Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

A personal watercraft $(\mathrm{PWC})$ is a vessel propelled by water jets, designed to be operated by a person sitting, standing, or kneeling on the vessel. In the early 1970 $\mathrm{s}$ , Kawasaki Motors Corp. U.S.A. introduced the JET SKI "watercraft, the first commercially successful PWC. Today, jet ski is commonly used as a generic term for personal watercraft. The following data show the weight (rounded to the nearest 10 lbs.) and the price (rounded to the nearest $\$ 50$ ) for 10 three-seater personal watercraft (Jetski News website, $2006 ) .$a. Develop a scatter diagram for these data with weight as the independent variable.b. What does the scatter diagram developed in part (a) indicate about the relationship between weight and price?c. Use the least squares method to develop the estimated regression equation.d. Predict the price for a three-seater $\mathrm{PWC}$ with a weight of 750 pounds.e. The Honda AquaTrax $\mathrm{F}-12$ weighs 750 pounds and has a price of $\$ 9500 .$ Shouldn't the predicted price you developed in part (d) for a PWC with a weight of 750 pounds also be $\$ 9500 ?$f. The Kawasaki $S X-R 800$ Jetski has a seating capacity of one and weighs 350 poundd Do you think the estimated regression equation developed in part (c) should be use to predict the price for this model?

a. See scatter diagramb. Positive linear relationshipc. $\hat{y}=-8129.44+22.444 x$d. $\$ 8703.56$e. $\mathrm{No}$f. $\mathrm{No}$

Intro Stats / AP Statistics

Chapter 12

Simple Linear Regression

Linear Regression and Correlation

Missouri State University

Piedmont College

Oregon State University

Idaho State University

Lectures

0:00

02:37

Waterskiing and wakeboardi…

13:16

The Ethan Allen tour boat …

03:17

Okay, Here's a solution to number 12 and I kind of gave away part of the answer right there, but we have a data set um and we're supposed to develop a scatter diagram for these data, This is with the jet skis. So I'm going to use this on the calculator because it's a lot neater and a lot quicker. And if you go to stat and then edit you can type in your data value. So L one is the weight of the jet ski and then L two is the price of the jet ski. Okay so whenever you do that you can turn on your scatter plot. So go to second Y equals and just make sure one of those on. I just turned the first one on and the type is this scatter plot here and then X. List is L one wireless dealt to. You may want to go back into Y equals and just make sure this is all cleared. So then you should be able to press graph and if you don't see that that's fine, you probably don't. Um you would just go to zoom and then this ninth option here going to nine zoom statin, you should see that. Okay so that's the scatter plot, it looks something like so and then the second part, what does the scatter diagram developed in part a indicated about the relationship of the weight and price. Well these seem to be a fairly strong, at least moderately strong positive correlations. Let's go and write that down the positive correlation. So moderately strong and positive correlation. Okay so as the independent variable is increasing. So is the dependent variable? Okay so that's part B. Now use the least squares method to get a regression equation an estimated regression equation. So again we're going to go back to the calculator here gets a lot quicker. You go to Calcutta and we're gonna go now you can either go to four or eight. The way this book is set up they like the Y intercept first. So it's a plus bx. The X. list is L. one. The wire list is L. two and we go ahead and calculate and this is what we get. So that's what you saw in the beginning. Now it has an R squared value about 0.49 which is okay, you know, decently strong. And there you're you see you're ours .7. But this is what we need this regression line here. So negative 8129 0.44 plus 22 +444 X. Okay so that's what I wrote down there. So this is this would be part B. This is part to see some kind of going backwards a little bit. But there's your regression line, your estimated regression line Y hat equals negative 81 29 44 plus 22 444 X. Okay so then part D says predict the price for a three cedar pwc um With the weight of £750. So that's your X value. Remember the X. Value was your independent variable is the weight. So part D. We're just predicting what it would cost Um if it weighed 750 lb so plus 22.444 Times 750. And here we again can go into the calculator. So negative negative 81 2944 Plus 22.444 times 7 50. And that gives us 87 03 56. Okay so that's predicted price is 87 03.56. Okay. Okay that looks good. And then part eases the Honda Awkward Tracks F £150 and has a price of 9 90 500 shouldn't the predicted price you developed in part D for PWc with the weight of 7 £50 also be 950. No the predicted prices not the exact so no predicted is not the actual. Okay so the actual is the actual observed data value. This is just your prediction line. That's why we have y hat and as you can see if we go back to this regression line whoops you know there's Some deviation here. Like we were only 50% of the variation that can be explained by the weight of the jet ski. So it's not an exact science here just because something way £750 doesn't mean it's a guarantee that it's going away. Um That it's going to cost $8,703 in this case. It doesn't, so the predicted is not the actual and then part F The Kawasaki SX are 800 jet ski has a seating capacity of one And weighs 350 lb. So this is a completely different jet ski. So it's asking do you think the estimated regression equation developed in partC should be used to predict the price? And the answer here is no. The £350 is outside the X. Values. Okay so you can extrapolate the data a little bit but that's pretty far out. You know the smallest one was like 720 or something? That's pretty far man that's less than half of the smallest ones. That's pretty far out there. You really can't extrapolate. And it's an entirely different model to one cedar as opposed to the three cedar. So no you can't use this regression line for the 350 lber

View More Answers From This Book

Find Another Textbook

01:16

Annual salary plus bonus data for chief executive officers are presented in …

03:58

Let $A$ denote the percentage of one constituent in a randomly selected rock…

06:02

Consider a regression study involving a dependent variable $y,$ a quantitati…

01:08

A sample of parts provided the following contingency table data on part qual…

10:07

Visa Card USA studied bow frequently consumers of various age groups use pla…

04:28

In exercise $5,$ the owner of Showtime Movie Theaters, Inc. used multiple re…

A lending institution supplied the following data on loan approvals by four …

08:13

Suppose the amount of rainfall in one region during a particular month has a…

06:21

In early $2009,$ the economy was experiencing a recession. But how was the r…

07:57

A 2003 New York Times/CBSNews poll sampled 523 adults who were planning a va…