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This Question: 18 pts Find Ihe Eqzualion Ihe regression line for Ihe given CAta Then cons Iruct scatter Pol cf the dala ard craw Ihe regression Cortenti mlllgrams) ...

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This Question: 18 pts Find Ihe Eqzualion Ihe regression line for Ihe given CAta Then cons Iruct scatter Pol cf the dala ard craw Ihe regression Cortenti mlllgrams) tor 6 beef hot ot 40 shorn ntho IAbletbelo' Culorts ScaunFud the regussion cqualionY-D-0 (Round Ia (hree dcoma Dlcneeced )Chcsecomeci grach bcciPteuciJana cfeIct tChoosttne cotart Jeonpy303 3L TR 73 21 173marrmnProdc#Eledyd, 30 ChenecuenciL176 J rJFfuiPienoaus GJut 4Choosu Iha0niJuzc,0'4 anstccne

This Question: 18 pts Find Ihe Eqzualion Ihe regression line for Ihe given CAta Then cons Iruct scatter Pol cf the dala ard craw Ihe regression Cortenti mlllgrams) tor 6 beef hot ot 40 shorn ntho IAbletbelo' Culorts Scaun Fud the regussion cqualion Y-D-0 (Round Ia (hree dcoma Dlc neeced ) Chcse comeci grach bcci Pteuci Jana cfeIct t Choosttne cotart Jeonpy 303 3L TR 73 21 173 marrmn Prodc #Eledyd, 30 Chene cuenci L 176 J rJ Ffui Pieno aus GJut 4 Choosu Iha 0ni Juzc,0'4 anstccne



Answers

$(a)$ 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.

So on question 28 I entered on my data into list one and list to and then I quick sketched the scatter plot and Got this regression equation 43.214 was the y intercept and the slope is almost 1.99 758 and acts. And I did get a correlation coefficient. It doesn't ask this but I got a correlation coefficient of close 2.9 about .88. And then I grabbed to the data just to make sure that I didn't enter the data incorrect in incorrectly. And again it did something like that. And then I could plug into my wife's of one to graph that equation. I could do my variable statistics BQ. And I could have it graft that equation on my my graph and it actually did something kind of like this where it kind of went like this whoops not like so and then went up like that. So there was a part that was above and apart below. So we can see that there is a little discrepancy could be that these people as they've worked years and years, maybe they aren't worth as much overtime. Um So that could be the reason why these lower values are there, although we are asked to talk about that, but there's our model.

This is problem. Number six, we are given the question that if all of the points fall exactly on the regression line, what is the value of our correlation coefficient? So if we have some set of data here with some arbitrary regression line and all of our points are exactly on this line. So recall that our correlation coefficient r squared is a measure of the deviation of these points from this line, and the higher the value the larger a the smaller a percentage of deviation we have. So if we have all of these values exactly on the line, that means that 100% of the variance in data, so they change from point to point can be explained directly by the correlation line, so r squared will be exactly one for our value. It depends on if it is increasing or decreasing in this case, since we have an increasing line, our our will be one. But in the case of a decreasing line we would have a negative value of our

So this is our question number 237 here with their expertise. And why will use so in t 83 calculator for every one column you need to enter the X values. And for a two column you need to enter the old wiring loose. My resting enter we have is it will do minus. You're a point, man. 01 Next, then be easy. Goto 26 point Therefore now, as you know, the equation of lion is wise equal to express me. Okay, Now put the value and B here. East negative. 0.90 Onyx and hear the east 26 points. 04 So this is your questionable least red line. Okay, Now, in our computer, we got our square is equal to your 0.937 Okay, now taking square root word sites. So here we have our is equal to negative 0.968 It is Our correlation coefficient are okay. Thank you.


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