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Timber yield is approximately equal to the volume of a tree, however, this value is difficult to measure without first cutting the tree down. Instead, other variables, such as height and diameter, may be used to predict a tree's volume and yield. Researchers wanting to understand the relationship between these variables for black cherry trees collected data from 31 such trees in the Allegheny National Forest, Pennsylvania. Height is measured in feet, diameter in inches (at 54 inches above ground), and volume in cubic feet.$$\begin{array}{rrrrr}\hline & \text { Estimate } & \text { Std. Error } & \text { t value } & \operatorname{Pr}(>|\mathrm{t}|) \\\hline \text { (Intercept) } & -57.99 & 8.64 & -6.71 & 0.00 \\\text { height } & 0.34 & 0.13 & 2.61 & 0.01 \\\text { diameter } & 4.71 & 0.26 & 17.82 & 0.00 \\\hline\end{array}$$(a) Calculate a $95 \%$ confidence interval for the coefficient of height, and interpret it in the context of the data.(b) One tree in this sample is 79 feet tall, has a diameter of 11.3 inches, and is 24.2 cubic feet in volume. Determine if the model overestimates or underestimates the volume of this tree, and by how much.

Intro Stats / AP Statistics

Chapter 6

Multiple and logistic regression

Linear Regression and Correlation

Missouri State University

Piedmont College

Cairn University

University of St. Thomas

Lectures

0:00

09:41

Imagine that you own a gro…

02:09

Determining tree biomass I…

01:52

It is difficult to measure…

05:45

The growth of a red oak tr…

03:11

The annual yield per lemon…

03:12

The annual yield per orang…

07:20

The value of a log is base…

02:53

Timber Yield The yield $V$…

06:07

03:43

07:36

Eastern Hemlock Ring shake…

03:57

Growth Rate The growth rat…

A tall tree is growing acr…

02:19

The yield $ V $ (in mill…

01:35

Forestry. The total wood v…

02:36

Carbon dioxide and tree gr…

00:49

An appropriate null hypoth…

09:10

The price along the West C…

01:47

The images of trees in Fig…

00:28

The estimated yield $Y$ of…

Okay, a question on another application off B for ah, for a linear equation. And this lips the ah, you or, you know, the off oranges. Okay, uh, as as a function off the number of priests plant. Okay, So experience apparently started. If you had let's say they're people Number of police and and the yes, so But one thing we know is that there's been Uranus. If you plant 100 please, they eat well. A tree is about 200 40 botanists. The authors are given that when you increase the number of please as aciego 100 plus the the number of please actually diminishes by 20 it becomes like 2 20 For every a listen tree the one or one becomes 2 20 There's something or something of that order. So in other words, we have a linear canopy. We have a linear or neck the relationship that decreasing off. There's increases the streets planted and that was a E. As the number of responded increase that you'll actually dropped. It could be for for competitive reasons. Because the trees will be competing for the same resource is the water with the fertilizer and but if those things are constrained, if you increase number, please completed so the poetry would would they expected actually decline? Not not. Always increase. Okay, so that's that's the kind of relationship be behavior this pose. Specifically, we're told that in other words, we're told that ah, 100 trees. So in other words, it will let when the place is 100 the US to a party. So that's one of the point, and we also given back the number off Orange is actually decreases by about 20 for every additional 300 other words, the Delta White or Delta X in an elevator produce 100 to 40 is one of the coordinates and then ah, training, in other words, of slope results given it's actually negative 20 like so as best that delta y over then the X increase the number please, for one you know, actually decreases by 20. So we have a negative 20. And so now we know this on this so we can play the expression of the line, right? So if you know, the question of the Linus was right again is why equals mx plus me where y is actually the number off the yield and excess the number of police. Okay, so let's let's plug in the and we know him, Emmis. Negative. 20. That would be needed. Us find B and we'll just plug in the values the known values your services to 40. Well, negative. 20 times. 100. Must be. Why? And so be hiss then learning 40. Well, 1000. But did he do for you? Therefore governing equation is the equals. Make it 20 times the number of that's less used to. Ah, feed off the number, please. Um, if it please less 22 foot. Okay. All right. So that's that's this part. Now you todo they kind of the 0.100. Okay, now this is just let your sister government eHarmony tree should be planted to play in the field of 400 oldest poetry. Okay, so how maney, please, would you planted toe pain? I eat a 400 on just poetry. So, in the delivery of the question, if the yield has to be 400 olders tree or dusty Mr Metal plugging in the question, but it's a 400 equals negative 20 times t last 20 to 40 or that three range and 20 times equals 2 to 40 minus 400. US in 40. So a P then if he would be delighted by 20 for the vittles and that look 92 okay, so makes sense, Right? No beginning either 400. If this is this values to 40 now, of course, this is 2 40 My value to get a value of 400 I wonder would be it on here. And then the X value would actually decrease. So who would lessen? Has to be left numbered to make a guess. But we came of it. I indeed to 400. Good answer. The final answer TS 92. Number of police pleasure has been 92 to get 400 on in the sport. All right, there was question Buk We'll be just answered. Question being Barbie. This is a that be and not want to see. Our question is that the group contains 95 please, what you can expect from each street. So in other words, if he was 95 what is they eat? And you know what you do Look in this, like in the value into our mass recreation here, like in the value 95 p to get the y equals first, minus 20 times. Okay. Plus, he was 20 to 40. I'm just relating the the master equation here. I want to plug in 95. So in life is identify with in this 20 time did you five last 20 to 40? It comes. That's 1900 40. And so the deal is? Yeah, but he answered the 40 20 minutes 19 that we got from 95. Please. The industry for so for 95. So 19 years between 1900 x. So it's somewhere in between this point at this point. So And the why also has to be corresponding between 2 40 and polar. That should in 40. That's good. So this six way this point here is for the 95 3 forties, Another in a point. Okay, fine. Lots of that little girl

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