Download the App!

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

Automobile racing, high-performance driving schools, and driver education programs run by automobile clubs continue to grow in popularity. All these activities require the participant to wear a helmet that is certified by the Snell Memorial Foundation, a not-for-profit organization dedicated to research, education, testing, and development of helmet safety standards. Snell "SA" (Sports Application) rated professional helmets are designed for auto racing and provide extreme impact resistance and high fire protection. One of the key factors in selecting a helmet is weight, since lower weight helmets tend to place less stress on the neck. The following data show the weight and price for 18 SA helmets (SoloRacer website, April $20,2008$ ).a. Develop a scatter diagram with weight as the independent variable.b. Does there appear to be any relationship between these two variables?c. Develop the estimated regression equation that could be used to predict the price given the weight.d. Test for the significance of the relationship at the 05 level of significance.e. Did the estimated regression equation provide a good fit? Explain.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

a) Scatter Diagram:b) Yes, there appears to be relationship between the variables weight and price.c) $$ \begin{array}{l}{\begin{aligned} \overline{x} &=\frac{\sum x}{n} \\ &=\frac{1060}{18} \\ \overline{x} &=\frac{6748}{18} \\ \overline{y} &=\frac{6748}{18} \\ \overline{y} &=374.89 \end{aligned}}\end{array} $$d) $$\begin{array}{l}{\text { The standard deviation is }} \\ {\begin{aligned} s_{h} &=\frac{s}{\sqrt{\sum\left(x_{i}-\overline{x}\right)^{2}}} \\ &=\frac{91.81}{\sqrt{575.78}} \\ s_{h} &=3.8261 \end{aligned}}\end{array}$$e) The coefficient of determination is$r^{2}=\frac{S S R}{S S T}$$\quad=\frac{462761.1}{597625.8}$$r^{2}=[0.774]$

Intro Stats / AP Statistics

Chapter 12

Simple Linear Regression

Linear Regression and Correlation

Temple University

Oregon State University

University of St. Thomas

Lectures

0:00

Auto Racing Helmet. Automo…

17:13

The National Highway Traff…

00:58

Each year, the National Hi…

02:40

The National Occupant Prot…

Following is a solution for number 44 and we're looking at the weight of, I can't remember what it is helmets or something and then the price. And we're going to see if there's any sort of relationship here. And so first thing we're supposed to do is to make a scatter plot. So let's go to insert and I'm gonna do all this in Excel because that's what this lessons about. So insert and then scatter plot and there you see. It seems like it's a pretty nice relationship There go and double click. You can pretty this up as much as you want. Maybe go to light from 40 to 70 I guess. You know, you can see a little better there. Um You can even go to 45 if he really wanted to. So 45. All right. And you know, you can add titles and whatnot. So that's good enough. And you can even add a trend line linear. So that appears to be a pretty good fit. So that'll come up come in a little bit later. So that's the first thing you're gonna do. And then the second question or part B. Um Is this uh does there seem to be a relationship? So this is part a part a and part B. Yes relationship appears to be a negative relationship. So as the X. Independent variables, weight increases the price temp tends to decrease their So now we're going to do the regression lines. This part to see so get the actual equation here. Um And what we're gonna do is we're gonna go to data and then data analysis and we'll type in regression there and the Y input is the price. So I went from B two to B 19 and then the X. Input is from A 2-8 19. Now I went ahead and made a residual plot just to kind of look at it. But you don't have to because that's what we haven't actually learned that yet. But that kind of helps me. And so you see here the R Square is .77 which is pretty good. That's pretty high R squared. I mean you can You can explain 77.4% of the variation and why by the X. value. And here you see a residual plot so you don't want to see a pattern there which you'll learn about next lesson. So we don't see a pattern there. So this seems to be a pretty good fit. And the regression line is this coefficient here. So if we make this bigger, So coefficient so the intercept. So this will be part C. And we'll go and say y hat equals the intercept which is 20 4 4.38. I'm sorry it's minus so droll minus because it's negative. Right? So minus 28 .35 X. So that's a regression line using these coefficients. And so now we're looking at is this is there a significant relationship here and you can look at the P value is the best thing to look at is the f statistic with the f significance. And that's basically zero. So it's 1.48 times 10 to the negative six. So basically you're looking at a zero which means the p value is less than alpha. And you can also look at your p values here. They're also you know pretty much zero. So p value is less than an alpha. Which means we're gonna reject H. Not and whenever you reject H. Not the null hypothesis that there is not a relationship. So you're rejecting that. So that means therefore there is a relationship. Okay so that's part d. It's a simple test and kind of nice whenever you have a um computer to do all that work for you. So the last question is a good fit. Yes it is a good fit for reasons already explained. Um The R Square value is quite large, so 77.4% is pretty good. The residual plot appears that we have randomness. And the residuals are statistics here are significant. And the trend line does the regression line does seem to fit that data pretty well. So I think I think that's good for the excel stuff

View More Answers From This Book

Find Another Textbook

Numerade Educator

00:34

' 2 Which of the following statements proves that AC EF?LHAJ ~ …

01:25

'29.2 Qulz: Medians and AltitudesQuestlon 1 of 10Which best des…

03:29

"Complete the square to determine the answer another tutor answered thi…

02:39

'Some punch is made by mixing grape juice and bubbly water in a ratio o…

02:48

'4. SPSS output from the GSS 2014 is presented here, reporting responde…