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The scales on Ihe X-axis and V-aris ure Ihe sarne for Match the coefficient of determination to the scatter diagram each scatter diagram (a) R?=1, (b) R? =0 58, (c)...

Question

The scales on Ihe X-axis and V-aris ure Ihe sarne for Match the coefficient of determination to the scatter diagram each scatter diagram (a) R?=1, (b) R? =0 58, (c) R? =0 90(a) Scatter diagram(b) Scatler diagram(c) Scatter diagram

The scales on Ihe X-axis and V-aris ure Ihe sarne for Match the coefficient of determination to the scatter diagram each scatter diagram (a) R?=1, (b) R? =0 58, (c) R? =0 90 (a) Scatter diagram (b) Scatler diagram (c) Scatter diagram



Answers

Match the linear correlation coefficient to the scatter diagram. The scales on the $x$ - and $y$ -axes are the same for each diagram. (a) $r=-0.969$ (b) $r=-0.049$ (c) $r=-1$ (d) $r=-0.992$

All right guys. So in order to do this one correctly, go ahead and take a peek your textbook with me and I'll go ahead and describe what to do. All right. So as I'm looking at A B. C. And D. I noticed that C. Has a value of exactly one. Okay. He hasn't value exactly one, meaning it is quite literally a perfect prediction. Okay. And so if I look at all of my um graphs here grabs 123 and four. The only one that's perfectly predicted is graph four. So C. Is going to be graph for their I don't know why it changed that. So see it's graph for okay, moving forward. All right. The next best one is going to be .9. Let's be and what's a really good predictor but not quite perfect. Um that's looking like Graph B. Notice on B. Uh It's 0.9 point nine is pretty good. And underneath that graph to you see that graph two is pretty darn close to that line. So that B is going to be graphed to next. We have next we have one that's like okay one that's really poor. The one that's okay. Um is looks like number three. And then the one that's really is a really poor prediction is um we're gonna be graph one. And so what's the uh so graph one must match with the lowest R squared value. So graph one must match with D. Because D. Has the lowest R. Squared value. So by default a. Would be three. And this makes sense right because the most scattered one or graph one belongs the lowest r squared value, so one must belong to letter D. And then the best prediction must go to the highest R squared values of the r squared value. Uh So the best prediction wanna is grabbed four, and the highest R squared is grab is number letters C, so C. And four must go together, and then you can feel the rest of them in from there.

We're working with correlation coefficients and scattered diagram. So were given four correlation coefficients that you can see up top here. And we'd like to match these with the scatter diagram that fits it. So let's start with our first diagram um in the upper left corner and this one looks to be a fairly straight line. So if we were to draw a trend line through it it would look something like that And it's fairly straight. So I'm going to assume that this one has that correlation coefficient of are equal to 0.946. So we can cross that one out. Let's move on to our second graph over here. Looking at this, it doesn't really appear to be a whole lot of a linear correlation from from looking at it doesn't seem like we can draw a straight line through it very well. So it's probably going to have a fairly low r value or that low correlation coefficient. So my guess for this one is that it's going to be equal to 0.053. Yeah. Now let's recall real quick actually that these correlation coefficients ranged from negative 12 positive one. Where zero means that we have no relationships. So we're looking at this correlation coefficient value of 0.53 that's really really close to zero suggesting that there's a very weak relationship between the variables and that appears to be so in that scattered diagram. Now let's move on to the one on the bottom left here. Looking at this one, it does appear that we could draw some sort of line through a good majority of these points So that was probably going to be fairly strong as well but not quite as strong as our first one. So we could maybe assume that this one is at zero 787 for its our value Which leaves us for the final one, a correlation coefficient equal 0.5-3. What we see here is that we could probably draw some sort of a line through it, but it doesn't quite match up the points. The points are a little bit more varied, so our strength of this relationship isn't quite as strong. And all in all, that's what we're looking at. We're trying to match these correlation coefficients to the graphs is just how strongly associated do these points appear to be and that are That our value, like I said again, it's going to range from negative 12 positive one. And the closer that value is 20, the weaker that relationship or the more scattered these points are likely to be.

The question here. It wants us to match a particular linear correlation coefficient, which again is going to be exemplified by the, um, letter that looks like an art. But this is actually gonna be pronounced as row here. So again, we have four different options A, B, C and D. So for a year, this is going to be 0.787 for being here. That's gonna be 0.5 to 3 C 0.810 So that should be a seven Onda de here should be 0.94 six year. So essentially, in this particular case here, we need to know what the actual graphics. So here this is going to be a very linear line, and essentially, this is going to be a very, very, very good fit. This is gonna be the second most linear that is going to be the third most linear, and this is gonna be not as linear, so you'll see a lot of variability in this particular case. However, with D here, you're going to see you barely any A. You're going to see very similar amounts to be. So if we're gonna pair it, it's a B C D who were gonna be close to each other

Yeah. Alright guys. So for this one um let's go ahead and take a look at this one here. So um what I'm gonna do is this right here I see a perfectly straight line. Okay I was going down so since I see a perfectly straight line is going down, that's gonna be negative one. So it looks like um Letter yeah one here. The Roman numeral one is connected with C. Okay. Room number one is connected with C. Okay over here. Um The next thing I see is B is very close to zero. Notice that zero negative 0.49 while very close to zero. So if for this one I'm going to be looking for dots kind of scattered all over the place. Okay? Um And the one that I see with the most scattered dots is going to be roman numeral three. So three is with B. So we have negative one. I'm sorry. We have letters C with Rome number one because that's a because that's a strong negative correlation and that's the strongest correlation. And then be is with roman numeral three because B. Is very close to zero and this is the most scattered. Zero is like completely scattered. Which is the most scattered. Okay. Which leaves us with A. Indeed now. And you're very closely to look at that negative nine negative 0.969 and D. Is negative 0.992 So um which is so D. Is slightly stronger than A. How do I know that? Since D. Is slightly closer to negative one? Um That means that it's slightly stronger so we have to afford to choose from. So of the two if we look at 11 is like a perfectly negative correlation. Which one of these looks more like number one, Number two or number four, I'm going to go with number two. Okay look at number two and number four. They're very similar if you notice, but number two the dots are just a touch closer together the number four. So number two has a stronger negative correlation, which is stronger. D. Is stronger than A. So D must go with number two and a go. Let's go with number four. So on summary A goes with four. B. goes with three. C. goes with one. D. goes with two.


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