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

The U.S. Department of Energy's Fuel Economy Guide provides fuel efficiency data forcars and trucks (U.S. Department of Energy website, February $22,2008 ) .$ A portion of thedata for 311 compact, midsize, and large cars follows. The column labeled Class identifiesthe size of the car: Compact, Midsize, or Large. The column labeled Displacement showsthe engine's displacement in liters. The column labeled Fuel Type shows whether the caruses premium (P) or regular (R) fuel, and the column labeled Hwy MPG shows the fuelefficiency rating for highway driving in terms of miles per gallon. The complete data setis contained in the file named FuelData.$\begin{array}{l}{\text { a. Develop an estimated regression equation that can be used to predict the fuel efficiency }} \\ {\text { for highway driving given the engine's displacement. Test for significance using } \alpha=.05}\end{array}$$\begin{array}{l}{\text { b. Consider the addition of the dummy variables ClassMidsize and ClassLarge. The }} \\ {\text { value of ClassMidsize is } 1 \text { if the car is a midsize car and } 0 \text { otherwise; the value of }} \\ {\text { ClassLarge is } 1 \text { if the car is a large car and } 0 \text { otherwise. Thus, for a compact car, }}\end{array}$he value of ClassMidsize and the value of ClassLarge is $0 .$ Develop the estimatedregression equation that can be used to predict the fuel efficiency for highwaydriving given the engine's displacement and the dummy variables ClassMidsizeand Classlarge.$\begin{array}{l}{\text { c. Use } \alpha=.05 \text { to determine whether the dummyvariables addedin part (b) are significant. }} \\ {\text { d. Consider the addition of the dummy variable FuelPremium, where the value of }}\end{array}$FuelPremium is 1 if the car uses premium fuel and 0 if the car uses regular fuel.Develop the estimated regression equation that can be used to predict the fuel effi-ciency for highway driving given the engine's displacement, the dummy variablesClass Midsize and Classlarge, and the dummy variable FuelPremium.$\begin{array}{l}{\text { e. For the estimated regression equation developed in part for overall signifi- }} \\ {\text { cance and individual significance using } \alpha=.05 .}\end{array}$

a) $\alpha=0.05$b) $\beta_{1}=1.66$c) 14.02d) $29.7624-1.63473 x_{1}+3.96336 x_{2}+1.64497 x_{3}-1.121 x_{4}$e) $-5.3636$

Intro Stats / AP Statistics

Chapter 13

Multiple Regression

Descriptive Statistics

Linear Regression and Correlation

Missouri State University

Piedmont College

Oregon State University

Idaho State University

Lectures

0:00

02:18

Car Fuel Efficiencies. The…

07:46

The U.S. Department of Ene…

So for this problem, what we're given is, and as our sample size, that's 3 11. We're going to let x one br displacement X two will be class. Mid size X three will be class Large x four will be fuel premium x five will be. Actually, it's not x five. Why is going to be fuel efficiency? And that's going to be calculated by a highway mpg. So now we have our regression equation, and we first have to determine the necessary sons. So you look at the sum of X I and that's 10 38. Then you look at the sum of X, I squared, and that's 3833.68 Then we look at the sum of why I and that's 80 36. And the sum of why I squared is 212,638 than the sum of X. I Y II gives us 2 25 432 7. So now we want to determine the slope of B um, and that's accomplished by B equals and times the sum of X y, minus the sum of X times the sum of why all over end times the sum of X squared minus the sum of acts square. This is going to end up giving us approximately negative 28825 So the mean is the sum of all the values divided by the number of values. So we're going to get that X mean is 3.3145 and the mean of why is 25 points 8392 The estimate of a of the intercept Alpha is going to be the average of wide decreased by the product of the estimate of the slope. So this is going to look like a is equal to the mean of Roy minus B times the medevacs, which is gonna give us 35.3933 Um, so we can replace Alpha or a with Alpha and be with beta. So now that's going to give us this value right here, which will now be 35 933 minus 2.8825 x one and then for part B, we will use. We can use excel to generate the multiple in your aggression model, and it will give us an output. Since this can't be done on Excel, Uh, we get a bunch of values, but if we put in the correct values will end up getting the correct output. So now we can move on to purchase E um, or actually, with part B, we can do part of us. So once you get the numbers in Excel, we see why hat is equal to be not. Plus B one x one plus b two, x two plus B three x three. Um, so we see that be not is going to equal 29 0074 b one is negative. 16581 B two is 4.4860 b three is 1.8190 and with that we end up getting as a result that are y is equal to 29. 0074 minus 1.6581 x one plus four point 44860 x two Move this for our last term, which is B three x three. That's gonna be plus one point 8190 x three. That's our final answer for beam and then foresee. We have our significance level Alpha. That's gonna be a 0.5 And the given claim is that b I or beta? I rather equals zero. So the null hypothesis states that even claim that the slope is zero. Um, So what we have now is that a church not equals. Uh, actually, h hot is given as b I equals zero and h A is given as b I. There's not equal zero. So the p values in this case we would end up getting abated. To corresponds to P equals zero, and beta three will correspond to p equaling zero point. Um, it's 1234 12345678 zeros 704 It's a very close to zero, but not quite. So if the P value is less than the significance than we will reject the null hypothesis hypothesis. So in this case, he is, um, less than zero and b two case, it's less than zero. So we reject the null hypothesis, which is h not. And in this case, um, it's less than zero is that we reject the significance is too Well, so you reject the null hypothesis again. Then, for part D, we do another excel generation of multiple linear regression model. Um, so we can't do anything with the sell side of things, but we have another one of these equations where it's be not, plus B one x one plus B two, x two plus B three, x three plus B four x four and then with all of our values what we end up getting as our estimated regression equation. It's going to be 29 7123 minus 1.6383 x one plus 3.9984 x two +16700 x three minus 1.585 x four In this case, the significance level. This is the last part. E. Alpha is going to equal 0.5 again. Um, and we and then all hypothesis we'll have data. One is equal to beta two, which equals beta three jiggles beta four, which is zero. And our H sub A is going to, um, ST that at least one of the FBI's is non zero. Besides, for some hi then the P values, uh, corresponding we want to look at, so we C p equals zero and P is less than zero. So we reject we reject h not because the P value is less than the significance. So I reject each nut are null hypothesis.

View More Answers From This Book

Find Another Textbook

11:23

The data from exercise 3 follow.$$\begin{array}{r}{x_{i} 2 \quad 6 \…

05:15

PC World rated four component characteristics for 10 ultraportable laptop co…

05:59

The following data are the monthly salaries $y$ and the grade point averages…

01:42

Refer to excercise $5,$ where the following data were used to investigate wh…

01:08

Barna Research Group collected data shoving church attendance by age group $…

07:09

Almost all U.S. light-rail systems use electric cars that run on tracks buil…

06:50

The data from exercise I follow.$$\frac{x_{i}|1 \quad 2 \quad 3 \qua…

17:53

Jupiter Media used a survey to determine how people use their free time. Wat…

01:10

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

01:59

In exercise $8,$ data on $x=$ temperature rating $\left(\mathrm{F}^{\circ}\r…