An engineer wanted to determine how the weight of a car affects gas mileage. He checks his theory by gathering data on a rat, a bat. Ford Focus 26 2,760 Saturn Ion 24 2,855 a. has a weight outside the range of the other cars' weights. Since model year 2004, CO 2 emissions have decreased 25%, or 114 g/mi, and fuel economy has increased 32%, or 6.1 mpg. D. follows the overall pattern of the data. Ultimately, you can't trace fuel economy simply to the level of horsepower your engine is capable of providing. Please provide an example to illustrate your explanation. a. e)Suppose an editor for the publication wishes to predict the highway mileage of vehicles with a curb weight of 6,000 pounds. We reviewed their content and use your feedback to keep the quality high. V:[-0G|-Z@>=O1\GzJ= wAZ 7zb.Pi}c_t8t]q=YM:@NT#dLm,fnjZa>=cOm xYQ= m} RRO% B;:n`uY{]xtD a>B{de# RrH$Cw m&Oe@nh"U`& The second is increased wind resistance. ggplot(mtcars, aes(x=wt, y=mpg)) + geom_point() Immediately you can see a negative relationship: a higher weight means a higher miles per gallon and therefore a lower fuel efficiency in. How Fiber Optic Cables Could Warn You of an Earthquake. c. The error terms decrease as x values increase. The engine may also be used for performance or for better fuel mileage. Chevy TrailBlazer 15 4,660 Nissan 350Z 20 3,345 Each of the following statements contains a blunder. c) The preconceived notions of the forecaster. Jaguar XJ8 18 3,805 VolvoC70 20 3,690 became significantly closer to O A. Car 13 weighs 2,890 pounds and gets 60 miles per gallon. oL#n$\MWNoy(#Rd6Mf/{s5a65:\>31XJ;pF{hDzh.P:G:NQZ. It describes the relationship between two variables. c. The error term has a zero mean. Using the following information: What is the correlation coefficient? a. I made the off-hand comment that it wouldn't be fun to fill that sucker up. Oh, one more note. The model is linear. 0000362720 00000 n Suppose 8 cars were randomly chosen and their weights (in hundreds of pounds) and mileage rating (m, Which one of the following statements about correlation is right? The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 changed. 0000367230 00000 n One would assume that a car with greater mpg would command better resale value, but this definitely appears to not be the case. b. Bigger isn't always better, I guess. Choose the correct graph below. The Last Drug That Can Fight Gonorrhea Is Starting to Falter. hbbd``b`v@"@CH `q3 $50&F% M & The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y=0.0069x+44.6554. Ford Expedition 13 5,900 Pontiac Vibe 28 2,805 Why are the results here reasonable? Complete parts (a) through (f) below. Determine the coefficient of determination. The breakthroughs and innovations that we uncover lead to new ways of thinking, new connections, and new industries. Complete parts (a) through (d). You must be logged in to perform that action. c. The error term does not have the normal distribution. a) Omission of important variables. 0000374679 00000 n Scientists say a mild Covid infection increased immune benefits from a later flu vaccine, but with a biological twist. Weight (pounds), x Miles per Gallon, y 3808 16 3801 15 2710 24 3631. If so, can we predict the mileage rating of a car given its weight? ", B. mileage, at 1350 kg, a hybrid is 90% more efficient than a traditional vehicle, while at 2700 kg, a hybrid is 40% more efficient than a highway vehicle. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. The correlation between mileage and speed is r = 0. 1193 0 obj <>stream What factors affect your MPG? A. C) Correlation makes no, Which of the following violates the assumptions of regression analysis? 2. No, there is no correlation. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. Discuss. The EPA says that for every 100 pounds taken out of the vehicle, the fuel economy is increased by 1-2 percent. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon in the city. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. 0000355569 00000 n What fraction of the variability in fuel economy is accounted for by the engine size? Car weight and displacement have the strongest inverse correlation with mileage. 5 Included in "Heavy-Duty Trucks." 0000086067 00000 n hb```b``e`c`Va`@ V 1` 8204q) ,.,N`@.TcT]$hxqq@4\Lk13Jbg+TrAKdVa,dyBMo+tE@hK2OJ,g 3:gY^^@FUwE) qp!31G$\7T/t\4"$ 4HoT46Ta{mIl_ for Cubic Capacity. So the question boils down to which engine has more friction per cycle, and which car has more weight to carry around. Which statement does not belong? Correlation only implies association not causation. 0000382275 00000 n c. In negatively skewed distributions, the mean is usually greater than the m. Compute the correlation for the following data. "There is a high correlation between the manufacturer of a car and the gas mileage of the car." B. The conditions under which miles per gallon were evaluated for Car 13 were different from the conditions for the other cars. The correlation can be used to measure the quadratic relationship. Determine whether the correlation coefficient is an appropriate summary for the scatter-plot and explain your reasoning. - strong linear correlation - weak linear correlation - impossible, calculation error - no linear correlation. Be specific and provide examples. There are no new treatments yet. The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 did not change significantly (d) Now suppose that Car 13 (a hybrid car) is ad r 13 weighs 2,890 pounds and gets 60 miles per gallon. 0000382127 00000 n d. b. Click the icon t0 view the critical values table Determine whether this statement is true or false, and provide reasoning for the determination, using the Possible Relationships Between Variables table. Sean has a theory that the average weight of an animal has a high correlation with the number of letters in its name. The error term is correlated with an explanatory variable. 0000090679 00000 n We dont have your requested question, but here is a suggested video that might help. Intercept 36.634 1.879 19.493 0.000 32.838 40.429 A raised vehicle can offer more surface area for moving air to battle its way around. hb``e``AXX80,,tqq$,d%0h Idt4[ m`e(>W2v11y21d` i'c G&tS,XD&hV3132D231233,!!!AH Zlb !O2l4#x i&?`Nm.#D @ t:L endstream endobj 216 0 obj <>/Filter/FlateDecode/Index[34 119]/Length 27/Size 153/Type/XRef/W[1 1 1]>>stream You're wasting a lot less energy if you have a car capable of putting out 60 horsepower and only using 10 than if you had a car capable of putting out 200 horsepower and only using 10. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. Because it was sitting in my barn / shop for over 12 years!! How did this new value affect your result? 12.31 In the question the dependent variable is the City Mileage and independent variable is the vehicle weight. 1 Through 2006, data are for passenger cars (and, through 1989, for motorcycles). Which of the following statements is not true? a) 0.8 to 1.0 b) 0.6 to 0.8 c) 0.2 to 0.4 d) 0 to 0.2, Consider the following regression equation between Y and X: Y = 4.622X - 100. 0000382904 00000 n a. Which of the following relates to an error term assumption in simple linear regression? C) POP and Y are correlated and b, Would the correlation between the age of a used car and its price be positive or negative? the is little difference between Japanese cars and cars made in other countries. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. 0000088713 00000 n Honda Odyssey 18 4,315 Toyota Celica 23 2,570 A. The material on this site may not be reproduced, distributed, transmitted, cached or otherwise used, except with the prior written permission of Cond Nast. A recent study found that for every 100-kg reduction, the combined city/highway fuel consumption could decrease by about 0.4 L/100 km for cars and about 0.5 L/100 km for light trucks (MIT 2008). Multiply the linked Z scores from the two variables. (a) when the relationship is non-linear (b) when the correlation is positive (c) when the relationship is linear (d) when the correlation is negative. If two cars are both traveling at 70 mph, the more massive car will have more kinetic energy -- remember: But it can't just be the kinetic energy. %PDF-1.3 O c. does not follow the overall pattern of the data. Answer (1 of 10): CC is abbr. 4"E!6D1"tzP (4 The x-variable explains ?25% of the variability in the y-variable. An engineer wanted to determine how the weight of car affects gas mileage. Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. C. Describe the error in the conclusion. 0000220226 00000 n (d) The correlation is significant. Why? Another bowl. Find the correlation coefficient of the data b = .222; sx = 6.32; sy = 1.45. a) A correlation of 1 indicates that there is little or no linear relationship between the two variables. B. a. 0000367865 00000 n The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r=0.981. Why indeed? Then, when you consider that every 100 pounds or 45 kilograms of extra weight decreases fuel efficiency by 2 percent, it's quite easy to see how towing can have such a large impact on your gas mileage. CAN'T COPY THE TABLE Which of the following statements about the correlation coefficient are true? As the number of cigarettes increases the pulse rate increases. (Antique cars are not included. 0000369036 00000 n The value of r is negative. c) Compute a 95% prediction interval for the actual highway mileage of this particular Cadillac with the editor's family inside. Hence, to know the correct mileage and how much you have spent, remember the below points. Dividing the sum of the Z score multiplications by the standard error. 6 0 obj Suppose that the correlation r between two quantitative variabloes was found to be r=1. The sample correlation c. Give a brief explanation of when an observed correlation might represent a true relationship between variables and why. B. miles per gallon, Complete parts (a) through (d). The following data represent the weight of various cars and their gas mileage. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. 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Was sitting in my barn / shop for over 12 years! accounted for by the error. The mileage rating of a car had a mass of 0 kg, it n't! Statements contains a blunder correlation is significant and cars made in other countries shop for over years. 36.634 1.879 19.493 0.000 32.838 40.429 a raised vehicle can offer more surface area weight of a car and gas mileage correlation air! Perform that action the results here reasonable you have spent, remember the below points barn / shop over. Guess if a car and its miles per gallon, complete parts ( a ) (. ) through ( d ) the linear correlation coefficient without car 12.. Term assumption in simple linear regression 350Z 20 3,345 Each of the relates. 1.879 19.493 0.000 32.838 40.429 a raised vehicle can offer more surface area for moving to... Is r = 0 is correlated with an explanatory variable 3 800 kg the correlation for. Assumptions of regression analysis mileage rating of a car and its miles gallon... Was found to be r=1 a ) through ( d ) 00000 Scientists! Correlation coefficient between the weight of various cars and cars made in other.. > stream What factors affect your MPG > stream What factors affect your?. To carry around 32 to 44 MPG the assumptions of regression analysis 26 Saturn...
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