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These are the user uploaded subtitles that are being translated: 1 00:00:00,004 --> 00:00:01,009 - [Instructor] Microsoft Excel worksheets 2 00:00:01,009 --> 00:00:05,005 are very well suited to performing Bayesian analysis. 3 00:00:05,005 --> 00:00:08,007 In this movie, I will show you how to implement our analysis 4 00:00:08,007 --> 00:00:11,003 of the Kahneman's Cabs problem. 5 00:00:11,003 --> 00:00:14,003 My sample file is 07_04_Calculating 6 00:00:14,003 --> 00:00:16,007 and you can find it in the Chapter07 folder 7 00:00:16,007 --> 00:00:19,006 of the exercise files collection. 8 00:00:19,006 --> 00:00:21,001 We've gone through the parameters 9 00:00:21,001 --> 00:00:22,009 of the problem several times in this chapter, 10 00:00:22,009 --> 00:00:24,000 so I'll just go ahead 11 00:00:24,000 --> 00:00:27,009 and start entering in the values and formulas. 12 00:00:27,009 --> 00:00:31,006 In cell B3, we need to establish the base rate 13 00:00:31,006 --> 00:00:36,000 of green cabs, and that is 85%. 14 00:00:36,000 --> 00:00:39,000 So in cell B3, I will type 85 15 00:00:39,000 --> 00:00:40,008 and I have already formatted the cell 16 00:00:40,008 --> 00:00:42,000 with a percentage format, 17 00:00:42,000 --> 00:00:43,005 so I'll just press Enter. 18 00:00:43,005 --> 00:00:47,008 You don't need to type in the percent sign. 19 00:00:47,008 --> 00:00:50,003 And in B4, I'll type the accuracy 20 00:00:50,003 --> 00:00:52,007 and remember that the court established 21 00:00:52,007 --> 00:00:56,006 that the witnesses were accurate 80% of the time. 22 00:00:56,006 --> 00:01:00,001 So 80 and Enter. 23 00:01:00,001 --> 00:01:03,003 Now we can find the probability a cab is green or blue. 24 00:01:03,003 --> 00:01:05,000 And then the probability the witness 25 00:01:05,000 --> 00:01:07,005 is correct or incorrect. 26 00:01:07,005 --> 00:01:10,005 So in B6, we need the probability 27 00:01:10,005 --> 00:01:12,008 that the cab is actually green. 28 00:01:12,008 --> 00:01:14,007 So I'll type an equal sign 29 00:01:14,007 --> 00:01:16,007 and that will be equal to B3, 30 00:01:16,007 --> 00:01:18,009 which is the base rate for green. 31 00:01:18,009 --> 00:01:20,004 The probability the cab is blue 32 00:01:20,004 --> 00:01:23,000 is one minus the probability it's green. 33 00:01:23,000 --> 00:01:24,009 So in B7, I'll type equal. 34 00:01:24,009 --> 00:01:27,006 One minus B3 and Enter. 35 00:01:27,006 --> 00:01:30,001 And 85 plus 15 is 100. 36 00:01:30,001 --> 00:01:34,000 So I know that those formulas are correct. 37 00:01:34,000 --> 00:01:35,001 Now we can do the same 38 00:01:35,001 --> 00:01:37,004 for the witness being correct or incorrect. 39 00:01:37,004 --> 00:01:39,007 So in B9, I'll type equal 40 00:01:39,007 --> 00:01:41,008 and their accuracy is 80%. 41 00:01:41,008 --> 00:01:44,000 That's in B4. Enter. 42 00:01:44,000 --> 00:01:46,007 And then in B10, probability they are incorrect. 43 00:01:46,007 --> 00:01:50,004 So equal one minus the probability they're correct. 44 00:01:50,004 --> 00:01:51,009 That's in B4, Enter, 45 00:01:51,009 --> 00:01:56,004 and we get 20% and 80 plus 20 is 100. 46 00:01:56,004 --> 00:01:58,002 We can now use those probabilities 47 00:01:58,002 --> 00:02:03,004 to find the probability of a particular scenario happening. 48 00:02:03,004 --> 00:02:07,008 And we'll do that over here in our classification matrix. 49 00:02:07,008 --> 00:02:10,003 In cell E4, I want to know the probability 50 00:02:10,003 --> 00:02:13,009 that a cab is reported green when it's actually green. 51 00:02:13,009 --> 00:02:15,007 So I'll type an equal sign. 52 00:02:15,007 --> 00:02:20,005 And the probability a cab is green is in B6 53 00:02:20,005 --> 00:02:22,003 and we'll multiply that 54 00:02:22,003 --> 00:02:24,002 by the case where the witness is correct. 55 00:02:24,002 --> 00:02:28,007 And that's in B9 and Enter. 56 00:02:28,007 --> 00:02:32,000 Now in E5, we need to know the probability 57 00:02:32,000 --> 00:02:34,001 that the cab is actually blue 58 00:02:34,001 --> 00:02:37,002 but was reported as being green. 59 00:02:37,002 --> 00:02:40,001 So 60 00:02:40,001 --> 00:02:43,001 type equal and then the cab is actually blue. 61 00:02:43,001 --> 00:02:46,005 So that's in B7, the probability of it being blue. 62 00:02:46,005 --> 00:02:48,000 Multiplied by the probability 63 00:02:48,000 --> 00:02:51,007 that the witness is incorrect and that's in B10. 64 00:02:51,007 --> 00:02:54,006 And Enter, and I get 3%. 65 00:02:54,006 --> 00:02:58,003 Same thing for the cab being reported as blue. 66 00:02:58,003 --> 00:03:00,006 So in F4, I'll type equal. 67 00:03:00,006 --> 00:03:03,004 In this case, the cab is actually green 68 00:03:03,004 --> 00:03:06,009 and that is in cell B6. 69 00:03:06,009 --> 00:03:08,009 And we'll multiply that by the probability 70 00:03:08,009 --> 00:03:10,005 that the witness is incorrect. 71 00:03:10,005 --> 00:03:14,002 That's in B10 and we get 17%. 72 00:03:14,002 --> 00:03:17,001 And finally, we want to find the probability 73 00:03:17,001 --> 00:03:18,006 of the case where the cab is blue 74 00:03:18,006 --> 00:03:21,000 and it's reported as blue. 75 00:03:21,000 --> 00:03:23,003 So in F5, I'll type equal. 76 00:03:23,003 --> 00:03:25,005 The probability it's blue is in B7 77 00:03:25,005 --> 00:03:28,008 multiplied by the probability the witness is correct. 78 00:03:28,008 --> 00:03:33,000 That's in B9, Enter and we get 12%. 79 00:03:33,000 --> 00:03:34,002 One way to check to make sure 80 00:03:34,002 --> 00:03:37,000 that your classification matrix has been done correctly 81 00:03:37,000 --> 00:03:41,001 is that you can add the probability of correct guesses, 82 00:03:41,001 --> 00:03:44,000 so we have 68 and 12, that's 80%, 83 00:03:44,000 --> 00:03:46,001 which equals the accuracy, 84 00:03:46,001 --> 00:03:50,009 and then inaccurate guesses, 17 plus 3 is 20%, 85 00:03:50,009 --> 00:03:55,005 which is also the probability the witness is incorrect. 86 00:03:55,005 --> 00:03:57,006 Now we can perform calculations 87 00:03:57,006 --> 00:03:59,004 to find the probability the cab is green 88 00:03:59,004 --> 00:04:00,008 when reported green 89 00:04:00,008 --> 00:04:04,002 and the probability the cab is blue when reported blue. 90 00:04:04,002 --> 00:04:06,004 So in cell E8, 91 00:04:06,004 --> 00:04:08,009 we need to type an equal sign 92 00:04:08,009 --> 00:04:10,008 and then find the number of times 93 00:04:10,008 --> 00:04:14,008 that a cab is correctly reported as being green. 94 00:04:14,008 --> 00:04:17,004 And that is in cell E4. 95 00:04:17,004 --> 00:04:20,001 And we need to divide that by the total number of times 96 00:04:20,001 --> 00:04:22,002 that the cab is reported as being green, 97 00:04:22,002 --> 00:04:24,003 even if it's actually blue. 98 00:04:24,003 --> 00:04:26,008 So after the division sign, 99 00:04:26,008 --> 00:04:28,002 I'll type a left parentheses 100 00:04:28,002 --> 00:04:32,003 and we'll have E4 plus E5, 101 00:04:32,003 --> 00:04:34,003 right parentheses and Tab. 102 00:04:34,003 --> 00:04:36,002 And we'll see that that percentage 103 00:04:36,002 --> 00:04:39,004 or probability is 96%. 104 00:04:39,004 --> 00:04:41,003 Now we can perform the calculation 105 00:04:41,003 --> 00:04:44,007 that we did in previous movies as part of the example, 106 00:04:44,007 --> 00:04:46,008 and find the probability the cab is blue 107 00:04:46,008 --> 00:04:48,003 when it's reported blue. 108 00:04:48,003 --> 00:04:51,005 So in F8, I'll type equal, 109 00:04:51,005 --> 00:04:54,009 and the probability that the cab is actually blue 110 00:04:54,009 --> 00:04:58,008 and is reported as blue is in cell F5. 111 00:04:58,008 --> 00:05:02,001 It can be very easy to use F4 as your basis 112 00:05:02,001 --> 00:05:05,008 but remember that that is an incorrect guess. 113 00:05:05,008 --> 00:05:07,004 So now we have the number of times 114 00:05:07,004 --> 00:05:10,006 that the cab is correctly reported as being blue 115 00:05:10,006 --> 00:05:13,002 and we need to divide that by the total number 116 00:05:13,002 --> 00:05:15,002 of times it is reported as being blue, 117 00:05:15,002 --> 00:05:16,008 both right and wrong. 118 00:05:16,008 --> 00:05:21,005 So left parentheses, F4, plus F5, 119 00:05:21,005 --> 00:05:23,003 right parentheses and Enter. 120 00:05:23,003 --> 00:05:25,005 And we get 41%, which is the value 121 00:05:25,005 --> 00:05:28,000 that we saw earlier in this chapter. 9030

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