Problem

According to Advertising Age's annual salary revi…

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Problem 9 Easy Difficulty

To avoid extra checked-bag fees, airline travelers often pack as much as they can into their suitcase. Finding a rolling suitcase that is durable, has good capacity, and is easy to pull can be difficult. The following table shows the results of tests conducted by Consumer Reports for 10 rolling suitcases; higher scores indicate better overall test result (Consumer Reports website, October 2008 ).
a. Develop a scatter diagram with price as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Use the least squares method to develop the estimated regression equation.
d. Provide an interpretation for the slope of the estimated regression equation.
e. The Eagle Creek Hovercraft suitcase has a price of $\$ 225 .$ Predict the score for this suitcase using the estimated regression equation developed in part (c).

Answer

a. See scatter diagram
b. Positive linear relationship
c. $\hat{y}=52.31+0.056 x$
d. The score increases, on average, by 0.056 per dollar.
e. 64.91

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Intro Stats / AP Statistics

Essentials of Modern Business Statistics

Chapter 12

Simple Linear Regression

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Video Transcript

All right, now, we're supposed to do the same thing. Only we're supposed to use cost per ounce. Um, so I'm gonna delete this whole table and equals cost divided by ounce. Drag it down. Now, I'm going to just go ahead and insert. You know what? Never mind. I'm gonna do this. And then this. I held down the control key. Um, so I highlighted everything. Hold down the control key and then highlight everything again. Insert chart. There we go. Um, so this is cost per ounce on the Y axis. I'm going, Teoh, insert a trend line. It looks even worse than the previous one. But let's go ahead and display the R squared value and use the equation. So are our value is going to be the square root of 0.638 So there's whips less correlation here. Um, and then we got predictions here, but I don't know if we're gonna have to do them again. So who's going to delete that? Let's go ahead and answer the questions. Hey. All right. Completed the table B drew the scatter plot. Good. There is a relationship, but it's not linear. Uh, and there is a relationship because as the size gets bigger, the cost per ounce gets smaller. So there is a relationship. Um, I calculated the line and put it in equation form. We figured out the court correlation coefficient. It's significant, but it's not as significant as the previous problems. And we're supposed to calculate 40 ounce, 90 aunts and 300 out. So back to here. Just put in my equation equals negative 2.77 times 10 to the negative four Power I'm Axe, which would be 40 plus zero point 179 So it's about 17 cents per ounce. And let's see if that makes sense. 40. Yet it's about 17 90 is going to be about 15 cents per ounce. That's not right. 90 is 15 cents. Prince 300 would be about 10 cents per rounds. That makes sense. But why? What's wrong with 90? Am I missing something here? How could 300 B right? 300 is 10 cents? It's, um, Valerie. 40 Looks to be around 17 cents. That's right. That makes sense. 90 is here. It's around 15 cents. Okay, they are correct. So again, I'm using two methods and using calculating with the equation. And I'm just looking at the graph Letter H Does it appear that this is the best line? Absolutely not. Um, let me show you what would be better. Um, let's let's look at exponential. Ah, slightly better. Um, but I'm still not thrilled about it. However, that might be the best one. Because when we look at polynomial, um, it's gonna try to create a parabola, which is gonna come right back up again. Um, let's look at log rhythmic. Oh, that's that. Seems better like that. Um What about what about polynomial? Jeez, that's not good about third degree polynomial. Oh, my goodness is not good about fourth degree. That's crazy. Okay, so polynomial did not work. So I'm thinking exponential or log arrhythmic and look at that equation up there for exponential and longer rhythmic here. CEO says Ln that's natural log. And so I don't like what's happening here at the end with the log arrhythmic. So I think I'm not sure which one's better. None of them are great. Okay, Was keep going. Are there any out liars? Um, yeah, I think we were linear. Um, let's calculate the standard deviation Inter deviation of this is that much so. Two standard deviations, um, from the prediction. So I'm saying either that 1st 1 or this 3rd 1 are out. Liars. Let's let's try the 1st 1 Um, it predicts that 16 should be 17.4 cents. But if we take the 25 cents plus two standard deviations, so that's still within two standard deviations. This is over here. And let's check if let's check. If, um, that 1 64 ounces is within two. Standard deviations to the prediction would be this. So this plus actually minus two standard deviations gives you that. So they're all within two standard deviations. So no, there are no out liars. Um, letter J is it valid for 300 ounces? Um, not really. Because this line does not fit the curve, so no. Okay, what's the slope mean? So what it means is that if you buy a bigger size drink than for every ounce, it is bigger, you pay this much less per ounce. Um, so 2.77 times 10 to the negative. Fourth power. 0.0 0 to 77 Um, if I convert that to a percent. I could just take two zeros off. So you're gonna end up paying three hundreds of a percent less per rounds for every ounce increase in the size of the beverage.

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