],[18,1,18,2],[21,4,21,5],[21,8,21,9],[22,4,22,5],[22,8,22,9],[23,4,23,5],[23,8,23,9],[24,4,24,5],[24,8,24,9],[25,4,25,5],[25,8,25,9],[26,4,26,5],[26,8,26,9],[27,4,27,5],[27,8,27,9],[28,4,28,5],[28,8,28,9],[29,4,29,5],[29,8,29,9],[30,4,30,5],[30,8,30,9],[31,4,31,5],[31,8,31,9],[39,4,39,5],[39,8,39,9],[34,4,34,5],[34,8,34,9],[35,4,35,5],[35,8,35,9],[36,4,36,5],[36,8,36,9],[16,5,16,6],[3,9,3,11],[43,4,43,5],[43,8,43,9],[44,4,44,5],[44,8,44,9],[40,4,40,5],[40,8,40,9],[41,4,41,5],[41,8,41,9],[42,4,42,5],[42,8,42,9],[37,4,37,5],[37,8,37,9],[38,4,38,5],[38,8,38,9]]}
[null,"PRACTICE CALCULATING SLOPE AND CONSTANT COEFFICIENTS\n(SIMPLE LINEAR REGRESSION)"]
[]
[null,"First, calculate the sum of products and the sum of squares X, in order to find the slope coefficient. \nThen, use the slope coefficient and the variable means to calculate the constant coefficient.  \nKeep two decimal places throughout your calculations.\nTo check your answers, click on the 'Show Slope Coefficient' and/or 'Show Constant Coefficient' buttons."]
[]
[]
[null,"Case #","Value on \nVariable X","Value on \nVariable Y",null,"Means"]
[null,null,null,null,null,"Mean of Variable X (x-bar):",null,12.9]
[null,1,4,29,null,"Mean of Variable Y (y-bar):",null,20]
[null,2,4,13]
[null,3,29,27,null,"Regression Coefficients"]
[null,4,2,23,null,"Sum of Products:",null,"hidden"]
[null,5,29,7,null,"Sum of Squares X:",null,"hidden"]
[null,6,19,29]
[null,7,5,11,null,"Slope Coefficient:",null,"hidden"]
[null,8,8,8,null,"Constant Coefficient:",null,"hidden"]
[null,9,7,29]
[null,10,22,24,null,"Need some help?"]
[]
[]
[]
[null,"SUM OF PRODUCTS CALCULATION"]
[null,"Case #","Value on \nVariable X\n","Mean of \nVariable X\n","(Value-Mean)\nVariable X \n",null,"Value on \nVariable Y\n","Mean of \nVariable Y\n","(Value-Mean)\nVariable Y\n",null,"(Value-Mean Variable X) x (Value-Mean Variable Y)\n"]
[null,1,4,12.9,"4 - 12.9 = ?",null,29,20,"29 - 20 = ?",null,"-8.9 x 9 = ?"]
[null,2,4,12.9,"4 - 12.9 = ?",null,13,20,"13 - 20 = ?",null,"-8.9 x -7 = ?"]
[null,3,29,12.9,"29 - 12.9 = ?",null,27,20,"27 - 20 = ?",null,"16.1 x 7 = ?"]
[null,4,2,12.9,"2 - 12.9 = ?",null,23,20,"23 - 20 = ?",null,"-10.9 x 3 = ?"]
[null,5,29,12.9,"29 - 12.9 = ?",null,7,20,"7 - 20 = ?",null,"16.1 x -13 = ?"]
[null,6,19,12.9,"19 - 12.9 = ?",null,29,20,"29 - 20 = ?",null,"6.1 x 9 = ?"]
[null,7,5,12.9,"5 - 12.9 = ?",null,11,20,"11 - 20 = ?",null,"-7.9 x -9 = ?"]
[null,8,8,12.9,"8 - 12.9 = ?",null,8,20,"8 - 20 = ?",null,"-4.9 x -12 = ?"]
[null,9,7,12.9,"7 - 12.9 = ?",null,29,20,"29 - 20 = ?",null,"-5.9 x 9 = ?"]
[null,10,22,12.9,"22 - 12.9 = ?",null,24,20,"24 - 20 = ?",null,"9.1 x 4 = ?"]
[null,null,null,null,null,null,null,null,null,"Column Sum (Σ)","= ?"]
[null,"SUM OF SQUARES X CALCULATION"]
[null,"Case #","Value of \nVariable X\n","Mean of \nVariable X\n","(Value-Mean)\nVariable X\n",null,"(Value-Mean)2 Variable X\n"]
[null,1,4,12.9,"4 - 12.9 = ?",null,"-8.9 x -8.9 = ?"]
[null,2,4,12.9,"4 - 12.9 = ?",null,"-8.9 x -8.9 = ?"]
[null,3,29,12.9,"29 - 12.9 = ?",null,"16.1 x 16.1 = ?"]
[null,4,2,12.9,"2 - 12.9 = ?",null,"-10.9 x -10.9 = ?"]
[null,5,29,12.9,"29 - 12.9 = ?",null,"16.1 x 16.1 = ?"]
[null,6,19,12.9,"19 - 12.9 = ?",null,"6.1 x 6.1 = ?"]
[null,7,5,12.9,"5 - 12.9 = ?",null,"-7.9 x -7.9 = ?"]
[null,8,8,12.9,"8 - 12.9 = ?",null,"-4.9 x -4.9 = ?"]
[null,9,7,12.9,"7 - 12.9 = ?",null,"-5.9 x -5.9 = ?"]
[null,10,22,12.9,"22 - 12.9 = ?",null,"9.1 x 9.1 = ?"]
[null,null,null,null,null,"Column Sum (Σ)","= ?"]
[]
[null,"REGRESSION COEFFICIENT CALCULATIONS"]
[null,"Slope Coefficient"]
[null,null,null,"= 21 ÷ 1036.9"]
[null,null,null,"= ?"]
[null,"Constant Coefficient"]
[null,null,null,"= 20 - (0.02 x 12.9)"]
[null,null,null,"= ? - ?"]
[null,null,null,"= ?"]

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[null,"PRACTICE CALCULATING STANDARD ERRORS AND T-STATISTICS\n(SIMPLE LINEAR REGRESSION)"]
[]
[null,"First, use the regression coefficients to calculate the predicted values on Variable Y for each case. Then, calculate the standard error of the estimate, and the standard error of the slope and \nconstant coefficients. Use the standard errors to calculate the T-statistic for the slope and constant coefficients, as well as the degrees of freedom of the t-statistic.  \nKeep two decimal places throughout your calculations.\nTo check your answers, click on the 'Show Standard Errors' and/or 'Show T-Statistics' buttons."]
[]
[]
[null,"Case #","Value on \nVariable X","Value on \nVariable Y",null,"Means"]
[null,null,null,null,null,"Mean of Variable X (x-bar):",null,15.5]
[null,1,19,19]
[null,2,7,18,null,"Regression Coefficients"]
[null,3,18,27,null,"Slope Coefficient (b):",null,0.03]
[null,4,30,18,null,"Constant Coefficient (a):",null,18.43]
[null,5,27,25]
[null,6,21,27,null,"Standard Errors"]
[null,7,1,27,null,"Standard Error of the Estimate:",null,"hidden"]
[null,8,4,13,null,"Standard Error of the Slope Coefficient:",null,"hidden"]
[null,9,21,1,null,"Standard Error of the Constant Coefficient:",null,"hidden"]
[null,10,7,14]
[null,null,null,null,null,"T-Statistics"]
[null,"Need some help?",null,null,null,"T-Statistic for the Slope Coefficient:",null,"hidden"]
[null,null,null,null,null,"T-Statistic for the Constant Coefficient:",null,"hidden"]
[null,null,null,null,null,"Degrees of Freedom of the T-Statistic:",null,"hidden"]
[]
[null,null,null,null,null,"If the t-statistic is beyond +/- 2.31 then p<0.05. "]
[]
[null,"PREDICTED VALUES CALCULATIONS"]
[null,"Case #","Value on \nVariable X\n","Constant Coefficient\n","(Slope Coefficient) x (Value on X)",null,"Predicted Value on Variable Y\n"]
[null,1,19,18.43,"0.03 x 19 = ?",null,"18.43 + (0.57) = ?"]
[null,2,7,18.43,"0.03 x 7 = ?",null,"18.43 + (0.21) = ?"]
[null,3,18,18.43,"0.03 x 18 = ?",null,"18.43 + (0.54) = ?"]
[null,4,30,18.43,"0.03 x 30 = ?",null,"18.43 + (0.9) = ?"]
[null,5,27,18.43,"0.03 x 27 = ?",null,"18.43 + (0.81) = ?"]
[null,6,21,18.43,"0.03 x 21 = ?",null,"18.43 + (0.63) = ?"]
[null,7,1,18.43,"0.03 x 1 = ?",null,"18.43 + (0.03) = ?"]
[null,8,4,18.43,"0.03 x 4 = ?",null,"18.43 + (0.12) = ?"]
[null,9,21,18.43,"0.03 x 21 = ?",null,"18.43 + (0.63) = ?"]
[null,10,7,18.43,"0.03 x 7 = ?",null,"18.43 + (0.21) = ?"]
[]
[null,"STANDARD ERROR OF THE ESTIMATE NUMERATOR CALCULATIONS"]
[null,"Case #","Value on \nVariable Y\n","Predicted Value \non Variable Y\n","Value - \nPredicted Value ",null,"(Value - \nPredicted Value)2"]
[null,1,19,19,"19 - 19 = ?",null,"0 x 0 = ?"]
[null,2,18,18.64,"18 - 18.64 = ?",null,"-0.64 x -0.64 = ?"]
[null,3,27,18.97,"27 - 18.97 = ?",null,"8.03 x 8.03 = ?"]
[null,4,18,19.329999999999998,"18 - 19.33 = ?",null,"-1.33 x -1.33 = ?"]
[null,5,25,19.239999999999998,"25 - 19.24 = ?",null,"5.76 x 5.76 = ?"]
[null,6,27,19.059999999999999,"27 - 19.06 = ?",null,"7.94 x 7.94 = ?"]
[null,7,27,18.46,"27 - 18.46 = ?",null,"8.54 x 8.54 = ?"]
[null,8,13,18.55,"13 - 18.55 = ?",null,"-5.55 x -5.55 = ?"]
[null,9,1,19.059999999999999,"1 - 19.06 = ?",null,"-18.06 x -18.06 = ?"]
[null,10,14,18.64,"14 - 18.64 = ?",null,"-4.64 x -4.64 = ?"]
[null,null,null,null,null,"Column Sum (Σ)","= ?"]
[]
[null,"STANDARD ERROR OF THE ESTIMATE CALCULATIONS"]
[null,"Standard Error of the Estimate"]
[null,null,null,"= square root of [614.3 ÷ (10-2)]"]
[null,null,null,"= square root of (? ÷ ?)"]
[null,null,null,"= square root of ?"]
[null,null,null,"= ?"]
[]
[null,"SUM OF SQUARES X CALCULATION"]
[null,"Case #","Value on \nVariable X\n","Mean of \nVariable X\n","(Value-Mean)\nVariable X\n",null,"(Value-Mean)2 \nVariable X\n"]
[null,1,19,15.5,"19 - 15.5 = ?",null,"3.5 x 3.5 = ?"]
[null,2,7,15.5,"7 - 15.5 = ?",null,"-8.5 x -8.5 = ?"]
[null,3,18,15.5,"18 - 15.5 = ?",null,"2.5 x 2.5 = ?"]
[null,4,30,15.5,"30 - 15.5 = ?",null,"14.5 x 14.5 = ?"]
[null,5,27,15.5,"27 - 15.5 = ?",null,"11.5 x 11.5 = ?"]
[null,6,21,15.5,"21 - 15.5 = ?",null,"5.5 x 5.5 = ?"]
[null,7,1,15.5,"1 - 15.5 = ?",null,"-14.5 x -14.5 = ?"]
[null,8,4,15.5,"4 - 15.5 = ?",null,"-11.5 x -11.5 = ?"]
[null,9,21,15.5,"21 - 15.5 = ?",null,"5.5 x 5.5 = ?"]
[null,10,7,15.5,"7 - 15.5 = ?",null,"-8.5 x -8.5 = ?"]
[null,null,null,null,null,"Column Sum (Σ)","= ?"]
[]
[null,"STANDARD ERROR OF THE SLOPE & CONSTANT COEFFICIENT CALCULATIONS"]
[null,"Standard error of the \nslope coefficient (seb)"]
[null,null,null,"= 8.76 ÷ (square root of 908.5)"]
[null,null,null,"= ? ÷ ?"]
[null,null,null,"= ?"]
[null,"Standard error of \nthe constant coefficient (sea)"]
[null,null,null,"= 8.76 x square root of [(1 ÷ 10) + (15.5² ÷ 908.5)]"]
[null,null,null,"= ? x square root of [(? ÷ ?) + (? ÷ ?)]"]
[null,null,null,"= ? x square root of (? + ?)"]
[null,null,null,"= ? x square root of ?"]
[null,null,null,"= ? x ?"]
[null,null,null,"= ?"]
[]
[null,"T-STATISTIC CALCULATIONS"]
[null,"T-Statistic for the slope coefficient"]
[null,null,null,"= 0.03 ÷ 0.29"]
[null,null,null,"= ?"]
[null,"T-Statistic for the constant coefficient"]
[null,null,null,"= 18.43 ÷ 5.26"]
[null,null,null,"= ?"]
[null,"Degrees of freedom for \nregression coefficients"]
[null,null,null,"= 10 - 1 - 1"]
[null,null,null,"= ?"]

{"sheet":"R-Squared","index":4,"n_rows":63,"n_cols":8,"rows_kept":63,"cut":false,"hidden":false,"merged":[[2,1,2,9],[0,1,0,9],[19,8,19,9],[15,5,16,6],[20,8,20,9],[3,9,3,11],[5,1,6,1],[5,2,6,2],[5,3,6,3],[9,5,9,7],[23,4,23,5],[21,8,21,9],[24,4,24,5],[22,8,22,9],[25,4,25,5],[23,8,23,9],[24,8,24,9],[27,4,27,5],[25,8,25,9],[28,4,28,5],[26,8,26,9],[29,4,29,5],[27,8,27,9],[28,8,28,9],[29,8,29,9],[26,4,26,5],[41,8,41,9],[42,8,42,9],[19,4,19,5],[32,4,32,5],[20,4,20,5],[21,4,21,5],[22,4,22,5],[38,8,38,9],[39,8,39,9],[40,8,40,9],[35,8,35,9],[36,8,36,9],[37,8,37,9],[32,8,32,9],[33,8,33,9],[34,8,34,9],[50,8,50,9],[47,4,47,5],[48,4,48,5],[49,4,49,5],[50,4,50,5],[46,4,46,5],[46,8,46,9],[47,8,47,9],[48,8,48,9],[49,8,49,9],[56,4,56,5],[51,8,51,9],[52,8,52,9],[53,8,53,9],[54,8,54,9],[55,8,55,9],[56,8,56,9],[51,4,51,5],[52,4,52,5],[53,4,53,5],[54,4,54,5],[55,4,55,5],[33,4,33,5],[34,4,34,5],[35,4,35,5],[36,4,36,5],[37,4,37,5],[38,4,38,5],[39,4,39,5],[40,4,40,5],[41,4,41,5],[42,4,42,5]]}
[null,"PRACTICE CALCULATING R-SQUARED\n(SIMPLE LINEAR REGRESSION)"]
[]
[null,"First, use the regression coefficients to calculate the predicted values on Variable Y for each case. Then, calculate R-squared.  \nKeep two decimal places throughout your calculations.\nTo check your answer, click on the 'Show Answer' button."]
[]
[]
[null,"Case #","Value on \nVariable X","Value on \nVariable Y",null,"Regression Coefficients"]
[null,null,null,null,null,"Slope Coefficient (a):",null,0.96]
[null,1,4,3,null,"Constant Coefficient (b):",null,4.26]
[null,2,17,30]
[null,3,19,20,null,"Means"]
[null,4,1,4,null,"Mean of Variable Y (y-bar):",null,17.7]
[null,5,16,26]
[null,6,2,9,null,"Coefficient of Determination"]
[null,7,15,12,null,"R-Squared:",null,"hidden"]
[null,8,17,24]
[null,9,24,20,null,"Need some help?"]
[null,10,25,29]
[]
[null,"PREDICTED VALUES CALCULATIONS"]
[null,"Case #","Value on \nVariable X\n","Constant Coefficient\n","(Slope Coefficient) x (Value on X)",null,"Predicted Value on Variable Y\n"]
[null,1,4,4.26,"0.96 x 4 = ?",null,"4.26 + (3.84) = ?"]
[null,2,17,4.26,"0.96 x 17 = ?",null,"4.26 + (16.32) = ?"]
[null,3,19,4.26,"0.96 x 19 = ?",null,"4.26 + (18.24) = ?"]
[null,4,1,4.26,"0.96 x 1 = ?",null,"4.26 + (0.96) = ?"]
[null,5,16,4.26,"0.96 x 16 = ?",null,"4.26 + (15.36) = ?"]
[null,6,2,4.26,"0.96 x 2 = ?",null,"4.26 + (1.92) = ?"]
[null,7,15,4.26,"0.96 x 15 = ?",null,"4.26 + (14.4) = ?"]
[null,8,17,4.26,"0.96 x 17 = ?",null,"4.26 + (16.32) = ?"]
[null,9,24,4.26,"0.96 x 24 = ?",null,"4.26 + (23.04) = ?"]
[null,10,25,4.26,"0.96 x 25 = ?",null,"4.26 + (24) = ?"]
[]
[null,"R2 NUMERATOR CALCULATION (EXPLAINED VARIATION)"]
[null,"Case #","Predicted Value \non Variable Y\n","Mean of \nVariable Y\n","Predicted Value\n- Mean",null,"(Predicted Value\n- Mean)2"]
[null,1,8.1,17.7,"8.1 - 17.7 = ?",null,"-9.6 x -9.6 = ?"]
[null,2,20.58,17.7,"20.58 - 17.7 = ?",null,"2.88 x 2.88 = ?"]
[null,3,22.5,17.7,"22.5 - 17.7 = ?",null,"4.8 x 4.8 = ?"]
[null,4,5.22,17.7,"5.22 - 17.7 = ?",null,"-12.48 x -12.48 = ?"]
[null,5,19.62,17.7,"19.62 - 17.7 = ?",null,"1.92 x 1.92 = ?"]
[null,6,6.18,17.7,"6.18 - 17.7 = ?",null,"-11.52 x -11.52 = ?"]
[null,7,18.66,17.7,"18.66 - 17.7 = ?",null,"0.96 x 0.96 = ?"]
[null,8,20.58,17.7,"20.58 - 17.7 = ?",null,"2.88 x 2.88 = ?"]
[null,9,27.3,17.7,"27.3 - 17.7 = ?",null,"9.6 x 9.6 = ?"]
[null,10,28.26,17.7,"28.26 - 17.7 = ?",null,"10.56 x 10.56 = ?"]
[null,null,null,null,null,"Column Sum (Σ)","= ?"]
[]
[null,"R2 DENOMINATOR CALCULATION (TOTAL VARIATION)"]
[null,"Case #","Value on \nVariable Y\n","Mean of \nVariable Y\n","\nValue - Mean",null,"\n(Value - Mean)2"]
[null,1,3,17.7,"3 - 17.7 = ?",null,"-14.7 x -14.7 = ?"]
[null,2,30,17.7,"30 - 17.7 = ?",null,"12.3 x 12.3 = ?"]
[null,3,20,17.7,"20 - 17.7 = ?",null,"2.3 x 2.3 = ?"]
[null,4,4,17.7,"4 - 17.7 = ?",null,"-13.7 x -13.7 = ?"]
[null,5,26,17.7,"26 - 17.7 = ?",null,"8.3 x 8.3 = ?"]
[null,6,9,17.7,"9 - 17.7 = ?",null,"-8.7 x -8.7 = ?"]
[null,7,12,17.7,"12 - 17.7 = ?",null,"-5.7 x -5.7 = ?"]
[null,8,24,17.7,"24 - 17.7 = ?",null,"6.3 x 6.3 = ?"]
[null,9,20,17.7,"20 - 17.7 = ?",null,"2.3 x 2.3 = ?"]
[null,10,29,17.7,"29 - 17.7 = ?",null,"11.3 x 11.3 = ?"]
[null,null,null,null,null,"Column Sum (Σ)","= ?"]
[]
[null,"R-SQUARED CALCULATIONS"]
[null,"R-Squared"]
[null,null,null,"= 628.52 ÷ 910.1"]
[null,null,null,"= ?"]

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[null,"PRACTICE CALCULATING REGRESSION PREDICTIONS\n(SIMPLE LINEAR REGRESSION)"]
[]
[]
[]
[null,"Linear Regression Coefficients"]
[{"$f":"RANDBETWEEN(100,5000)/100","v":44.27},"Constant Coefficient (a)",16.41]
[{"$f":"RANDBETWEEN(100,1000)/100","v":9.48},"Slope Coefficient (b)",8.9700000000000006]
[]
[null,"The Case you are Making Predictions for"]
[{"$f":"RANDBETWEEN(100,5000)/100","v":12.32},"Value on Variable X",31.37]
[null,"Predicted Value on Variable Y",{"$f":"D19","v":297.8}]
[]
[null,"Need some help?"]
[]
[null,"REGRESSION PREDICTION CALCULATIONS"]
[null,"Predicted value on variable Y","FORMULA"]
[null,null,{"$f":"CONCATENATE(\"'= \",C6,\" + (\",C7,\" x \",C10,\")\")","v":"'= 16.41 + (8.97 x 31.37)"}]
[null,null,{"$f":"CONCATENATE(\"'= \",C6,\" + \",D18)","v":"'= 16.41 + 281.39"},{"$f":"ROUND(C10*C7,2)","v":281.39}]
[null,null,{"$f":"CONCATENATE(\"'= \",D19)","v":"'= 297.8"},{"$f":"C6+D18","v":297.8}]

{"sheet":"Slope & Constant-A","index":6,"n_rows":55,"n_cols":20,"rows_kept":55,"cut":false,"hidden":true,"merged":[[40,15,40,16],[41,15,41,16],[42,15,42,16],[43,15,43,16],[44,15,44,16],[35,15,35,16],[36,15,36,16],[37,15,37,16],[38,15,38,16],[39,15,39,16],[27,17,27,18],[28,17,28,18],[29,17,29,18],[30,17,30,18],[31,17,31,18],[22,17,22,18],[23,17,23,18],[24,17,24,18],[25,17,25,18],[26,17,26,18],[27,15,27,16],[28,15,28,16],[29,15,29,16],[30,15,30,16],[31,15,31,16],[22,15,22,16],[23,15,23,16],[24,15,24,16],[25,15,25,16],[26,15,26,16],[35,4,35,5],[35,8,35,9],[0,1,0,11],[2,1,2,11],[5,1,6,1],[5,2,6,2],[5,3,6,3],[5,5,5,7],[16,5,16,6],[18,1,18,2],[34,4,34,5],[34,8,34,9],[21,4,21,5],[21,8,21,9],[22,4,22,5],[22,8,22,9],[36,4,36,5],[36,8,36,9],[37,4,37,5],[37,8,37,9],[38,4,38,5],[38,8,38,9],[39,4,39,5],[39,8,39,9],[40,4,40,5],[40,8,40,9],[41,4,41,5],[41,8,41,9],[42,4,42,5],[42,8,42,9],[43,4,43,5],[43,8,43,9],[44,4,44,5],[44,8,44,9],[23,4,23,5],[23,8,23,9],[24,4,24,5],[24,8,24,9],[25,4,25,5],[25,8,25,9],[26,4,26,5],[26,8,26,9],[30,4,30,5],[30,8,30,9],[31,4,31,5],[31,8,31,9],[27,4,27,5],[27,8,27,9],[28,4,28,5],[28,8,28,9],[29,4,29,5],[29,8,29,9]]}
[null,"PRACTICE CALCULATING SLOPE AND CONSTANT COEFFICIENTS\n(SIMPLE LINEAR REGRESSION)"]
[]
[]
[]
[]
[null,"Case #","Value of \nVariable X","Value of \nVariable Y",null,"Means"]
[null,null,null,null,null,"Mean of Variable X",null,{"$f":"ROUND(AVERAGE(C8:C17),2)","v":12.9}]
[null,1,4,29,null,"Mean of Variable Y",null,{"$f":"ROUND(AVERAGE(D8:D17),2)","v":20},null,{"$f":"RANDBETWEEN(1,30)","v":12},{"$f":"RANDBETWEEN(1,30)","v":29}]
[null,2,4,13,null,null,null,null,null,{"$f":"RANDBETWEEN(1,30)","v":11},27]
[null,3,29,27,null,"Regression Coefficients",null,null,null,30,29]
[null,4,2,23,null,"Sum of Products",null,{"$f":"$N$33","v":21},null,29,9]
[null,5,29,7,null,"Sum of Squares X",null,{"$f":"$J$46","v":1036.9000000000001},null,25,20]
[null,6,19,29,null,null,null,null,null,23,12]
[null,7,5,11,null,"Slope Coefficient",null,{"$f":"$F$51","v":0.02},null,12,4]
[null,8,8,8,null,"Constant Coefficient",null,{"$f":"$F$55","v":19.739999999999998},null,10,25]
[null,9,7,29,null,null,null,null,null,2,1]
[null,10,22,24,null,"Need some help?",null,null,null,14,18]
[]
[]
[]
[null,"SUM OF PRODUCTS CALCULATION"]
[null,"Case #","Value of \nVariable X\n","Mean of \nVariable X\n","(Value-Mean)\nVariable X\n",null,"Value of \nVariable Y\n","Mean of \nVariable Y\n","(Value-Mean)\nVariable Y\n",null,"(Value-Mean Variable X) x (Value-Mean Variable Y)\n"]
[null,1,{"$f":"C8","v":4},{"$f":"$H$7","v":12.9},{"$f":"CONCATENATE(C23,\" - \",D23,\" = \",L23)","v":"4 - 12.9 = -8.9"},null,{"$f":"D8","v":29},{"$f":"$H$8","v":20},{"$f":"CONCATENATE(G23,\" - \",H23,\" = \",M23)","v":"29 - 20 = 9"},null,{"$f":"CONCATENATE(L23,\" x \",M23,\" = \",N23)","v":"-8.9 x 9 = -80.1"},{"$f":"ROUND(C23-D23,2)","v":-8.9},{"$f":"ROUND(G23-H23,2)","v":9},{"$f":"ROUND(L23*M23,2)","v":-80.099999999999994},null,{"$f":"CONCATENATE(C23,\" - \",D23,\" = ?\")","v":"4 - 12.9 = ?"},null,{"$f":"CONCATENATE(G23,\" - \",H23,\" = ?\")","v":"29 - 20 = ?"},null,{"$f":"CONCATENATE(L23,\" x \",M23,\" = ?\")","v":"-8.9 x 9 = ?"}]
[null,2,4,{"$f":"$H$7","v":12.9},{"$f":"CONCATENATE(C24,\" - \",D24,\" = \",L24)","v":"4 - 12.9 = -8.9"},null,13,{"$f":"$H$8","v":20},{"$f":"CONCATENATE(G24,\" - \",H24,\" = \",M24)","v":"13 - 20 = -7"},null,{"$f":"CONCATENATE(L24,\" x \",M24,\" = \",N24)","v":"-8.9 x -7 = 62.3"},{"$f":"ROUND(C24-D24,2)","v":-8.9},{"$f":"ROUND(G24-H24,2)","v":-7},{"$f":"ROUND(L24*M24,2)","v":62.3},null,{"$f":"CONCATENATE(C24,\" - \",D24,\" = ?\")","v":"4 - 12.9 = ?"},null,{"$f":"CONCATENATE(G24,\" - \",H24,\" = ?\")","v":"13 - 20 = ?"},null,{"$f":"CONCATENATE(L24,\" x \",M24,\" = ?\")","v":"-8.9 x -7 = ?"}]
[null,3,29,12.9,"29 - 12.9 = 16.1",null,27,20,"27 - 20 = 7",null,"16.1 x 7 = 112.7",16.100000000000001,7,112.7,null,"29 - 12.9 = ?",null,"27 - 20 = ?",null,"16.1 x 7 = ?"]
[null,4,2,12.9,"2 - 12.9 = -10.9",null,23,20,"23 - 20 = 3",null,"-10.9 x 3 = -32.7",-10.9,3,-32.700000000000003,null,"2 - 12.9 = ?",null,"23 - 20 = ?",null,"-10.9 x 3 = ?"]
[null,5,29,12.9,"29 - 12.9 = 16.1",null,7,20,"7 - 20 = -13",null,"16.1 x -13 = -209.3",16.100000000000001,-13,-209.3,null,"29 - 12.9 = ?",null,"7 - 20 = ?",null,"16.1 x -13 = ?"]
[null,6,19,12.9,"19 - 12.9 = 6.1",null,29,20,"29 - 20 = 9",null,"6.1 x 9 = 54.9",6.1,9,54.9,null,"19 - 12.9 = ?",null,"29 - 20 = ?",null,"6.1 x 9 = ?"]
[null,7,5,12.9,"5 - 12.9 = -7.9",null,11,20,"11 - 20 = -9",null,"-7.9 x -9 = 71.1",-7.9,-9,71.099999999999994,null,"5 - 12.9 = ?",null,"11 - 20 = ?",null,"-7.9 x -9 = ?"]
[null,8,8,12.9,"8 - 12.9 = -4.9",null,8,20,"8 - 20 = -12",null,"-4.9 x -12 = 58.8",-4.9000000000000004,-12,58.8,null,"8 - 12.9 = ?",null,"8 - 20 = ?",null,"-4.9 x -12 = ?"]
[null,9,7,12.9,"7 - 12.9 = -5.9",null,29,20,"29 - 20 = 9",null,"-5.9 x 9 = -53.1",-5.9,9,-53.1,null,"7 - 12.9 = ?",null,"29 - 20 = ?",null,"-5.9 x 9 = ?"]
[null,10,22,12.9,"22 - 12.9 = 9.1",null,24,20,"24 - 20 = 4",null,"9.1 x 4 = 36.4",9.1,4,36.4,null,"22 - 12.9 = ?",null,"24 - 20 = ?",null,"9.1 x 4 = ?"]
[null,null,null,null,null,null,null,null,null,"Column Sum (Σ)",{"$f":"CONCATENATE(\"'= \",N33)","v":"'= 21"},null,null,{"$f":"ROUND(SUM(N23:N32),2)","v":21}]
[null,"SUM OF SQUARES X CALCULATION"]
[null,"Case #","Value of \nVariable X\n","Mean of \nVariable X\n","(Value-Mean)\nVariable X\n",null,"(Value-Mean)2 Variable X\n"]
[null,1,{"$f":"C8","v":4},{"$f":"$H$7","v":12.9},{"$f":"CONCATENATE(C36,\" - \",D36,\" = \",H36)","v":"4 - 12.9 = -8.9"},null,{"$f":"CONCATENATE(H36,\" x \",H36,\" = \",I36)","v":"-8.9 x -8.9 = 79.21"},{"$f":"ROUND(C36-D36,2)","v":-8.9},{"$f":"ROUND(H36*H36,2)","v":79.209999999999994},null,null,null,null,null,null,{"$f":"CONCATENATE(C36,\" - \",D36,\" = ?\")","v":"4 - 12.9 = ?"},null,{"$f":"CONCATENATE(H36,\" x \",H36,\" = ?\")","v":"-8.9 x -8.9 = ?"}]
[null,2,4,{"$f":"$H$7","v":12.9},{"$f":"CONCATENATE(C37,\" - \",D37,\" = \",H37)","v":"4 - 12.9 = -8.9"},null,{"$f":"CONCATENATE(H37,\" x \",H37,\" = \",I37)","v":"-8.9 x -8.9 = 79.21"},{"$f":"ROUND(C37-D37,2)","v":-8.9},{"$f":"ROUND(H37*H37,2)","v":79.209999999999994},null,null,null,null,null,null,"4 - 12.9 = ?",null,{"$f":"CONCATENATE(H37,\" x \",H37,\" = ?\")","v":"-8.9 x -8.9 = ?"}]
[null,3,29,12.9,"29 - 12.9 = 16.1",null,"16.1 x 16.1 = 259.21",16.100000000000001,259.20999999999998,null,null,null,null,null,null,"29 - 12.9 = ?",null,"16.1 x 16.1 = ?"]
[null,4,2,12.9,"2 - 12.9 = -10.9",null,"-10.9 x -10.9 = 118.81",-10.9,118.81,null,null,null,null,null,null,"2 - 12.9 = ?",null,"-10.9 x -10.9 = ?"]
[null,5,29,12.9,"29 - 12.9 = 16.1",null,"16.1 x 16.1 = 259.21",16.100000000000001,259.20999999999998,null,null,null,null,null,null,"29 - 12.9 = ?",null,"16.1 x 16.1 = ?"]
[null,6,19,12.9,"19 - 12.9 = 6.1",null,"6.1 x 6.1 = 37.21",6.1,37.21,null,null,null,null,null,null,"19 - 12.9 = ?",null,"6.1 x 6.1 = ?"]
[null,7,5,12.9,"5 - 12.9 = -7.9",null,"-7.9 x -7.9 = 62.41",-7.9,62.41,null,null,null,null,null,null,"5 - 12.9 = ?",null,"-7.9 x -7.9 = ?"]
[null,8,8,12.9,"8 - 12.9 = -4.9",null,"-4.9 x -4.9 = 24.01",-4.9000000000000004,24.01,null,null,null,null,null,null,"8 - 12.9 = ?",null,"-4.9 x -4.9 = ?"]
[null,9,7,12.9,"7 - 12.9 = -5.9",null,"-5.9 x -5.9 = 34.81",-5.9,34.81,null,null,null,null,null,null,"7 - 12.9 = ?",null,"-5.9 x -5.9 = ?"]
[null,10,22,12.9,"22 - 12.9 = 9.1",null,"9.1 x 9.1 = 82.81",9.1,82.81,null,null,null,null,null,null,"22 - 12.9 = ?",null,"9.1 x 9.1 = ?"]
[null,null,null,null,null,"Column Sum (Σ)",{"$f":"CONCATENATE(\"'= \",J46)","v":"'= 1036.9"},null,null,{"$f":"ROUND(SUM(I36:J45),2)","v":1036.9000000000001}]
[]
[null,"REGRESSION COEFFICIENT CALCULATIONS"]
[null,"Slope Coefficient"]
[null,null,null,{"$f":"CONCATENATE(\"'= \",N33,\" ÷ \",J46)","v":"'= 21 ÷ 1036.9"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",F51)","v":"'= 0.02"},null,{"$f":"ROUND(N33/J46,2)","v":0.02}]
[null,"Constant Coefficient"]
[null,null,null,{"$f":"CONCATENATE(\"'= \",H8,\" - (\",F51,\" x \",H7,\")\")","v":"'= 20 - (0.02 x 12.9)"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",H8,\" - (\",F54,\")\")","v":"'= 20 - (0.26)"},null,{"$f":"ROUND(F51*H7,2)","v":0.26}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",F55)","v":"'= 19.74"},null,{"$f":"ROUND(H8-F54,2)","v":19.739999999999998}]

{"sheet":"Standard Errors & T-stat-A","index":7,"n_rows":95,"n_cols":18,"rows_kept":95,"cut":false,"hidden":true,"merged":[[66,10,66,11],[67,10,67,11],[68,10,68,11],[69,10,69,11],[60,10,60,11],[61,10,61,11],[62,10,62,11],[63,10,63,11],[64,10,64,11],[46,10,46,11],[47,10,47,11],[48,10,48,11],[39,10,39,11],[40,10,40,11],[41,10,41,11],[42,10,42,11],[43,10,43,11],[65,10,65,11],[34,10,34,11],[35,10,35,11],[26,10,26,11],[27,10,27,11],[28,10,28,11],[29,10,29,11],[30,10,30,11],[44,10,44,11],[45,10,45,11],[0,1,0,9],[2,1,2,9],[3,9,3,11],[5,1,6,1],[5,2,6,2],[5,3,6,3],[31,10,31,11],[32,10,32,11],[33,10,33,11],[28,4,28,5],[28,8,28,9],[25,8,25,9],[26,4,26,5],[26,8,26,9],[27,4,27,5],[27,8,27,9],[18,1,18,2],[25,4,25,5],[29,4,29,5],[29,8,29,9],[30,4,30,5],[30,8,30,9],[31,4,31,5],[31,8,31,9],[32,4,32,5],[32,8,32,9],[33,4,33,5],[33,8,33,9],[34,4,34,5],[34,8,34,9],[35,4,35,5],[35,8,35,9],[38,4,38,5],[38,8,38,9],[39,4,39,5],[39,8,39,9],[40,4,40,5],[40,8,40,9],[41,4,41,5],[41,8,41,9],[42,4,42,5],[42,8,42,9],[43,4,43,5],[43,8,43,9],[44,4,44,5],[44,8,44,9],[45,4,45,5],[45,8,45,9],[46,4,46,5],[46,8,46,9],[47,4,47,5],[47,8,47,9],[48,4,48,5],[48,8,48,9],[59,4,59,5],[59,8,59,9],[60,4,60,5],[60,8,60,9],[61,4,61,5],[61,8,61,9],[62,4,62,5],[62,8,62,9],[63,4,63,5],[63,8,63,9],[64,4,64,5],[64,8,64,9],[92,1,93,2],[65,4,65,5],[65,8,65,9],[66,4,66,5],[66,8,66,9],[67,4,67,5],[67,8,67,9],[68,4,68,5],[68,8,68,9],[69,4,69,5],[69,8,69,9],[77,1,77,2]]}
[null,"PRACTICE CALCULATING STANDARD ERRORS AND T-STATISTICS\n(SIMPLE LINEAR REGRESSION)"]
[]
[]
[]
[]
[null,"Case #","Value on \nVariable X","Value on \nVariable Y",null,"Means"]
[null,null,null,null,null,"Mean of Variable X",null,{"$f":"ROUND(AVERAGE(C8:C17),2)","v":15.5}]
[null,1,19,19,null,null,null,null,{"$f":"ROUND(C8-$H$7,2)","v":3.5},{"$f":"ROUND(I8*I8,2)","v":12.25},{"$f":"ROUND(D8-$D$18,2)","v":0.1},{"$f":"ROUND(I8*K8,2)","v":0.35},null,{"$f":"RANDBETWEEN(1,30)","v":18},{"$f":"RANDBETWEEN(1,30)","v":6}]
[null,2,7,18,null,"Regression Coefficients",null,null,{"$f":"ROUND(C9-$H$7,2)","v":-8.5},{"$f":"ROUND(I9*I9,2)","v":72.25},{"$f":"ROUND(D9-$D$18,2)","v":-0.9},{"$f":"ROUND(I9*K9,2)","v":7.65},null,{"$f":"RANDBETWEEN(1,30)","v":11},16]
[null,3,18,27,null,"Slope Coefficient",null,{"$f":"L19","v":0.03},2.5,6.25,8.1,20.25,null,26,12]
[null,4,30,18,null,"Constant Coefficient",null,{"$f":"L20","v":18.43},14.5,210.25,-0.9,-13.05,null,26,2]
[null,5,27,25,null,null,null,null,11.5,132.25,6.1,70.150000000000006,null,28,25]
[null,6,21,27,null,"Standard Errors",null,null,5.5,30.25,8.1,44.55,null,15,8]
[null,7,1,27,null,"Standard Error of the Estimate",null,{"$f":"G57","v":8.76},-14.5,210.25,8.1,-117.45,null,15,26]
[null,8,4,13,null,"Standard Error of the Slope Coefficient",null,{"$f":"G77","v":0.28999999999999998},-11.5,132.25,-5.9,67.849999999999994,null,10,1]
[null,9,21,1,null,"Standard Error of the Constant Coefficient",null,{"$f":"G84","v":5.26},5.5,30.25,-17.899999999999999,-98.45,null,3,4]
[null,10,7,14,null,null,null,null,-8.5,72.25,-4.9000000000000004,41.65,null,9,26]
[null,null,null,{"$f":"ROUND(AVERAGE(D8:D17),2)","v":18.899999999999999},null,"T-Statistics",null,null,null,{"$f":"SUM(J8:J17)","v":908.5},null,{"$f":"SUM(L8:L17)","v":23.499999999999993}]
[null,"Need some help?",null,null,null,"T-Statistic for the Slope Coefficient",null,{"$f":"G89","v":0.1},null,null,null,{"$f":"ROUND(L18/J18,2)","v":0.03}]
[null,null,null,null,null,"T-Statistic for the Constant Coefficient",null,{"$f":"G92","v":3.5},null,null,{"$f":"ROUND(L19*H7,2)","v":0.47},{"$f":"ROUND($D$18-K20,2)","v":18.43}]
[null,null,null,null,null,"Degrees of Freedom of the T-Statistic",null,{"$f":"8","v":8}]
[]
[]
[]
[null,"PREDICTED VALUES CALCULATIONS"]
[null,"Case #","Value on \nVariable X\n","Constant Coefficient\n","(Slope Coefficient) x (Value on X)",null,"Predicted Value on Variable Y\n"]
[null,1,{"$f":"C8","v":19},{"$f":"$H$11","v":18.43},{"$f":"CONCATENATE($H$10,\" x \",C27,\" = \",H27)","v":"0.03 x 19 = 0.57"},null,{"$f":"CONCATENATE(D27,\" + (\",H27,\") = \",I27)","v":"18.43 + (0.57) = 19"},{"$f":"ROUND(C27*$H$10,2)","v":0.56999999999999995},{"$f":"ROUND(SUM(D27,H27),2)","v":19},null,{"$f":"CONCATENATE($H$10,\" x \",C27,\" = ?\")","v":"0.03 x 19 = ?"},null,{"$f":"CONCATENATE(D27,\" + (\",H27,\") = ?\")","v":"18.43 + (0.57) = ?"}]
[null,2,7,18.43,"0.03 x 7 = 0.21",null,{"$f":"CONCATENATE(D28,\" + (\",H28,\") = \",I28)","v":"18.43 + (0.21) = 18.64"},0.21,{"$f":"ROUND(SUM(D28,H28),2)","v":18.64},null,"0.03 x 7 = ?",null,"18.43 + (0.21) = ?"]
[null,3,18,18.43,"0.03 x 18 = 0.54",null,"18.43 + (0.54) = 18.97",0.54,18.97,null,"0.03 x 18 = ?",null,"18.43 + (0.54) = ?"]
[null,4,30,18.43,"0.03 x 30 = 0.9",null,"18.43 + (0.9) = 19.33",0.9,19.329999999999998,null,"0.03 x 30 = ?",null,"18.43 + (0.9) = ?"]
[null,5,27,18.43,"0.03 x 27 = 0.81",null,"18.43 + (0.81) = 19.24",0.81,19.239999999999998,null,"0.03 x 27 = ?",null,"18.43 + (0.81) = ?"]
[null,6,21,18.43,"0.03 x 21 = 0.63",null,"18.43 + (0.63) = 19.06",0.63,19.059999999999999,null,"0.03 x 21 = ?",null,"18.43 + (0.63) = ?"]
[null,7,1,18.43,"0.03 x 1 = 0.03",null,"18.43 + (0.03) = 18.46",0.03,18.46,null,"0.03 x 1 = ?",null,"18.43 + (0.03) = ?"]
[null,8,4,18.43,"0.03 x 4 = 0.12",null,"18.43 + (0.12) = 18.55",0.12,18.55,null,"0.03 x 4 = ?",null,"18.43 + (0.12) = ?"]
[null,9,21,18.43,"0.03 x 21 = 0.63",null,"18.43 + (0.63) = 19.06",0.63,19.059999999999999,null,"0.03 x 21 = ?",null,"18.43 + (0.63) = ?"]
[null,10,7,18.43,"0.03 x 7 = 0.21",null,"18.43 + (0.21) = 18.64",0.21,18.64,null,"0.03 x 7 = ?",null,"18.43 + (0.21) = ?"]
[]
[null,"STANDARD ERROR OF THE ESTIMATE NUMERATOR CALCULATIONS"]
[null,"Case #","Value on \nVariable Y\n","Predicted Value \non Variable Y\n","Value - \nPredicted Value ",null,"(Value - \nPredicted Value)2"]
[null,1,{"$f":"D8","v":19},{"$f":"I27","v":19},{"$f":"CONCATENATE(C40,\" - (\",D40,\") = \",H40)","v":"19 - (19) = 0"},null,{"$f":"CONCATENATE(H40,\" x \",H40,\" = \",I40)","v":"0 x 0 = 0"},{"$f":"ROUND(C40-D40,2)","v":0},{"$f":"ROUND(H40*H40,2)","v":0},null,{"$f":"CONCATENATE(C40,\" - \",D40,\" = ?\")","v":"19 - 19 = ?"},null,{"$f":"CONCATENATE(H40,\" x \",H40,\" = ?\")","v":"0 x 0 = ?"}]
[null,2,18,{"$f":"I28","v":18.64},{"$f":"CONCATENATE(C41,\" - (\",D41,\") = \",H41)","v":"18 - (18.64) = -0.64"},null,{"$f":"CONCATENATE(H41,\" x \",H41,\" = \",I41)","v":"-0.64 x -0.64 = 0.41"},{"$f":"ROUND(C41-D41,2)","v":-0.64},{"$f":"ROUND(H41*H41,2)","v":0.41},null,{"$f":"CONCATENATE(C41,\" - \",D41,\" = ?\")","v":"18 - 18.64 = ?"},null,{"$f":"CONCATENATE(H41,\" x \",H41,\" = ?\")","v":"-0.64 x -0.64 = ?"}]
[null,3,27,18.97,"27 - (18.97) = 8.03",null,"8.03 x 8.03 = 64.48",8.0299999999999994,64.48,null,"27 - 18.97 = ?",null,"8.03 x 8.03 = ?"]
[null,4,18,19.329999999999998,"18 - (19.33) = -1.33",null,"-1.33 x -1.33 = 1.77",-1.33,1.77,null,"18 - 19.33 = ?",null,"-1.33 x -1.33 = ?"]
[null,5,25,19.239999999999998,"25 - (19.24) = 5.76",null,"5.76 x 5.76 = 33.18",5.76,33.18,null,"25 - 19.24 = ?",null,"5.76 x 5.76 = ?"]
[null,6,27,19.059999999999999,"27 - (19.06) = 7.94",null,"7.94 x 7.94 = 63.04",7.94,63.04,null,"27 - 19.06 = ?",null,"7.94 x 7.94 = ?"]
[null,7,27,18.46,"27 - (18.46) = 8.54",null,"8.54 x 8.54 = 72.93",8.5399999999999991,72.930000000000007,null,"27 - 18.46 = ?",null,"8.54 x 8.54 = ?"]
[null,8,13,18.55,"13 - (18.55) = -5.55",null,"-5.55 x -5.55 = 30.8",-5.55,30.8,null,"13 - 18.55 = ?",null,"-5.55 x -5.55 = ?"]
[null,9,1,19.059999999999999,"1 - (19.06) = -18.06",null,"-18.06 x -18.06 = 326.16",-18.059999999999999,326.16000000000003,null,"1 - 19.06 = ?",null,"-18.06 x -18.06 = ?"]
[null,10,14,18.64,"14 - (18.64) = -4.64",null,"-4.64 x -4.64 = 21.53",-4.6399999999999997,21.53,null,"14 - 18.64 = ?",null,"-4.64 x -4.64 = ?"]
[null,null,null,null,null,"Column Sum (Σ)",{"$f":"CONCATENATE(\"'= \",J50)","v":"'= 614.3"},null,null,{"$f":"ROUND(SUM(I40:J49),2)","v":614.29999999999995}]
[]
[null,"STANDARD ERROR OF THE ESTIMATE CALCULATIONS"]
[null,"Standard Error of the Estimate"]
[null,null,null,{"$f":"CONCATENATE(\"'= square root of [\",J50,\" ÷ (10-2)]\")","v":"'= square root of [614.3 ÷ (10-2)]"}]
[null,null,null,{"$f":"CONCATENATE(\"'= square root of (\",J50,\" ÷ 8)\")","v":"'= square root of (614.3 ÷ 8)"}]
[null,null,null,{"$f":"CONCATENATE(\"'= square root of \",G56)","v":"'= square root of 76.79"},null,null,{"$f":"ROUND(J50/8,2)","v":76.790000000000006}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G57)","v":"'= 8.76"},null,null,{"$f":"ROUND(SQRT(G56),2)","v":8.76}]
[]
[null,"SUM OF SQUARES X CALCULATION"]
[null,"Case #","Value on \nVariable X\n","Mean of \nVariable X\n","(Value-Mean)\nVariable X\n",null,"(Value-Mean)2 \nVariable X\n"]
[null,1,{"$f":"C8","v":19},{"$f":"$H$7","v":15.5},{"$f":"CONCATENATE(C61,\" - \",D61,\" = \",H61)","v":"19 - 15.5 = 3.5"},null,{"$f":"CONCATENATE(H61,\" x \",H61,\" = \",I61)","v":"3.5 x 3.5 = 12.25"},{"$f":"ROUND(C61-D61,2)","v":3.5},{"$f":"ROUND(H61*H61,2)","v":12.25},null,{"$f":"CONCATENATE(C61,\" - \",D61,\" = ?\")","v":"19 - 15.5 = ?"},null,{"$f":"CONCATENATE(H61,\" x \",H61,\" = ?\")","v":"3.5 x 3.5 = ?"},null,null,null,null,{"$f":"CONCATENATE(H61,\" x \",H61,\" = ?\")","v":"3.5 x 3.5 = ?"}]
[null,2,7,{"$f":"$H$7","v":15.5},{"$f":"CONCATENATE(C62,\" - \",D62,\" = \",H62)","v":"7 - 15.5 = -8.5"},null,{"$f":"CONCATENATE(H62,\" x \",H62,\" = \",I62)","v":"-8.5 x -8.5 = 72.25"},{"$f":"ROUND(C62-D62,2)","v":-8.5},{"$f":"ROUND(H62*H62,2)","v":72.25},null,{"$f":"CONCATENATE(C62,\" - \",D62,\" = ?\")","v":"7 - 15.5 = ?"},null,"-8.5 x -8.5 = ?"]
[null,3,18,15.5,"18 - 15.5 = 2.5",null,"2.5 x 2.5 = 6.25",2.5,6.25,null,"18 - 15.5 = ?",null,"2.5 x 2.5 = ?"]
[null,4,30,15.5,"30 - 15.5 = 14.5",null,"14.5 x 14.5 = 210.25",14.5,210.25,null,"30 - 15.5 = ?",null,"14.5 x 14.5 = ?"]
[null,5,27,15.5,"27 - 15.5 = 11.5",null,"11.5 x 11.5 = 132.25",11.5,132.25,null,"27 - 15.5 = ?",null,"11.5 x 11.5 = ?"]
[null,6,21,15.5,"21 - 15.5 = 5.5",null,"5.5 x 5.5 = 30.25",5.5,30.25,null,"21 - 15.5 = ?",null,"5.5 x 5.5 = ?"]
[null,7,1,15.5,"1 - 15.5 = -14.5",null,"-14.5 x -14.5 = 210.25",-14.5,210.25,null,"1 - 15.5 = ?",null,"-14.5 x -14.5 = ?"]
[null,8,4,15.5,"4 - 15.5 = -11.5",null,"-11.5 x -11.5 = 132.25",-11.5,132.25,null,"4 - 15.5 = ?",null,"-11.5 x -11.5 = ?"]
[null,9,21,15.5,"21 - 15.5 = 5.5",null,"5.5 x 5.5 = 30.25",5.5,30.25,null,"21 - 15.5 = ?",null,"5.5 x 5.5 = ?"]
[null,10,7,15.5,"7 - 15.5 = -8.5",null,"-8.5 x -8.5 = 72.25",-8.5,72.25,null,"7 - 15.5 = ?",null,"-8.5 x -8.5 = ?"]
[null,null,null,null,null,"Column Sum (Σ)",{"$f":"CONCATENATE(\"'= \",J71)","v":"'= 908.5"},null,null,{"$f":"ROUND(SUM(I61:J70),2)","v":908.5}]
[]
[null,"STANDARD ERROR OF THE SLOPE & CONSTANT COEFFICIENT CALCULATIONS"]
[null,"Standard error of the slope coefficient "]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G57,\" ÷ (square root of \",J71,\")\")","v":"'= 8.76 ÷ (square root of 908.5)"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G57,\" ÷ \",G76)","v":"'= 8.76 ÷ 30.14"},null,null,{"$f":"ROUND(SQRT(J71),2)","v":30.14}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G77)","v":"'= 0.29"},null,null,{"$f":"ROUND(G57/G76,2)","v":0.28999999999999998}]
[null,"Standard error of \nthe constant coefficient "]
[null,null,null,{"$f":"CONCATENATE(\"'= \",$G$57,\" x square root of [(1 ÷ 10) + (\",$H$7,G79,\" ÷ \",$J$71,\")]\")","v":"'= 8.76 x square root of [(1 ÷ 10) + (15.5² ÷ 908.5)]"},null,null,"²"]
[null,null,null,{"$f":"CONCATENATE(\"'= \",$G$57,\" x square root of [(1 ÷ 10) + (\",G80,\" ÷ \",$J$71,\")]\")","v":"'= 8.76 x square root of [(1 ÷ 10) + (240.25 ÷ 908.5)]"},null,null,{"$f":"ROUND($H$7*$H$7,2)","v":240.25}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",$G$57,\" x square root of (\",G81,\" + \",H81,\")\")","v":"'= 8.76 x square root of (0.1 + 0.26)"},null,null,{"$f":"ROUND(1/10,2)","v":0.1},{"$f":"ROUND(G80/J71,2)","v":0.26}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",$G$57,\" x square root of \",G82)","v":"'= 8.76 x square root of 0.36"},null,null,{"$f":"G81+H81","v":0.36}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",$G$57,\" x \",G83)","v":"'= 8.76 x 0.6"},null,null,{"$f":"ROUND(SQRT(G82),2)","v":0.6}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G84)","v":"'= 5.26"},null,null,{"$f":"ROUND(G57*G83,2)","v":5.26}]
[]
[null,"T-STATISTIC CALCULATIONS"]
[null,"T-Statistic for the slope coefficient"]
[null,null,null,{"$f":"CONCATENATE(\"'= \",H10,\" ÷ \",G77)","v":"'= 0.03 ÷ 0.29"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G89)","v":"'= 0.1"},null,null,{"$f":"ROUND(H10/G77,2)","v":0.1}]
[null,"T-Statistic for the constant coefficient"]
[null,null,null,{"$f":"CONCATENATE(\"'= \",H11,\" ÷ \",G84)","v":"'= 18.43 ÷ 5.26"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G92)","v":"'= 3.5"},null,null,{"$f":"ROUND(H11/G84,2)","v":3.5}]
[null,"Degrees of freedom for \nregression coefficients"]
[null,null,null,"'= 10 - 1 - 1"]
[null,null,null,"'= 8"]

{"sheet":"R-Squared-A","index":8,"n_rows":63,"n_cols":17,"rows_kept":63,"cut":false,"hidden":true,"merged":[[20,4,20,5],[20,8,20,9],[0,1,0,11],[2,1,2,11],[3,9,3,11],[5,1,6,1],[5,2,6,2],[5,3,6,3],[9,5,9,7],[15,5,15,6],[19,4,19,5],[19,8,19,9],[21,4,21,5],[21,8,21,9],[22,4,22,5],[22,8,22,9],[23,4,23,5],[23,8,23,9],[24,4,24,5],[24,8,24,9],[25,4,25,5],[25,8,25,9],[26,4,26,5],[26,8,26,9],[27,4,27,5],[27,8,27,9],[28,4,28,5],[28,8,28,9],[29,4,29,5],[29,8,29,9],[42,8,42,9],[32,4,32,5],[32,8,32,9],[33,8,33,9],[34,8,34,9],[35,8,35,9],[36,8,36,9],[37,8,37,9],[38,8,38,9],[39,8,39,9],[40,8,40,9],[41,8,41,9],[33,4,33,5],[34,4,34,5],[35,4,35,5],[36,4,36,5],[46,4,46,5],[46,8,46,9],[47,4,47,5],[47,8,47,9],[48,4,48,5],[48,8,48,9],[49,4,49,5],[49,8,49,9],[50,4,50,5],[50,8,50,9],[51,4,51,5],[51,8,51,9],[55,4,55,5],[55,8,55,9],[56,4,56,5],[56,8,56,9],[52,4,52,5],[52,8,52,9],[53,4,53,5],[53,8,53,9],[54,4,54,5],[54,8,54,9],[42,4,42,5],[33,10,33,11],[34,10,34,11],[35,10,35,11],[36,10,36,11],[37,10,37,11],[38,10,38,11],[39,10,39,11],[40,10,40,11],[41,10,41,11],[42,10,42,11],[37,4,37,5],[38,4,38,5],[39,4,39,5],[40,4,40,5],[41,4,41,5],[47,10,47,11],[48,10,48,11],[49,10,49,11],[50,10,50,11],[51,10,51,11],[52,10,52,11],[53,10,53,11],[54,10,54,11],[55,10,55,11],[56,10,56,11]]}
[null,"PRACTICE CALCULATING R-SQUARED\n(SIMPLE LINEAR REGRESSION)"]
[]
[]
[]
[]
[null,"Case #","Value of \nVariable X","Value of \nVariable Y",null,"Regression Coefficients"]
[null,null,null,null,null,"Slope Coefficient",null,{"$f":"ROUND(M18,2)","v":0.96}]
[null,1,4,3,null,"Constant Coefficient",null,{"$f":"ROUND(O18,2)","v":4.26},{"$f":"ROUND(C8-$H$12,2)","v":-10},{"$f":"ROUND(I8*I8,2)","v":100},{"$f":"ROUND(D8-$H$11,2)","v":-14.7},{"$f":"ROUND(I8*K8,2)","v":147},null,null,null,{"$f":"RANDBETWEEN(1,30)","v":19},{"$f":"IF(P8<15,RANDBETWEEN(1,20),RANDBETWEEN(10,30))","v":26}]
[null,2,17,30,null,null,null,null,{"$f":"ROUND(C9-$H$12,2)","v":3},{"$f":"ROUND(I9*I9,2)","v":9},{"$f":"ROUND(D9-$H$11,2)","v":12.3},{"$f":"ROUND(I9*K9,2)","v":36.9},null,null,null,{"$f":"RANDBETWEEN(1,30)","v":27},{"$f":"IF(P9<15,RANDBETWEEN(1,20),RANDBETWEEN(10,30))","v":10}]
[null,3,19,20,null,"Means",null,null,5,25,2.2999999999999998,11.5,null,null,null,3,3]
[null,4,1,4,null,"Mean of Variable Y",null,{"$f":"ROUND(AVERAGE(D8:D17),2)","v":17.7},-13,169,-13.7,178.1,null,null,null,5,8]
[null,5,16,26,null,"Mean of Variable X",null,{"$f":"ROUND(AVERAGE(C8:C17),2)","v":14},2,4,8.3000000000000007,16.600000000000001,null,null,null,5,14]
[null,6,2,9,null,"Coefficient of Determination",null,null,-12,144,-8.6999999999999993,104.4,null,null,null,20,28]
[null,7,15,12,null,"R-Squared",null,{"$f":"F63","v":0.69},1,1,-5.7,-5.7,null,null,null,20,26]
[null,8,17,24,null,null,null,null,3,9,6.3,18.899999999999999,null,null,null,12,8]
[null,9,24,20,null,"Need some help?",null,null,10,100,2.2999999999999998,23,null,null,null,21,21]
[null,10,25,29,null,null,null,null,11,121,11.3,124.3,null,null,null,22,15]
[null,null,null,null,null,null,null,null,null,{"$f":"SUM(J8:J17)","v":682},null,{"$f":"SUM(L8:L17)","v":655},{"$f":"ROUND(L18/J18,2)","v":0.96},{"$f":"ROUND(H12*M18,2)","v":13.44},{"$f":"H11-N18","v":4.26}]
[null,"PREDICTED VALUES CALCULATIONS"]
[null,"Case #","Value on \nVariable X\n","Constant Coefficient\n","Slope Coefficient x Value on X",null,"Predicted Value on Variable Y\n"]
[null,1,{"$f":"C8","v":4},{"$f":"$H$8","v":4.26},{"$f":"CONCATENATE($H$7,\" x \",C21,\" = \",H21)","v":"0.96 x 4 = 3.84"},null,{"$f":"CONCATENATE(D21,\" + (\",H21,\") = \",I21)","v":"4.26 + (3.84) = 8.1"},{"$f":"ROUND(C21*$H$7,2)","v":3.84},{"$f":"ROUND(SUM(D21,H21),2)","v":8.1},null,{"$f":"CONCATENATE($H$7,\" x \",C21,\" = ?\")","v":"0.96 x 4 = ?"},null,{"$f":"CONCATENATE(D21,\" + (\",H21,\") = ?\")","v":"4.26 + (3.84) = ?"}]
[null,2,17,{"$f":"$H$8","v":4.26},{"$f":"CONCATENATE($H$7,\" x \",C22,\" = \",H22)","v":"0.96 x 17 = 16.32"},null,{"$f":"CONCATENATE(D22,\" + (\",H22,\") = \",I22)","v":"4.26 + (16.32) = 20.58"},{"$f":"ROUND(C22*$H$7,2)","v":16.32},{"$f":"ROUND(SUM(D22,H22),2)","v":20.58},null,{"$f":"CONCATENATE($H$7,\" x \",C22,\" = ?\")","v":"0.96 x 17 = ?"},null,{"$f":"CONCATENATE(D22,\" + (\",H22,\") = ?\")","v":"4.26 + (16.32) = ?"}]
[null,3,19,4.26,"0.96 x 19 = 18.24",null,"4.26 + (18.24) = 22.5",18.239999999999998,22.5,null,"0.96 x 19 = ?",null,"4.26 + (18.24) = ?"]
[null,4,1,4.26,"0.96 x 1 = 0.96",null,"4.26 + (0.96) = 5.22",0.96,5.22,null,"0.96 x 1 = ?",null,"4.26 + (0.96) = ?"]
[null,5,16,4.26,"0.96 x 16 = 15.36",null,"4.26 + (15.36) = 19.62",15.36,19.62,null,"0.96 x 16 = ?",null,"4.26 + (15.36) = ?"]
[null,6,2,4.26,"0.96 x 2 = 1.92",null,"4.26 + (1.92) = 6.18",1.92,6.18,null,"0.96 x 2 = ?",null,"4.26 + (1.92) = ?"]
[null,7,15,4.26,"0.96 x 15 = 14.4",null,"4.26 + (14.4) = 18.66",14.4,18.66,null,"0.96 x 15 = ?",null,"4.26 + (14.4) = ?"]
[null,8,17,4.26,"0.96 x 17 = 16.32",null,"4.26 + (16.32) = 20.58",16.32,20.58,null,"0.96 x 17 = ?",null,"4.26 + (16.32) = ?"]
[null,9,24,4.26,"0.96 x 24 = 23.04",null,"4.26 + (23.04) = 27.3",23.04,27.3,null,"0.96 x 24 = ?",null,"4.26 + (23.04) = ?"]
[null,10,25,{"$f":"$H$8","v":4.26},"0.96 x 25 = 24",null,"4.26 + (24) = 28.26",24,28.26,null,"0.96 x 25 = ?",null,"4.26 + (24) = ?"]
[]
[null,"EXPLAINED VARIATION CALCULATIONS"]
[null,"Case #","Predicted Value \non Variable Y\n","Mean of \nVariable Y\n","Predicted Value\n- Mean",null,"(Predicted Value\n- Mean)2"]
[null,1,{"$f":"I21","v":8.1},{"$f":"$H$11","v":17.7},{"$f":"CONCATENATE(C34,\" - \",D34,\" = \",H34)","v":"8.1 - 17.7 = -9.6"},null,{"$f":"CONCATENATE(H34,\" x \",H34,\" = \",I34)","v":"-9.6 x -9.6 = 92.16"},{"$f":"ROUND(C34-D34,2)","v":-9.6},{"$f":"ROUND(H34*H34,2)","v":92.16},null,{"$f":"CONCATENATE(C34,\" - \",D34,\" = ?\")","v":"8.1 - 17.7 = ?"},null,{"$f":"CONCATENATE(H34,\" x \",H34,\" = ?\")","v":"-9.6 x -9.6 = ?"}]
[null,2,{"$f":"I22","v":20.58},{"$f":"$H$11","v":17.7},{"$f":"CONCATENATE(C35,\" - \",D35,\" = \",H35)","v":"20.58 - 17.7 = 2.88"},null,{"$f":"CONCATENATE(H35,\" x \",H35,\" = \",I35)","v":"2.88 x 2.88 = 8.29"},{"$f":"ROUND(C35-D35,2)","v":2.88},{"$f":"ROUND(H35*H35,2)","v":8.2899999999999991},null,{"$f":"CONCATENATE(C35,\" - \",D35,\" = ?\")","v":"20.58 - 17.7 = ?"},null,{"$f":"CONCATENATE(H35,\" x \",H35,\" = ?\")","v":"2.88 x 2.88 = ?"}]
[null,3,{"$f":"I23","v":22.5},17.7,"22.5 - 17.7 = 4.8",null,"4.8 x 4.8 = 23.04",4.8,23.04,null,"22.5 - 17.7 = ?",null,"4.8 x 4.8 = ?"]
[null,4,5.22,17.7,"5.22 - 17.7 = -12.48",null,"-12.48 x -12.48 = 155.75",-12.48,155.75,null,"5.22 - 17.7 = ?",null,"-12.48 x -12.48 = ?"]
[null,5,19.62,17.7,"19.62 - 17.7 = 1.92",null,"1.92 x 1.92 = 3.69",1.92,3.69,null,"19.62 - 17.7 = ?",null,"1.92 x 1.92 = ?"]
[null,6,6.18,17.7,"6.18 - 17.7 = -11.52",null,"-11.52 x -11.52 = 132.71",-11.52,132.71,null,"6.18 - 17.7 = ?",null,"-11.52 x -11.52 = ?"]
[null,7,18.66,17.7,"18.66 - 17.7 = 0.96",null,"0.96 x 0.96 = 0.92",0.96,0.92,null,"18.66 - 17.7 = ?",null,"0.96 x 0.96 = ?"]
[null,8,20.58,17.7,"20.58 - 17.7 = 2.88",null,"2.88 x 2.88 = 8.29",2.88,8.2899999999999991,null,"20.58 - 17.7 = ?",null,"2.88 x 2.88 = ?"]
[null,9,27.3,17.7,"27.3 - 17.7 = 9.6",null,"9.6 x 9.6 = 92.16",9.6,92.16,null,"27.3 - 17.7 = ?",null,"9.6 x 9.6 = ?"]
[null,10,28.26,17.7,"28.26 - 17.7 = 10.56",null,"10.56 x 10.56 = 111.51",10.56,111.51,null,"28.26 - 17.7 = ?",null,"10.56 x 10.56 = ?"]
[null,null,null,null,null,"Column Sum (Σ)",{"$f":"CONCATENATE(\"'= \",J44)","v":"'= 628.52"},null,null,{"$f":"ROUND(SUM(I34:J43),2)","v":628.52}]
[]
[null,"TOTAL VARIATION CALCULATIONS"]
[null,"Case #","Value \non Variable Y\n","Mean of \nVariable Y\n","\nValue - Mean",null,"\n(Value - Mean)2"]
[null,1,{"$f":"D8","v":3},{"$f":"$H$11","v":17.7},{"$f":"CONCATENATE(C48,\" - \",D48,\" = \",H48)","v":"3 - 17.7 = -14.7"},null,{"$f":"CONCATENATE(H48,\" x \",H48,\" = \",I48)","v":"-14.7 x -14.7 = 216.09"},{"$f":"ROUND(C48-D48,2)","v":-14.7},{"$f":"ROUND(H48*H48,2)","v":216.09},null,{"$f":"CONCATENATE(C48,\" - \",D48,\" = ?\")","v":"3 - 17.7 = ?"},null,{"$f":"CONCATENATE(H48,\" x \",H48,\" = ?\")","v":"-14.7 x -14.7 = ?"}]
[null,2,30,{"$f":"$H$11","v":17.7},{"$f":"CONCATENATE(C49,\" - \",D49,\" = \",H49)","v":"30 - 17.7 = 12.3"},null,{"$f":"CONCATENATE(H49,\" x \",H49,\" = \",I49)","v":"12.3 x 12.3 = 151.29"},{"$f":"ROUND(C49-D49,2)","v":12.3},{"$f":"ROUND(H49*H49,2)","v":151.29},null,{"$f":"CONCATENATE(C49,\" - \",D49,\" = ?\")","v":"30 - 17.7 = ?"},null,{"$f":"CONCATENATE(H49,\" x \",H49,\" = ?\")","v":"12.3 x 12.3 = ?"}]
[null,3,20,17.7,"20 - 17.7 = 2.3",null,"2.3 x 2.3 = 5.29",2.2999999999999998,5.29,null,"20 - 17.7 = ?",null,"2.3 x 2.3 = ?"]
[null,4,4,17.7,"4 - 17.7 = -13.7",null,"-13.7 x -13.7 = 187.69",-13.7,187.69,null,"4 - 17.7 = ?",null,"-13.7 x -13.7 = ?"]
[null,5,26,17.7,"26 - 17.7 = 8.3",null,"8.3 x 8.3 = 68.89",8.3000000000000007,68.89,null,"26 - 17.7 = ?",null,"8.3 x 8.3 = ?"]
[null,6,9,17.7,"9 - 17.7 = -8.7",null,"-8.7 x -8.7 = 75.69",-8.6999999999999993,75.69,null,"9 - 17.7 = ?",null,"-8.7 x -8.7 = ?"]
[null,7,12,17.7,"12 - 17.7 = -5.7",null,"-5.7 x -5.7 = 32.49",-5.7,32.49,null,"12 - 17.7 = ?",null,"-5.7 x -5.7 = ?"]
[null,8,24,17.7,"24 - 17.7 = 6.3",null,"6.3 x 6.3 = 39.69",6.3,39.69,null,"24 - 17.7 = ?",null,"6.3 x 6.3 = ?"]
[null,9,20,17.7,"20 - 17.7 = 2.3",null,"2.3 x 2.3 = 5.29",2.2999999999999998,5.29,null,"20 - 17.7 = ?",null,"2.3 x 2.3 = ?"]
[null,10,29,17.7,"29 - 17.7 = 11.3",null,"11.3 x 11.3 = 127.69",11.3,127.69,null,"29 - 17.7 = ?",null,"11.3 x 11.3 = ?"]
[null,null,null,null,null,"Column Sum (Σ)",{"$f":"CONCATENATE(\"'= \",J58)","v":"'= 910.1"},null,null,{"$f":"ROUND(SUM(I48:J57),2)","v":910.1}]
[]
[null,"R-SQUARED CALCULATIONS"]
[null,"R-Squared",null,"formula"]
[null,null,null,{"$f":"CONCATENATE(\"'= \",J44,\" ÷ \",J58)","v":"'= 628.52 ÷ 910.1"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",F63)","v":"'= 0.69"},null,{"$f":"ROUND(J44/J58,2)","v":0.69}]