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Numerade Educator

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Problem 25 Hard Difficulty

The data in the table below list the Life Expectancy for white males in the United States every decade during the last century $(1=1900 \text { to } 1910,2=1911 \text { to } 1920, \text { etc.. }) .$ Create a
model to predict future increases in life expectancy. (National Vital Statistics Report)
$$\begin{array}{lcl}{\text { Decade }} & {1} & {2} & {3} & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\ {\text { Life exp. }} & {48.6} & {54.4} & 59.7 & 62 .1 & 66 .5 & 67 .4 & 68 .0 & 70 .7 & 72 .7 & 74 .9 & 76 .5\end{array}$$

Answer

$\log \hat{y}=1.68+0.187 \log x$

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Video Transcript

all right. So for number 25 overs, asked to look at the different decades and the life expectancies over the last several decades and to compare them to see what kind of relationship they haven't, our goal is to have a linear relationship. Um, so if these original plots do not create a linear relationship, then that's when we're gonna have to re express and then determine what our model is going to be. And so it's It's a few steps, but it's all gonna be one problem and done, so I am on desk. Most stop calm when you go to desk most dot com, um, you'll be able to click on start graphing in the center of the home page. It's a big orange er reddish button, and then you'll see this image. So in order to get a table, you're going to the upper left hand corner of At Item and you're going to add a table since what they gave us was a table, and we're just gonna go ahead and input all of those points. So we had one for the one decade Ah, 1919 10 and so on. So forth a 48.6 was the average life expectancy. Use your tab button to help you navigate from place to place on these tables, and then we'll go from there and this doesn't being a little bit tedious. And you do have to be very careful when you input information, because if you're off ah, by a number or digit, they could definitely affect your equation of the line sometimes. And so you do not want that to happen. So once this gets done, though, everything else seems to be a little bit better with everything. Last one, it's a 6.5 is the average. Okay? So with that being said, we have this graph right here and you noticed we don't see anything. Um, and that was because all of these y values are definitely bigger than six. So you're going to go to this little tool symbol graph settings, and this very any cause you're gonna just your X axis motion needed. So we're honestly, we need to see probably zero toe 15 will say to so you can get a bigger picture and on the Y axis needs to go all the way from zero to well, say, 80 for good measure. And there we have everything we need to see. So there is a curb s. So it is strong positive, but it is curved. So we can't, um, do this without re expression. So I'm going to go ahead and do the ladder of powers. And it turns out that if I were to go through and try and see what's gonna take, what's it going to take to get this to be straighter? Um, we could always try the log log method. Um, when in doubt. So we're gonna do the log of everything, So I'm going to do the log of one. And so I don't support. So you wanna go ahead and get that typed up in there? So you just select the number that you want. I've been the word love, and then you just repeat that process doesn tedious. But it was over, and in theory we will see how much things straight. Now they could do the natural log See with that does as well. And I mean, you might get different results than somebody else, but they won't be necessarily incorrect as long as you are straightening your curb out. That is the whole point of free expression. So its not one size fits all it can be. A few answers are still going to be valid. So we're doing that look long method. I'm sorry. And then what Will dio after this is we're going to input, like ALS of exposed be with in terms of this equation. So real quick. Everything got zoomed in, right? So we gotta cut a zoom in just so we could kind of see what's happening. And if you zoom in, it's definitely lost some of that curve of straighten itself out for good measure. We're gonna type in white girls and expose people. We've got to do it in terms of this desk, most so x one and why one So I'm gonna have y wanted this type wide one. And then the shift and in the upper left hand corner of the squiggly line is called the tilde. That's kind of serving as our equal sign when referencing at this with best most. And then you got em x one plus vite, and that creates our line. And it is pretty close to being 100% If you look at our r squared, it's really close to one. It's 99.3% approximately. And here's our parameters. This is our slope, and then this is our Y intercept. So I'm gonna go ahead and using this information and so I can write it out kind of nicely. Go ahead and write it out over here. Um, we're gonna go ahead and write out our model for our final answer for Number 25 is this model. The log of the life expectancy is equal to approximately one 0.68 as our inner set weiners up and it's 0.187 approximately times the log of the decade number. All right, and it's probably good also know that the R squared was approximately 99% which is very good. It's close to one. So it's taking 99% of the variability of what we are seeing in the graph