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The table gives enrollments at North Shore High School.
a. Find the equation of the regression line. Round the slope and $y$-intercept to the nearest hundredth.
b. What is the slope of the linear regression line?
c. What are the units of the slope expressed as a rate?
d. Based on the linear regression line, how many students will be enrolled in the year 2016? Round to the nearest integer.
e. Is your answer to part d an example of interpolation or extrapolation? Explain.
f. Find the correlation coefficient to the nearest hundredth.
g. Describe the correlation.

So this is the graph that we have. And when we want to approximate the points where the peaks in the landscape are appearing eso we see that there are appear to be three peaks. Um, the 1st 1 looks like it's dead center. So the X and Y values are going to be at zero and 00 And then we also see if we set up a grid. If we show the X by grid lines, um, and look at this and we will look at the the level plot. So if we look at the little plot, it appears that there's 100 And then there's one at approximately negative 53 and then, um, one down here, which looks like it's about four negative one. So those would be, um, or three peaks. And then if we look at the plot again the elevations, Um, if you go back to that day, elevations are gonna be at about. This is 1234 uh, five would be this elevation. I see. 2345678 So it should be about 10. It appears if we were to plug in 00 In fact, we would get 10 and then if we were to plug in four negative one here. Ah, looking back at our equation, we would have an elevation of about four. So those would be the different elevations that we have. And then, um, that is all that were has to do. So using this craft were able to see elevation as well as the different places that where there are peaks.

For the different problem were given the U. S. Degree granting institutions um for both undergraduate and graduate. And this is the enrollment. So why is going to equal Your .17 x Plus 10.1? And this is where X. is representing years since 1980. And why is undergraduate enrollment and millions of students? So we want to predict the undergraduate student enrollment In 2016 to the nearest 100,000. So uh in 2016, since this is since 1980 will have 2016 minus 1980 so 30 60 equals 36 or in this case X equals 36. And we see at that point we'll have 16 Uh .22 million students. And that is to the nearest 100,000 because we're doing this by the millions.

So you want to go in and put your data in as years after 19 eighties 05 and so on all the way up and then put that population into your list one and list to and then you want to go to uh stat calculate and then go all the way down probably to the bottom and get that logistics model. And it will spit out this model to you and it's said to use three significant digits. So the numerator would be 906 and then we have one plus and that coefficient a 23 significant digits is going to be 2.27 And then E. To the power of negative 0.169 X. And again that's all using three significant digits. And then you wanted in part B to determine for 2010 what that model would predict and for 2020. And so seeing that this was for 1919 80 this is 30 years. We would want to substitute in place of X 30. And if we go to variables, statistics, e que and hit enter, you will get this model spit out and you just want to change that X value so that it has that 30 in place of it. And when you do, you'll find out that to this will come out to be 893 as the predicted value. And likewise, if I go back and hit second entry or go back and uh and plug in and we would want to now have 40 input for X. We'll find out that that is getting closer to that limiting value of 909 106 is what the limiting value will end up being and we're going to end up getting close to that after 40 years. Mhm.

Hello and welcome to this video solution of numerous. Here we are given a link comprehension. So here in statement one were given that and iron or a on roasting with sodium carbonate and lying in the presence of air gives to compound PNC. And you're from option the second part the solution be in concentrated. It's alan reaction with production furrows and it gives a blue color on precipitated of compound their cost solution of C. On treatment with considerate statistical gives a yellow colored compound E. And the compound even treat it with a seal gives an orange red compound F. Which is used as an ox raise anything. So you have to make certain predictions to come into the solution. So let me show you how it's made. So first of all we take for if he oh she had to poetry thus eight and a two freedom global neck And with air that is given seven or 2 good line gives you to a free two or three that's eight the name so Seattle four. That's it. It's a frustration. Next we have if we two or three reacting with concentrate sales that is given gives you who official three Last three H 2. Right now this official tree reacts with who before if he 10 6 that is protection fellow sign a great this gives you the blue solution pushing blue solution of if the four if he CN six whole trade plus 12 cases. Mm Next From three we have two any he wanted to see our well for That's 8/10 of food gives you we need to the odd 47 is the yellow color solution. Greatness in A. Two so four. That's it too. No you have in A to see our two or seven. Okay, last case here is the orange color substance of people pr two or seven that's 2010. So this is the so let us state what is A what is B. The first we have me is If you see a 23, this is a Next we have every two or 3 SCB or Yes. So this suits also be ready And in in 204 this is C. Right BNC. That is mentioned. Yes. Now this pushing blue books. Mhm. Yeah. Yeah. Whoa it is. Mhm. Okay. To see again this election with the this one your local er this is E and we have orange. What are some common? It does if Yeah. Right. I hope this is clear to you and have a very good rest of the day. Thank you.


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