In this video, we're going to look at log arrhythmic transformations and the power law model. We can use a law algorithmic transformation to determine if the power law is a good power law model is actually a good fit for our data. Now, the power law formula is right here, Y equals alpha X to the beta. And in our particular example, X represents the time in microseconds and Y equals the amps built up in the circuit at time X. So here are exes and here's our why. First thing we're asked to do is we're asked to find ex prime and why prime these are transformations. So ex prime will be log of X and Y. Prime will be log of Y. And then we're asked to graph. Actually we're asked to find the regression model for the graph of ex prime Y. Prime. So I would find a log of two. This would be my first ex and then I'm going to round it, so Log of two again on the calculator log too. And then I would also need to find log 1.81 and I can do that for each of my values. And then I would graph that information. But there's actually a faster way to do it. So I'll go back to my calculator but this time I'm going to go to my lists. So stat number one. Edit notice I already have the information in L. One and L. Two. What I'm gonna do on L. three and L four is figure out the logs of those values. So I'm going to type log to so log of my original X. Value and press enter and you can see this automatically calculates it for me. So I don't have to go through and do it all by hand, log for log six, log eight, log 10. Remember the log of 10 is one because those are in verses. All right. I'm going to pause the video and then I'm going to enter in the logs of the Y. Values. And when I come back or in a second you will see the results of that. So, now I have the log of my Y. Each Y value entered into al. For so to find the regression model, select stat cursor over to couch, choose number eight. The linear regression model in the form of A plus B. X. But I don't want L one, L two. I want L. Three and L. Four. So second three will put L. Three under my ex list. Second four puts L four under my wild list, cursor down to calculate and now I have the X. Value or the A. Value, the B. Value. And my correlation coefficient so is 0.128 B is 0.492 depending again on how you need around. And rs 0.987 So my model will be Why prime is approximately 0.128 plus 0.492 Ex prime. So there's my linear regression model. So that is part B. So part C. Then is to find my model the my power model. And I can do that algebraic lee by using this Y. Prime equation. But we're actually just going to use our calculator. And then if you'd like to see how you find the model drive it from the linear regression model you can but I figured most of you will just want the answer. So we'll go through and I go back to my calculator stat calc But this time I want to calculate power regression. If you cursor down you'll see here that it is at letter A. When I select it. I don't want L. three and L. four because remember those weren't my original Values. So I'm gonna do l. 1 2nd 1 second to. So all one L two years might already be default to L. One L. Two, Calculate enter and you can see now I have alpha or in this case a 1.34 37 Or 1.3438 And then .4919. Now this will depend on again how how your instructor wants you around or how the textbook wants you around it. So it may be a little bit different. Okay so there is your power model and again rounding some texts might have it like this. There would be another model again rounded differently. Okay so if you're done, pause the video. If you want to find out how we take our linear regression model and make it into a power model, then stick around. So recall that the UAE prime and the ex prime are actually logs of those values. Now I'm gonna exponentially eight both sides. Bye. 10 And 10 log of Y will become why. And now I need to remember some of my exponential rules or exponents rules. So when I'm adding exponents, that means in my original equation I was multiplying like bases. So this actually will end up being our alpha and then this one I have to do a little more work. I have to rearrange it a little bit more. So I'm going to rearrange it because remember with our power roll you copy down the base and you multiply the exponents. So I'm going to reverse the power rule. Can remember this is multiplication. So 10 log of x becomes x. So this will be alpha, here's beta and when I use my calculator, second quit. So 10 carrot .128 for at the decimal point, You can see there's our 1.343 When we round it or 1.34-7. So again, it's a little different from when we use our calculator. And again, that has to do with how we end up a rounding our information.