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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 15"]
[]
[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":"Predicted Probability v1","index":1,"n_rows":33,"n_cols":7,"rows_kept":33,"cut":false,"hidden":false,"merged":[[10,1,10,3],[10,6,10,7],[0,1,0,6],[2,1,2,6],[5,1,5,2],[6,1,6,2],[9,1,9,3]]}
[null,"PRACTICE CALCULATING PREDICTED PROBABILITIES\n(LOGISTIC REGRESSION)"]
[]
[null,"Use the logistic regression slope and constant coefficients in the yellow highlighed cells to find the predicted probability that the dependent variable (y) is equal to 1\nfor a case with a \"0\" value on the independent dummy variable (x) and for a case with a \"1\" value on the independent dummy variable (x). \nKeep two decimal places throughout your calculations.\nTo check your answers, click on the 'Show Answers' button."]
[]
[null,"Logistic Regression Coefficients",null,"b","Exp(b)"]
[null,"Constant Coefficient (a):",null,1.51,4.5267307943142523]
[null,"Slope Coefficient for a Dummy Variable (b):",null,-1.52,0.21871188695221475]
[]
[null,"Predicted Probabilities"]
[null,"Predicted probability that the DV (y) equals 1 for a case with a \"0\" value on the independent dummy variable (x):",null,null,"hidden",null,"Need some help?"]
[null,"Predicted probability that the DV (y) equals 1 for a case with a \"1\" value on the independent dummy variable (x):",null,null,"hidden"]
[]
[null,"PREDICTED PROBABILITY CALCULATIONS FOR A CASE WITH A \"0\" VALUE ON THE DUMMY VARIABLE"]
[null,"Z-value"]
[null,null,"= 1.51 + (-1.52 x 0)"]
[null,null,"= ? + ?"]
[null,null,"= ?"]
[null,"Predicted Probability"]
[null,null,"= e¹·⁵¹ ÷ (1 + e¹·⁵¹)"]
[null,null,"= ? ÷ (? + ?)"]
[null,null,"= ? ÷ ?"]
[null,null,"= ?"]
[]
[null,"PREDICTED PROBABILITY CALCULATIONS FOR A CASE WITH A \"1\" VALUE ON THE DUMMY VARIABLE"]
[null,"Z-value"]
[null,null,"= 1.51 + (-1.52 x 1)"]
[null,null,"= ? + ?"]
[null,null,"= ?"]
[null,"Predicted Probability"]
[null,null,"= e⁻⁰·⁰¹ ÷ (1 + e⁻⁰·⁰¹)"]
[null,null,"= ? ÷ (? + ?)"]
[null,null,"= ? ÷ ?"]
[null,null,"= ?"]

{"sheet":"Predicted Probability v2","index":2,"n_rows":28,"n_cols":7,"rows_kept":28,"cut":false,"hidden":false,"merged":[[16,1,16,2],[0,1,0,6],[2,1,2,6],[5,1,5,2],[8,1,8,2],[11,6,11,7]]}
[null,"PRACTICE CALCULATING PREDICTED PROBABILITIES\n(LOGISTIC REGRESSION)"]
[]
[null,"Use the logistic regression slope and constant coefficients in the yellow highlighed cells to find the predicted probability that the dependent variable (y) is equal to 1\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,"Logistic Regression Coefficients",null,"b","Exp(b)"]
[null,"Constant Coefficient (a):",null,-0.34,0.71177032276260965]
[null,"Slope Coefficient for Variable X1 (b1):",null,0.04,1.0408107741923882]
[null,"Slope Coefficient for Variable X2 (b2):",null,-0.06,0.94176453358424872]
[null,"Slope Coefficient for Variable X3 (b3):",null,1.76,5.8124373944025889]
[]
[null,"The Case you are Making a Prediction for:",null,"Value"]
[null,"Value on Variable X1:",null,31,null,null,"Need some help?"]
[null,"Value on Variable X2:",null,3.36]
[null,"Value on Variable X3 (dummy variable):",null,0]
[]
[null,"Predicted Probability"]
[null,"Predicted probability that the DV (y) equals 1 for the specified case:",null,"hidden"]
[]
[null,"PREDICTED PROBABILITY CALCULATIONS"]
[null,"Z-value"]
[null,null,"= -0.34 + (0.04 x 31) + (-0.06 x 3.36) + (1.76 x 0)"]
[null,null,"= ? + ? + ? + ?"]
[null,null,"= ?"]
[null,"Predicted Probability"]
[null,null,"= e⁰·⁷ ÷ (1 + e⁰·⁷)"]
[null,null,"= ? ÷ (? + ?)"]
[null,null,"= ? ÷ ?"]
[null,null,"= ?"]

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[null,"LOG TRANSFORMATIONS"]
[]
[null,"Enter a z-value, a log odds or an odds ratio in the yellow highlighted cells\nto find the corresponding (natural) log transformations. "]
[]
[]
[null,"FIND ez"]
[null,"For the z-value: ",null,null,"ez is:    ",{"$f":"'Log transformation-A'!F7","v":"   ← enter a z-value"}]
[]
[]
[null,"TRANSLATE FROM LOG ODDS (b's) TO ODDS RATIOS [EXP(b)'s]"]
[null,"A log odds (b) of:",null,null,"corresponds with an odds ratio [Exp(b)] of:      ",null,{"$f":"'Log transformation-A'!G11","v":"   ← enter a log odds"}]
[]
[]
[null,"TRANSLATE FROM ODDS RATIOS [EXP(b)'s] TO LOG ODDS (b's) "]
[null,"An odds ratio [Exp(b)] of:",null,null,"corresponds with a log odds (b) of: ",null,{"$f":"'Log transformation-A'!G15","v":"   ← enter an odds ratio"}]

{"sheet":"Predicted Probability v1-A","index":4,"n_rows":37,"n_cols":10,"rows_kept":37,"cut":false,"hidden":true,"merged":[[10,1,10,3],[10,6,10,7],[0,1,0,6],[2,1,2,6],[5,1,5,2],[6,1,6,2],[9,1,9,3]]}
[null,"PRACTICE CALCULATING PREDICTED PROBABILITIES\n(LOGISTIC REGRESSION)"]
[]
[]
[]
[null,"Logistic Regression Coefficients",null,"b","Exp(b)"]
[null,"Constant Coefficient (a):",null,1.51,4.5267307943142523,{"$f":"RANDBETWEEN(-200,200)/100","v":1.65},{"$f":"EXP(F6)","v":5.2069798271798486}]
[null,"Slope Coefficient for a Dummy Variable (b):",null,-1.52,0.21871188695221475,{"$f":"RANDBETWEEN(-200,200)/100","v":1.89},{"$f":"EXP(F7)","v":6.6193686810430767}]
[]
[null,"Predicted Probabilities"]
[null,"Predicted Probability of the DV outcome for a case with a \"0\" value on the dummy variable:",null,null,{"$f":"IF(F22<0.0005,\"<0.001 or 0.1%\",IF(F22>0.995,\">0.999 or 99.9%\",CONCATENATE(F22,\" or \",(F22*100),\"%\")))","v":"0.82 or 82%"}]
[null,"Predicted Probability of the DV outcome for a case with a \"1\" value on the dummy variable:",null,null,{"$f":"IF(F33<0.0005,\"<0.001 or 0.1%\",IF(F33>0.995,\">0.999 or 99.9%\",CONCATENATE(F33,\" or \",(F33*100),\"%\")))","v":"0.5 or 50%"},null,"Need some help?"]
[]
[null,"PREDICTED PROBABILITY CALCULATIONS FOR A CASE WITH A \"0\" VALUE ON THE DUMMY VARIABLE"]
[null,"Z-value"]
[null,null,{"$f":"CONCATENATE(\"'= \",D6,\" + (\",D7,\" x 0)\")","v":"'= 1.51 + (-1.52 x 0)"}]
[null,null,{"$f":"CONCATENATE(\"'= \",D6,\" + 0\")","v":"'= 1.51 + 0"}]
[null,null,{"$f":"CONCATENATE(\"'= \",D6)","v":"'= 1.51"}]
[null,"Predicted Probability",null,null,null,{"$f":"D6","v":1.51},{"$f":"LEN(F18)","v":4},null,null,"·"]
[null,null,{"$f":"CONCATENATE(\"'= e\",F19,\" ÷ (1 + e\",F19,\")\")","v":"'= e¹·⁵¹ ÷ (1 + e¹·⁵¹)"},null,null,{"$f":"CONCATENATE(H19,H20,H21,H22,H23,H24,H25,H26)","v":"¹·⁵¹"},{"$f":"IF($G$18>=1,MID($F$18,1,1),\"\")","v":"1"},{"$f":"IF(G19=\".\",$J$18,IF(G19=\"-\",$J$19,IF(G19=\"0\",$J$20,IF(G19=\"1\",$J$21,IF(G19=\"2\",$J$22,IF(G19=\"3\",$J$23,IF(G19=\"4\",$J$24,IF(G19=\"5\",$J$25,IF(G19=\"6\",$J$26,IF(G19=\"7\",$J$27,IF(G19=\"8\",$J$28,IF(G19=\"9\",$J$29,\"\"))))))))))))","v":"¹"},null,"⁻"]
[null,null,{"$f":"CONCATENATE(\"'= \",F20,\" ÷ (1 + \",F20,\")\")","v":"'= 4.53 ÷ (1 + 4.53)"},null,null,{"$f":"ROUND(EXP(D6),2)","v":4.53},{"$f":"IF($G$18>=2,MID($F$18,2,1),\"\")","v":"."},{"$f":"IF(G20=\".\",$J$18,IF(G20=\"-\",$J$19,IF(G20=\"0\",$J$20,IF(G20=\"1\",$J$21,IF(G20=\"2\",$J$22,IF(G20=\"3\",$J$23,IF(G20=\"4\",$J$24,IF(G20=\"5\",$J$25,IF(G20=\"6\",$J$26,IF(G20=\"7\",$J$27,IF(G20=\"8\",$J$28,IF(G20=\"9\",$J$29,\"\"))))))))))))","v":"·"},null,"⁰"]
[null,null,{"$f":"CONCATENATE(\"'= \",F20,\" ÷ \",F21,)","v":"'= 4.53 ÷ 5.53"},null,null,{"$f":"F20+1","v":5.53},{"$f":"IF($G$18>=3,MID($F$18,3,1),\"\")","v":"5"},"⁵",null,"¹"]
[null,null,{"$f":"CONCATENATE(\"'= \",F22)","v":"'= 0.82"},null,null,{"$f":"ROUND(F20/F21,2)","v":0.82},{"$f":"IF($G$18>=4,MID($F$18,4,1),\"\")","v":"1"},"¹",null,"²"]
[null,null,null,null,null,null,{"$f":"IF($G$18>=5,MID($F$18,5,1),\"\")","v":""},"",null,"³"]
[null,"PREDICTED PROBABILITY CALCULATIONS FOR A CASE WITH A \"1\" VALUE ON THE DUMMY VARIABLE",null,null,null,null,{"$f":"IF($G$18>=6,MID($F$18,6,1),\"\")","v":""},"",null,"⁴"]
[null,"Z-value",null,null,null,null,{"$f":"IF($G$18>=7,MID($F$18,7,1),\"\")","v":""},"",null,"⁵"]
[null,null,{"$f":"CONCATENATE(\"'= \",D6,\" + (\",D7,\" x 1)\")","v":"'= 1.51 + (-1.52 x 1)"},null,null,null,{"$f":"IF($G$18>=8,MID($F$18,8,1),\"\")","v":""},"",null,"⁶"]
[null,null,{"$f":"CONCATENATE(\"'= \",D6,\" + \",F27)","v":"'= 1.51 + -1.52"},null,null,{"$f":"D7","v":-1.52},null,null,null,"⁷"]
[null,null,{"$f":"CONCATENATE(\"'= \",F28)","v":"'= -0.01"},null,null,{"$f":"D6+F27","v":-1.0000000000000009E-2},null,null,null,"⁸"]
[null,"Predicted Probability",null,null,null,{"$f":"F28","v":-1.0000000000000009E-2},{"$f":"LEN(F29)","v":5},null,null,"⁹"]
[null,null,{"$f":"CONCATENATE(\"'= e\",F30,\" ÷ (1 + e\",F30,\")\")","v":"'= e⁻⁰·⁰¹ ÷ (1 + e⁻⁰·⁰¹)"},null,null,{"$f":"CONCATENATE(H30,H31,H32,H33,H34,H35,H36,H37)","v":"⁻⁰·⁰¹"},{"$f":"IF($G$29>=1,MID($F$29,1,1),\"\")","v":"-"},{"$f":"IF(G30=\".\",$J$18,IF(G30=\"-\",$J$19,IF(G30=\"0\",$J$20,IF(G30=\"1\",$J$21,IF(G30=\"2\",$J$22,IF(G30=\"3\",$J$23,IF(G30=\"4\",$J$24,IF(G30=\"5\",$J$25,IF(G30=\"6\",$J$26,IF(G30=\"7\",$J$27,IF(G30=\"8\",$J$28,IF(G30=\"9\",$J$29,\"\"))))))))))))","v":"⁻"}]
[null,null,{"$f":"CONCATENATE(\"'= \",F31,\" ÷ (1 + \",F31,\")\")","v":"'= 0.99 ÷ (1 + 0.99)"},null,null,{"$f":"ROUND(EXP(F28),2)","v":0.99},{"$f":"IF($G$29>=2,MID($F$29,2,1),\"\")","v":"0"},{"$f":"IF(G31=\".\",$J$18,IF(G31=\"-\",$J$19,IF(G31=\"0\",$J$20,IF(G31=\"1\",$J$21,IF(G31=\"2\",$J$22,IF(G31=\"3\",$J$23,IF(G31=\"4\",$J$24,IF(G31=\"5\",$J$25,IF(G31=\"6\",$J$26,IF(G31=\"7\",$J$27,IF(G31=\"8\",$J$28,IF(G31=\"9\",$J$29,\"\"))))))))))))","v":"⁰"}]
[null,null,{"$f":"CONCATENATE(\"'= \",F31,\" ÷ \",F32,)","v":"'= 0.99 ÷ 1.99"},null,null,{"$f":"F31+1","v":1.99},{"$f":"IF($G$29>=3,MID($F$29,3,1),\"\")","v":"."},"·"]
[null,null,{"$f":"CONCATENATE(\"'= \",F33)","v":"'= 0.5"},null,null,{"$f":"ROUND(F31/F32,2)","v":0.5},{"$f":"IF($G$29>=4,MID($F$29,4,1),\"\")","v":"0"},"⁰"]
[null,null,null,null,null,null,{"$f":"IF($G$29>=5,MID($F$29,5,1),\"\")","v":"1"},"¹"]
[null,null,null,null,null,null,{"$f":"IF($G$29>=6,MID($F$29,6,1),\"\")","v":""},""]
[null,null,null,null,null,null,{"$f":"IF($G$29>=7,MID($F$29,7,1),\"\")","v":""},""]
[null,null,null,null,null,null,{"$f":"IF($G$29>=8,MID($F$29,8,1),\"\")","v":""},""]

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[null,"PRACTICE CALCULATING PREDICTED PROBABILITIES\n(LOGISTIC REGRESSION)"]
[]
[]
[]
[null,"Logistic Regression Coefficients",null,"b","Exp(b)"]
[null,"Constant Coefficient (a):",null,-0.34,0.71177032276260965,null,{"$f":"RANDBETWEEN(-100,100)/100","v":-0.03},{"$f":"EXP(G6)","v":0.97044553354850815}]
[null,"Slope Coefficient for Variable X1 (b1):",null,0.04,1.0408107741923882,null,{"$f":"RANDBETWEEN(1,10)/100","v":0.02},{"$f":"EXP(G7)","v":1.0202013400267558}]
[null,"Slope Coefficient for Variable X2 (b2):",null,-0.06,0.94176453358424872,null,{"$f":"RANDBETWEEN(-20,-1)/100","v":-0.01},0.99004983374916811]
[null,"Slope Coefficient for Variable X3 (b3):",null,1.76,5.8124373944025889,null,{"$f":"RANDBETWEEN(-200,200)/100","v":1.53},4.6181768222997812]
[]
[null,"The Case you are Making a Prediction for:",null,"Value"]
[null,"Value on Variable X1:",null,31,null,null,{"$f":"RANDBETWEEN(16,40)","v":33}]
[null,"Value on Variable X2:",null,3.36,null,null,{"$f":"RANDBETWEEN(100,500)/100","v":2.2999999999999998}]
[null,"Value on Variable X3 (dummy variable):",null,0,null,null,{"$f":"RANDBETWEEN(0,1)","v":0}]
[]
[null,"Predicted Probability"]
[null,"Predicted probability that the DV (y) equals 1 for the specified case:",null,{"$f":"IF(F28<0.0005,\"<0.001 or 0.1%\",IF(F28>0.995,\">0.999 or 99.9%\",CONCATENATE(F28,\" or \",(F28*100),\"%\")))","v":"0.67 or 67%"}]
[]
[null,"PREDICTED PROBABILITY CALCULATIONS"]
[null,"Z-value"]
[null,null,{"$f":"CONCATENATE(\"'= \",D6,\" + (\",D7,\" x \",D12,\") + (\",D8,\" x \",D13,\") + (\",D9,\" x \",D14,\")\")","v":"'= -0.34 + (0.04 x 31) + (-0.06 x 3.36) + (1.76 x 0)"}]
[null,null,{"$f":"CONCATENATE(\"'= \",D6,\" + (\",F22,\") + (\",G22,\") + (\",H22,\")\")","v":"'= -0.34 + (1.24) + (-0.2) + (0)"},null,null,{"$f":"ROUND(D7*D12,2)","v":1.24},{"$f":"ROUND(D8*D13,2)","v":-0.2},{"$f":"ROUND(D9*D14,2)","v":0}]
[null,null,{"$f":"CONCATENATE(\"'= \",F23)","v":"'= 0.7"},null,null,{"$f":"D6+F22+G22+H22","v":0.7}]
[null,"Predicted Probability",null,null,null,{"$f":"F23","v":0.7},{"$f":"LEN(F24)","v":3},null,null,"·"]
[null,null,{"$f":"CONCATENATE(\"'= e\",F25,\" ÷ (1 + e\",F25,\")\")","v":"'= e⁰·⁷ ÷ (1 + e⁰·⁷)"},null,null,{"$f":"CONCATENATE(H25,H26,H27,H28,H29,H30,H31,H32)","v":"⁰·⁷"},{"$f":"IF($G$24>=1,MID($F$24,1,1),\"\")","v":"0"},{"$f":"IF(G25=\".\",$J$24,IF(G25=\"-\",$J$25,IF(G25=\"0\",$J$26,IF(G25=\"1\",$J$27,IF(G25=\"2\",$J$28,IF(G25=\"3\",$J$29,IF(G25=\"4\",$J$30,IF(G25=\"5\",$J$31,IF(G25=\"6\",$J$32,IF(G25=\"7\",$J$33,IF(G25=\"8\",$J$34,IF(G25=\"9\",$J$35,\"\"))))))))))))","v":"⁰"},null,"⁻"]
[null,null,{"$f":"CONCATENATE(\"'= \",F26,\" ÷ (1 + \",F26,\")\")","v":"'= 2.01 ÷ (1 + 2.01)"},null,null,{"$f":"ROUND(EXP(F24),2)","v":2.0099999999999998},{"$f":"IF($G$24>=2,MID($F$24,2,1),\"\")","v":"."},{"$f":"IF(G26=\".\",$J$24,IF(G26=\"-\",$J$25,IF(G26=\"0\",$J$26,IF(G26=\"1\",$J$27,IF(G26=\"2\",$J$28,IF(G26=\"3\",$J$29,IF(G26=\"4\",$J$30,IF(G26=\"5\",$J$31,IF(G26=\"6\",$J$32,IF(G26=\"7\",$J$33,IF(G26=\"8\",$J$34,IF(G26=\"9\",$J$35,\"\"))))))))))))","v":"·"},null,"⁰"]
[null,null,{"$f":"CONCATENATE(\"'= \",F26,\" ÷ \",F27,)","v":"'= 2.01 ÷ 3.01"},null,null,{"$f":"F26+1","v":3.01},{"$f":"IF($G$24>=3,MID($F$24,3,1),\"\")","v":"7"},"⁷",null,"¹"]
[null,null,{"$f":"CONCATENATE(\"'= \",F28)","v":"'= 0.67"},null,null,{"$f":"ROUND(F26/F27,2)","v":0.67},{"$f":"IF($G$24>=4,MID($F$24,4,1),\"\")","v":""},"",null,"²"]
[null,null,null,null,null,null,{"$f":"IF($G$24>=5,MID($F$24,5,1),\"\")","v":""},"",null,"³"]
[null,null,null,null,null,null,{"$f":"IF($G$24>=6,MID($F$24,6,1),\"\")","v":""},"",null,"⁴"]
[null,null,null,null,null,null,{"$f":"IF($G$24>=7,MID($F$24,7,1),\"\")","v":""},"",null,"⁵"]
[null,null,null,null,null,null,{"$f":"IF($G$24>=8,MID($F$24,8,1),\"\")","v":""},"",null,"⁶"]
[null,null,null,null,null,null,null,null,null,"⁷"]
[null,null,null,null,null,null,null,null,null,"⁸"]
[null,null,null,null,null,null,null,null,null,"⁹"]

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[null,"AREA UNDER THE Z-DISTRIBUTION (STANDARD NORMAL DISTRIBUTION)"]
[]
[]
[]
[]
[null,"FIND ez"]
[null,"For the z-value: ",null,{"$f":"IF(ISNUMBER('Log transformations'!D7),'Log transformations'!D7,\"\")","v":""},"ez is:    ",{"$f":"IF(ISNUMBER(D7),CONCATENATE(\"   \",H7),\"   ← enter a z-value\")","v":"   ← enter a z-value"},null,{"$f":"ROUND(EXP(D7),2)","v":{"$error":"#VALUE!"}}]
[]
[]
[null,"TRANSLATE FROM LOG ODDS (b's) TO ODDS RATIOS [EXP(b)'s]"]
[null,"A log odds (b) of:",null,{"$f":"IF(ISNUMBER('Log transformations'!D11),'Log transformations'!D11,\"\")","v":""},"corresponds with an odds ratio [Exp(b)] of:      ",null,{"$f":"IF(ISNUMBER(D11),CONCATENATE(\"   \",H11),\"   ← enter a log odds\")","v":"   ← enter a log odds"},{"$f":"ROUND(EXP(D11),3)","v":{"$error":"#VALUE!"}}]
[]
[]
[null,"TRANSLATE FROM ODDS RATIOS [EXP(b)'s] TO LOG ODDS (b's) "]
[null,"An odds ratio [Exp(b)] of:",null,{"$f":"IF(ISNUMBER('Log transformations'!D15),'Log transformations'!D15,\"\")","v":""},"corresponds with a log odds (b) of: ",null,{"$f":"IF(ISNUMBER(D15),CONCATENATE(\"   \",H15),\"   ← enter an odds ratio\")","v":"   ← enter an odds ratio"},{"$f":"ROUND(LN(D15),3)","v":{"$error":"#VALUE!"}}]