justify-the-conclusion-made-about-power-regression-on-page-299

Question

Justify the conclusion made about power regression on page
$299 .$

Amrita Bhasin · Accepted Answer

okay for part a of this question, we&#x27;re gonna be using a graft to graft this function. We can notice that it will look like us. Okay. And then use the regression model on your calculator to obtain why equals 8.9 to 35 Axe to the negative. 0.11228 to five. So this is part A, and we got this using the calculator. Okay, part be, we&#x27;re gonna be using this. The model we just found to predict the value for X equals 9.2. So 8.9 to 35 times 9.2 to the negative. 0.1128 three fought to 3 8 to 5 equals approximately 6.3 onto part. See, we see that for each point, X comma y you can take the natural log to find the corresponding point. So I&#x27;m gonna make a chart over here. A little table, naturally. Axe, unnatural of Of why? Okay. 0.69 Approximately 2.1 approximately. And then we have one point 09 and 1.97 1.557 0.92 1.8 sex. You can see that we could make a scatter part of the data and we&#x27;ll notice that they seem toe look like they&#x27;re in a line. 34 If I were to connect these draw dotted line to show, you could see how the points look like their end a line approximately, which is what we&#x27;re ending. Toe obtain. Okay, now we&#x27;re onto Part D. That&#x27;s a four part problem. We&#x27;re using a linear regression model based on the data points that we got in part. See? And we can obtain a graph that looks something like Thus, we have four points. One, 223 four And the model. You should obtain your calculation. Be natural. Log of why equals negatives. Your 0.113121 natural of ax plus 2.9 131 This should be the linear regression model that we obtained

Heather Zimmers · Answer

in this problem. We&#x27;re using regression, and we&#x27;re going to do almost the entire problem on the graphing calculator. So the first thing we want to do is grab a calculator and then go to stat and then go to edit. And we&#x27;re going to type R X values into List one and R Y values into list, too. Now that we have all the data in the lists, our job is to find the power regression model. So we go to stat and then over to calculate and then go down until you find power regression. It&#x27;s just under exponential regression. If you&#x27;re using the T I a graphing calculator, press enter and then we&#x27;re using list. One we&#x27;re using was, too. You don&#x27;t need to put anything in frequency list. And here in store regression equation, I&#x27;m going to store my equation in my y equals menu. And so if I go to Alfa Trace, that&#x27;s a shortcut to find the Y one. Then select why one that tells the calculator where to store the equation and then we press enter and this is our regression equation. Now if we go to y equals well, see, that was pasted in. And just for the sake of writing down the answer, we can round those numbers a little bit and write that down. So that model was about why equals 2.75 x to the fifth in the next part of the problem. We&#x27;re making a prediction. So if X is 7.1, let&#x27;s find it&#x27;s why Value. So I&#x27;m going to do this graphically, and I already have the function in y equals. And now I&#x27;m going to go to Zoom Stat, which is Zoom nine, because it creates a good window for a statistics graph. And I&#x27;m interested in what&#x27;s happening when X is 7.1. So if I press trace and type in 7.1, well, I get a value that&#x27;s off my screen. Apparently. So now I need to fiddle with that and see what&#x27;s going on. Okay, so the problem is that to you, zoom stat, we need to turn on our scatter plot, so I&#x27;m going to go up to plot one. Turn it on. Now the calculator knows to you zoom stat with list one endless too Zoom nine and there&#x27;s our power curve. So now if we press trace and make sure the cursor is on the curve and we type in 7.1. We can see the Y value there at the bottom of the screen. 49,616 0.3. All right, so we&#x27;ll write down this answer when X is 7.1. Why is approximately 16 49,616 160.3. Now we&#x27;re on to part. See, now we&#x27;re converting our data from X and Y two natural log of X natural log of y. So we&#x27;re going back to the calculator back to stat back to edit and then change the value. So instead of four, it&#x27;s going to be natural law before you can just type that right in instead of 6.5 natural log, 6.5 et cetera. Keep doing that for all of the values. All right, so once those were all done, we have our new lists, and our goal is to show the scatter plot so we can go back to y equals plot. One is turned on already. So that&#x27;s our scatter plot. I&#x27;m going to remove the y equals so that curve doesn&#x27;t graph anymore. so we&#x27;ll just clear that. And now back to zoom and back to Zoom nine for zoom stat. So what we&#x27;ve done is your natural logs to convert this from a power curve into a line. So here&#x27;s our scatter plot. Next, What we want for Part D is the linear regression model. So the regression equation that fits this line So we go back to stat over to Cal HQ, and then we choose linear Regression, which is number four. Press enter. We don&#x27;t need to store this one because it doesn&#x27;t look like a rest too graphic or predict from it. And here&#x27;s what we get. Why equals approximately five X plus one so well, jot that down. Okay, so our linear regression model was y equals five x plus one. And finally, for part E. We&#x27;re doing sort of, ah, verification that this power model does relate to the linear regression model. And if you recall from your calculator screen when it found a linear regression model, it called the slope be are a excuse me. It called the Slope A and it called the Y intercept to be because the model was of the form y equals X plus be. And so what we&#x27;re doing is we&#x27;re taking our value of a five and substituting it in there. And we&#x27;re taking our value of B one and substituting it in there and showing that we really do get the power model that we said we were going to get in the beginning. So if I do that, I have y equals e to the first times X to the fifth. Now each of the first is right around 2.7. And keep in mind that it&#x27;s not truly exactly a one here. That was around ID number. So this is not truly e to the first. It&#x27;s e to the something close to one, so it may be a little bit more than 2.7, and then we have X to the fifth. So how does that compare to the power model? We got for part? A pretty much the same thing

Brandon Cleary · Answer

This is problem. Number two, we are test with giving all of our assumptions for taking a regression of a set of data. The first assumption of our three is that the sample is random. So this means that out of a full population, we have taken an arbitrary set of data and there is no favouring towards certain characteristics. For number two we have that any specific value of X. The value of why must be normally distributed about the regression line. So we have normally distributed data. This essentially means that we have very few points that are outliers are very distant from our line, and most of our points will lie somewhere very close to our line. Our third and final assumption is that the standard deviation. So sigma of each dependent variable of X must be the same for each value. So the standard deviation is consistent over ex head. So this essentially means that the standard deviation does not change depending on which independent variable you use.

Arwa Ali · Answer

Normally, the assumption the values of the oil variable are normally distributed for any specific value off the independent Valium, equal variance or something. The Reince is four the a variable for the same for each value of the independent value. Linearity assumption. There is a senior relationship between the dependent variable and the independent Variable than Monty. Cool. Linearity Assumption. The independent variables are not pretty. Thank you.

Jeremiah Mbaria · Answer

in this problem, we shall be stating the hypotheses in their Nova test. The non hypothesis hitch not is Mu one equals Mewtwo equals all the way until we get to the last. Me, you and this simply means that all that means are equal. And that gives us the knowledge. But this is there now are the alternative hippo This is each one. Is that at least one mean is different from the others.

Problem

In Exercises $73-78,$ solve the equation or inequ…

Problem 72 Easy Difficulty

Justify the conclusion made about power regression on page
$299 .$

Answer

The conclusion model about power regression is $\left[y=c\left(x^{a}\right)\right.$
Where $c=e^{b}$ the power regression model for the data $(x, y)$

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Franklin D. Demana,Bert K. Waits,Gregory D. Foley,Daniel Kennedy

Precalculus: Graphical, Numerical, Algebraic

Catherine R.

Anna Marie V.

Alayna H.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

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The conclusion model about power regression is $\left[y=c\left(x^{a}\right)\right.$Where $c=e^{b}$ the power regression model for the data $(x, y)$

Precalculus: Graphical, Numerical, Algebraic

Catherine R.

Anna Marie V.

Alayna H.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

Franklin D. Demana,Bert K. Waits,Gregory D. Foley,Daniel KennedyPrecalculus: Graphical, Numerical, Algebraic

Catherine R.

Anna Marie V.

Alayna H.

Caleb E.

The conclusion model about power regression is $\left[y=c\left(x^{a}\right)\right.$
Where $c=e^{b}$ the power regression model for the data $(x, y)$

Franklin D. Demana,Bert K. Waits,Gregory D. Foley,Daniel Kennedy

Precalculus: Graphical, Numerical, Algebraic