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Use XL Stat Regression with prediction:As part of a research program for a new cholesterol drug, apharmaceutical company would like to investigate the relationshipb...

Question

Use XL Stat Regression with prediction:As part of a research program for a new cholesterol drug, apharmaceutical company would like to investigate the relationshipbetween the ages and LDL (low-density lipoprotein) cholesterol ofmen. The accompanying data set shows the ages and LDL cholesterollevels of seven randomly selected men. Construct a 95% predictioninterval to estimate the LDL cholesterol level of a 32-year-oldman. Determine the upper and lower limits of the PREDICTIONinterval.AgeCholeste

Use XL Stat Regression with prediction: As part of a research program for a new cholesterol drug, a pharmaceutical company would like to investigate the relationship between the ages and LDL (low-density lipoprotein) cholesterol of men. The accompanying data set shows the ages and LDL cholesterol levels of seven randomly selected men. Construct a 95% prediction interval to estimate the LDL cholesterol level of a 32-year-old man. Determine the upper and lower limits of the PREDICTION interval. Age Cholesterol 23 140 38 179 25 157 31 196 42 155 30 145 40 205 UPL= LPL= (Round to one decimal place as needed.)



Answers

Does a person’s cholesterol level tend to change with age? Data collected from 1406 adults aged 45 to 62 produced the regression analysis shown. Assuming that the data satisfy the conditions for inference, examine the association between age and cholesterol level.

Dependent variable is: Chol
s = 46.16

\begin{array}{lll}{\text { Variable }} & {\text { Coefficient }} & {\text { SE(Coeff) }} & {\text { t-ratio }} & {\text { P-value }} \\ {\text { Intercept }} & {194.232} & {13.55} & {14.3} & {\leq 0.0001} \\ {\text { Age }} & {0.771639} & {0.2574} & {3.00} & {0.0027}\end{array}$

a) State the appropriate hypothesis for the slope.
b) Test your hypothesis and state your conclusion in the proper context.

The following is a solution video. It's number 29 and this looks at dr I'm gonna butcher this name. But the doctor um Asswipe Muskie's 20-29 year old patients, they're mean serum HDL cholesterol level And were given a data set. Now it's hypothesized that the mean is 47 that from previous studies the population standard deviation is 12.5. So we're assuming actually in fact it even says we're assuming normality here so we can use the z interval because we know the population standard deviation. We actually know what sigma is. Whenever you know what sigma is. You can use the Z interval. So the first part is to find the point estimate. Now I use technology to do that but you can use the formula if you so wish. But if you have a T. I, 84 83 you go to stat and then edit and you can see here the data values here. So I don't know if you It's all those but there's there should be 15 data values I think they were 15. Which still check real quick 15 data values. And if you go to stat again and then air over the couch and then you click on one of our stats. Now I put my list in L. One so I'm gonna keep that as L. One And then you press calculate and that X. Bar that's your point estimate for the main. So 48.33 three repeating I guess 48 3rd. So 48 we'll just say 48.3 is the point estimate. Okay so now we gotta find the 95% confidence intervals. So again I'm going to turn to the calculator because it's a lot quicker this way. But you can certainly use the formula and we go to tests and it's the seventh option here. Like I said we can use the Z interval whenever we know what sigma is. Um And we are working in data here so we're going to keep the data up here highlighted for input. So it's not summary stats, it's actual data set. The sigma, the standard deviation was 12.5. The list was L one at least. Mine was I put it in a one frequency should be one and then the sea level, the confidence level remember was 10.95 or 95%. And then we calculate in this top band here that's our confidence and also 42.008 All the way up to 54.659. Let's go and write that down and then we'll interpret it so 42 .008 two. points 659 Okay? And then as for the interpretation will say we can be 95% confident that the mean serum H. D. L. Cholesterol for all Dr I'm not going to try to press this. Yeah I can't even feel it right. I don't know who it is but someone smart on me. So dr owes 2022 29 year old patients is between 42.008. And you can round differently if you want. I'm not gonna go in and around And 54.659. I'm not 100% sure on the units here. I'll just put HDL. Okay and then the part c um It says is that different from the hypothesized value of 47? And it's not because, so no because 47 lies within that range. In fact it's almost exactly right. So it's it's pretty darn close. I mean it's right in the middle of that confidence interval, but as long as it's contained in that confidence interval, we can say that, you know, there is no difference from our confidence interval from the previous study, so No, Because new equals 47 is contained. And the interval. Okay. And then part D. A says, what would you do to be more precise? The best thing, there are a few things you can do at least to make it narrower, the confidence that were narrow. So you can kind of like Shorten that up. So maybe instead of between 42 and 54, if you want to get it to maybe like, you know, 44 and 52 or something if you wanted to have a narrower interval. Um the best thing to do is just increase your sample size to be more precise. Ah I would say this is kind of a professional but I would say I would increase the sample size. The n. That's probably the best thing you can do if possible. Now, if it's not possible. The other thing you can do um If you wanted to narrow that confidence interval down, you could say or decrease confidence level. Now this is where it gets a little bit hazy because you know, what do we mean by more precise? Do we need mean like we want to be as exact as possible? Because if that's the case then we would want to increase the confidence interval confidence level, but that's going to make it wider. So I don't know if that's, you know, 100% precise. If you wanted to make it a narrower interval, which I think that's what they mean by being more precise, then you would need to decrease that confidence that. But to make it, you know the best answer here really, you need to increase your sample size. If you want to be more precise, that's the best thing to do.

All right guys, let's get started on problem number 29 here and here we go. So we're talking about agent cholesterol and so it wants us to have a job as the explanatory variable. So agent X. While um cholesterol is why. Okay, so let's input our ages here in our google sheet and I know it takes a second to do this. However it is a great way. Get the rest of the data down, definitely worth the time upfront. It'll save you time in the long run. And so those are our ages. And now let's stick a cholesterol in there. Almost just got to keep going. Yeah. Yeah okay and there it is. Okay so there are ages are XR cholesterol is why? And now we need to do our scatter plot. So let's go and highlight all the data that we just typed in um chart and there goes, cool, okay, so what I just did, so let's see what I did there. So go insert highly data insert charts and I'm not gonna click it again. But yeah, there it is. So there is all the data that I need. It's right there. Very nice. Okay, the next order of business is to get the linear correlation coefficient. Do that down here. Oh, actually, almost forgot the last part of part a the type of relation exists. Uh well, it asked me for a type of relationship and I'm actually not sure. I don't know if I see one here. That's interesting. Let's let's see what the linear correlation coefficient tells us, because I'm looking at the graph and I don't really see much of a relationship. Maybe I'm wrong. So, but let's go ahead and ask the linear correlation coefficients, see what it says. So how do I do that in a google sheet. First off you open a new cell. I just did this to label my work and then I'm going to open a new cell and then I'm going to type in C. O R. E. L. That's short for correlation open parentheses. And then the first thing you do is gonna highlight all your X values comma highlight all your Y values. Close parentheses enter And that's the number we get negative 0.16. For if I round. Okay so comment on the type. Okay so looking at this it seems like my initial suspicion of not seeing much of a correlation was right. And here's why I don't see much of a correlation on the scatter plot. Also when you look at that -0.16 that is much closer to zero than it is to negative one. Which means we are unable to find a relationship between age and HDL cholesterol.

Problem number CBC Fine. Ah, from the givens. Were you? We have Ah, that's Ah, it's Ah, Water one is equipped for 68 17 Ah, explore toe is equal to 54.1 s. One is equal to There's being foreign three. It's too. It's important. Tool. Ah, 11.93 in one week with proof and include his efforts to 40. Okay. Ah, remember, I processes. So it's note here we have I mean one and minus me two is equal to 10. And the alternative five buses you bet me and one minus mean two is bigger than Ben. It reminded the ah test Ah, statistics so that even where we know that he is equal to its broad one. So it's a 4 to 68.7 minus exports, which is 54.1 over is the square root off. This one is squared over in one buses to spread over in. And so is it mine. Eight. Me too. Uh, let's remind that the reason Freedom, we know that the reason created with the minimum between the three bodies in one minus one, which is a marine, this one and in. Poor miners want you, Swifty more in this world. So but the meeting with Bill you would be at 30. The B value is the program TiVo killing the very off the test and that he justice to this. We're a value more into the tree and be very the number in the kind of title off evil being containing with the value in through off the green of freedom at 13. Eso you with being the meal freedom for 13 And you know the your table be We know that the value air lies between ah, well 0.15 and open accordingly. We know that that value is bigger than the significance level. So we fail to reject Reinold high processes. That's why we, um can see the There is no self questions. Evidence your events through support. We're clean. That we mean ah, crystal crystal reduction. Well, and then you drunk no more, then in really grands there. Ah, here. It's your lighter. And this is the answer for a question. 56 question A If we look toe point b. So here, um and we reject in appoint a the and no hypotheses Each note and and we know that type one error is to reject it on a high positions when the null hypothesis is true And time to error is to fail to reject the null hypothesis, win heaven on high possibilities fools. So here we feel ah to Regeneron high passes in part 65 8 So, uh, the errors which could be maids is I to to enter is feel good, Jack. Email hypothesis is Korean and general hypotheses is

In this question, it is given that well equals Thank you went swimming. But 0.691 Next one. Thus, 219 xto, my aunts 299 60 Fire blazing. Knicks won with 55 next to with 194 and 60 Way 142. We get boy equal 97.7 26 91 But the blood boy you see if I but 219. But the Blade boy 194 minus 299 But the break bar 100 that you? 100 49 point or approximately 100. Thank you.


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