Use the following dataset to answer the following...

Use the following dataset to answer the following questions: x1 x2 4.3 3.54 8.2 3.7 7.81 3.65 9.3 3.37 2.91 2.26 6.13 3.58 4.02 1.29 6.58 3.37 4.14 2.32 5.71 4.22 What is the Euclidean distance between the first two observations? Round to 2 decimal places. What is the Manhattan distance between the first two observations? Round to 2 decimal places. Using z-scores to standardize the values, compute the new Euclidean distance between the first two observations. Round to 2 decimal places. Using the min-max transformation to normalize the values, compute the new Euclidean distance between the first two observations. Round to 2 decimal places.

Transcript

00:01 So for what i'll refer to as part a, we have that the euclidean distance between two points, i'll just call them p and q, equal to the square root of p1 plus, or one second here, pardon me.

00:22 Actually, i should say it's going to be the square root of p2 minus p1.

00:28 Or let me be more careful here.

00:31 It's going to be using the notation that i'm using, saying we're going from point p to point q.

00:36 You would properly say this as it's going to be equal to q1 minus p1 squared plus q2 minus p2 squared.

00:51 If we're looking at just two points in two dimensions.

00:54 So i'm just going to bring up my preferred software for doing these kinds of calculations.

00:58 One moment.

00:59 Okay, so we have that this is going to then be the square root of 8 .2 minus 4 .3 squared.

01:08 Plus 3 .7 minus 3 .54.

01:15 We can see that the euclidean distance is equal to 3 .90328, or rounded to two decimal places, that's just 3 .90.

01:25 For part b, where we're asked for the manhattan distance, the manhattan distance, which i'll call just dm for short here, between two points pq in two dimensions, is equal to the sum of the abatant.

01:41 Values of the differences between the coordinates.

01:46 So it would be equal to the absolute value of q1 minus p1, plus the absolute value of q2 minus p2.

02:00 So we have that that is going to be equal to 8 .2 minus 4 .3 plus 3 .7 minus 3 .54.

02:13 We have that the manhattan distance is equal to 4.

02:18 Now for the part c, quote unquote, one thing that we'll need to do is, as suggested, use z scores to standardize the values.

02:30 So to do that, i'm going to hop over into excel.

02:33 Okay, so now that we have all of the data in excel here, first thing that i'm going to do is calculate out the mean and standard deviation for our two dimensions.

02:46 So we do the average of all of the data.

02:52 We have that the average for x1 is 5 .91, and for x2 is 3 .13.

02:58 Then we have the standard deviation.

03:00 I'll calculate this as a population standard deviation, because we have no reason to think otherwise.

03:11 The standard deviations, as shown there, then we'll call these z1 and z2.

03:19 What we have to do is just to take each one of our data points.

03:23 And basically plug them into the formula for how you would find the z score.

03:27 So we would do 4 .3 minus the mean...

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