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5 a)Explain LOESS smoothing and how is it used get informationabout trends in a series?7.a. Talk about how smoothing methods are used in coming up with thestandard ...

Question

5 a)Explain LOESS smoothing and how is it used get informationabout trends in a series?7.a. Talk about how smoothing methods are used in coming up with thestandard decomposition of a time series.b. Explain information is provided in a decompositionand what is the meaning of each aspect of the plotc. Explain how you can tell a decomposition is showing thebehavior of a series? Explain seasonality and sub graphs relativeto decomposition.

5 a)Explain LOESS smoothing and how is it used get information about trends in a series? 7. a. Talk about how smoothing methods are used in coming up with the standard decomposition of a time series. b. Explain information is provided in a decomposition and what is the meaning of each aspect of the plot c. Explain how you can tell a decomposition is showing the behavior of a series? Explain seasonality and sub graphs relative to decomposition.



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$(a)$ find the equation of the regression line, (b) construct a scatter plot of the data and draw the regression line, (c) construct a residual plot, and $(d)$ determine whether there are any patterns in the residual plot and explain what they suggest about the relationship between the variables. $$\begin{array}{|cc|c|c|c|c|c|c|c|c|} \hline \boldsymbol{x} & 8 & 4 & 15 & 7 & 6 & 3 & 12 & 10 & 5 \\ \hline \boldsymbol{y} & 18 & 11 & 29 & 18 & 14 & 8 & 25 & 20 & 12 \\ \hline \end{array}$$

So I'm using a. T. I. 84. And I put my data in list one and list too. And when I did I find the equation Regression equation to be 21.024 plus .1389 x. And then I grabbed a scatter plot of the data and the scatter plot of the data. The data ends up looking like a pattern kind of like this. And then the regression equation ends up looking like that. So we can see that there is curvature in that data and that regardless of what the correlation coefficient we can see that there's definitely a pattern. And then you are asked to have a residual plot. And so a couple things you can do you can go over here in a to list three and you can um go into your editor and you can find the residuals longhand by putting the regression equation up here so go to variables and statistics and eq. And it will put the equation in there. And the only thing I need to do is change the X. value into list one. And when I do I get my residual excuse me, my predicted value. And that comes out to be 26.3, 25.7 and etc those are the first couple. And then we could take list to minus list three to find my residuals and make sure you're up in this L for icon not to do that and list to minus list three. And when I do I get the residuals of negative 2.3 is my first one, negative 3.7 point 42 and so on and not. That will give you an idea of what the residual should look like. And then I can go back and do a stat plot And my step plot would have list one versus list for. And also I would clear out that Y equals because we don't need that anymore and I don't want that to when I hit zoom and number nine presumed staff, I end up getting a residual plot that looks like clips, we put the axis there we go. And the residual plot will always have that access in the center by the way, and the residual plot has a couple dots and it does this and like so. And anyway, we definitely see a pattern of a curb, a curved pattern on here that tells us that our linear model is really not suited to this, that there's probably a different curved model that would fit this data better.


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