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This is a video to help you with Objective 3.4, which is to evaluate a nonlinear model.
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So in this class we've got our three models.
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Let's say, let's have three different models here.
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I don't know, let's make them functions of T. So we have G of T, and we have H of T.
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And F of T is going to be a quadratic model. So it has two parameters.
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And the previous objective, Objective 3.2, you learn how to find out what those values of those parameters are given some information.
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In this case, for the quadratic, you need the equivalent of three pieces of information. If you have the exponential, you have to have the equivalent of two pieces of information.
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Of course, the exponential comes in another flavor that looks like this.
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So two flavors, but each flavor requires two pieces of information. Doesn't matter.
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And then there was a logistic that also requires three pieces of information in order to find the parameters.
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Well, if you want to evaluate one of these nonlinear models, you're not going to be able to evaluate anything unless you know what the values of these parameters are.
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So how you going to do that? Well, you got to go back to 3.2.
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So this video doesn't teach you how to find these parameters. You, this video is only about how to evaluate.
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And what I'm suggesting is that if you just remember that you've already learned how to evaluate functions, any function, back an Objective 3.1, you learn to evaluate them at various inputs.
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You also learned to evaluate them at other functions, which would be the equivalent of a composition. So now we just have to apply what we already know, evaluation of functions, which is what somebody gives you an input.
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In this case, a T, and they're asking you to find an output.
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And we haven't specified what the variable is of the output, but we could say in each case it was P.
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So here I mean given a T, and I'm going to find a associated P.
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Now if you remember, except 1.13, this is actually fairly easy to do.
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You could do the computation on the home screen, but we also learned if you go back to Objective 1.13 and refer to the appropriate calculator skill that we can type any one of these into Y1 and have a way to evaluate it.
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But we also have an alternative way to evaluate and to find the parameters, which is to use Solver.
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Solver can solve for any unknown, so we can solve for the output given the input, which is indeed evaluation.
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So in a way, Solver can evaluate, right? Solver can solve for the output, that's true.
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But Solver can do a lot more than that. Solver can solve for the input given the output. That's true solving.
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Solver can also solve for parameters if you know everything else.
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Solver is a little bit of a misnomer because Solving usually means finding an input given an output of a function.
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But it can also mean just to find whatever is unknown out of everything that was given.
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So let's take a look at one of the problems. For example, let's take a look at this problem right here.
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We have a weekly business selling gummy bear bags, weekly revenue is blah blah blah, when the price is a buck 90 but is when the...
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Okay, so what does the quadratic model predict will be the revenue when the price is $2.93? Well, it would be a lot better if they just gave us the model.
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We would be done, we could evaluate it. But here I'm asking you to put two steps together.
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In other words, do 3.2 then evaluate it. Of course, in 3.5, I'm going to ask you to solve. I actually have to go backwards, right?
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So let's see. Hold on for a second and I'll bring up the calculator and we can describe what it is we're going to do to solve this thing.
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Okay, so when we look at this problem here, we have two different values, right?
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The weekly revenue is $8200 when the price is $1.90 but is what? Is $5208 when the price is $310?
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So how are we going to find the parameters? Well, remember the quadratic model is what? The quadratic model is what?
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It needs $3, right? Apparently there's only $2 there. So what's the other one?
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Well, it's a function of price. So when the price is $0, the revenue is $0. So that's the one we were missing.
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So you remember that from 3.2 that you need 3 points for the quadratic and one of them when you have a price, or a revenue as a function of price, is going to be $0,000.
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So what am I going to do? Well, I think in this case, I want to do regression because I have 3 points and that's the easiest way to do this.
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So I'm going to go stat, edit, and I'm going to do 3 points. So I got 1 at 0, 1 at a buck 90, and 1 at $3.10.
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And up here, the corresponding revenue is 0. The corresponding price for a buck 90 is a revenue of $8208.
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And we also have, for $3.10, we have 50 to 08. Okay. So now I'm going to do a quadratic regression.
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And up it comes. And then if you remember, we learned how to do this. When you do a regression of any type, you can create or put the regression equation wherever you want it.
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So I'm going to put it in Y1. So here I go. I went to the Y equals. I got on Y1. I went Vars, Statistics, EQ, Reg EQ, and I dumped it right in there.
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And now I just have to evaluate it. Well, evaluating is pretty straightforward. Right? Evaluating is what?
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Second, I can go to my table, for example, if I'm in the ask mode, looks like I'm in an ask mode. So when the price is $2.93, I can ask what it is.
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618.2 into the nearest $10 I would round up to 602. Okay. So that's how you put together objective 3.1 together with objective 3.2.
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It's like objective 3.2 plus an extra step, right? And of course, I could have given you the revenue and asked you to compute the price that would have been a solving situation.
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And it would have been just the same techniques you learned in 1.14. So we're really not learning anything new here. We're just applying what we learned and object as 3.13 and when we do solving 3.14.
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And we've got this extra step, which is we've got to come up with the parameters of one of the non-linear models before we can do it. So we've got to be able to do that. That's objective 3.2.
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Okay. So we'll call this part 1 and then I'll do a couple more parts, at least one more part for 3.4.