So the next thing we're going to examine with conjoint analysis is determining how important each of the attributes are in the overall decision process. So is price a very important attribute, or sort of just a minor attribute when people make decisions? Now, look at this formula. This is big and ugly, but it's actually quite intuitive. I bet you figured out by now, that the difference between the effects or the utility levels tells you something about how much more, or how much less people prefer a particular level of a given attribute, that's true. It's also true that you can look at the spreads between the highest and the lowest preferred level of any different attribute. And those spreads will give you an indication of how important the attribute is all in the choice process. So for example, if I looked at brand, the highest preferred level is 0.56, and that's with the high-flyer pro brand. The least preferred is the long shot at negative 0.60. Suppose instead of 0.56 and 0.60, all those numbers were very close to zero. What that would mean is it doesn't make much difference one way or the other, which brand that you choose. People don't rely care. It doesn't add a lot to utility and it doesn't subtract a lot from utility. So intuitively, that tells you that the higher the spread between the most preferred and least preferred level, the more important the attribute is. So how do we do that mathematically? Typically in conjoint analysis, the way that's done is to take any individual attribute, and let's call that attribute k. It could be any attribute. And look at the value of the most preferred level, so for brand that will be 0.56. And subtract from that the value from the least preferred level. Now the least preferred level, because these always add up to zero, is typically going to be a negative number. So, it's going to be minus, minus a number, right? It's minus a negative number, so that this whole numerator will be a positive number. That's the numerator. What's this in the denominator, this big, ugly summation? That's just the sum of the spreads of all the different attributes in your conjoint analysis, including the attribute that was included in the numerator. So, in our output this was include brand, it will include the spread for distance, and would also include this brand for price. So let's take this big, ugly, messy looking thing and apply to some data. So, in our golf ball example, the attribute importance of distance is. Okay, where did I get that? For distance, the least preferred level is 0.48, the most preferred level is 0.36, and that is the difference between that positive and negative number. Remember, that turns into an addition. And then in the denominator, you have the spread for the distance, you also have the spread for the brand, is setting here, and you have the utility spread for the price, and that gives you .24. And mathematically, I suspect a lot of you can intuitively understand, that that number always has to be between zero and one. Because whatever is included in the numerator is also always included in the denominator. And that bounds that number between zero and one. And because of that, the typical way that this is interpreted is, this is the percent decision weight of a particular attribute. So distance in our example, receives 24% of the decision weight. So it's not real high, it's not real low. It's just kind of somewhere in the middle in terms of attribute importance.