 Greetings. This screencast is actually a continuation of a previous screencast where we found a sinusoidal model for the number of hours of daylight in Ettenberg, Scotland. This is actually what we found. We used this data for the number of hours on first day of each month and we numbered the months one through 12 and ended up with this sinusoidal model for the number of hours of daylight and we see the graph there and how well the graph actually fits the data. What we're going to do now is compare this to an equation that we would get from the calculator. In particular, we're going to compare this to the sine regression equation that we obtained using the TI-84 calculator and this is what was obtained using the calculator and again a graph of this sinusoidal model of sine regression equation and the data and again you can see it does a very good job of fitting the data. What we would like to do is compare these two models in terms of amplitude, period, phase shift, and vertical shift. So here's our two models and remember the meaning of our coefficients or parameters a, b, c, and d and what we're going to do here is write down some information about these two models, some of which will be pretty easy to pick up in particular like the amplitude is easy in model number one it's 5.22 and model number two it's 5.153. So again a slight difference model number one having a slightly higher amplitude. We had set up model number one so it would have a period of 12 and for model number two we have to do just a little calculation. It would be 2 pi divided by that number right there the b value 0.511 and if we do that computation that comes out to be 12.30 and so again it's kind of interesting that it gave a period slightly greater than 12 months. The vertical shift is also easy to read and for model number one it's 12.28 and for model number two it's 12.174 and again for the phase shift for model number one that's already set up that's equal to 3.7. For model number two we have to do a little work because notice how the calculator gave us this part right here and how it compares to this it is not in the correct form to be able to read the phase shift from that so we have to do a little bit of algebra to rewrite the equation for model number two into this form right here and really the only work we have to do is within the argument of the sine function. So that's what we're going to do here and as we pointed out here what we're going to do is work with the part inside the sine function and we're going to do actually kind of a little bit of factoring and if you if you remember what we need on this is b and n and parentheses t plus or minus something so what we're going to do is factor out the 0.511 and what that will leave us with is a t and then a subtraction and just to kind of emphasize what we're doing here what we get is 1.829 divided by 0.511 sometimes seems a little strange to make things a little more quote complicated but in this case this more complicated form helps us determine the phase shift and if we're unsure about this factorization another way to look at this is start with the right hand side and you can see if I multiply the 0.511 times t I get this and if I multiply the 0.511 times this number 1.829 divided by 0.511 I get this so I've done the factorization correctly and what that then allows me to do is to write this sinusoidal model in a slightly different form with 0.511 factored out and if I do that computation of 1.829 divided by 0.511 I get 3.579 and of course we've got the plus 12.174 so we now can determine the phase shift as 3.579 and here's a final comparison then of our two models things we have done before and the one thing we just completed was determining the phase shift for model number two which model is better to use it probably doesn't make a whole lot of difference but model number one was sort of fit by eyesight and doing some computations by hand model number two the sine regression actually uses a mathematical method for determining that equation there is a numerical measure of the error of a sinusoidal model between the sinusoidal model and the actual data and you calculate this error and what the sine regression formula does then is chooses the model with the smallest possible error so there you have two different ways to model data that is period that is a period from a periodic phenomenon and that's it for now so long