Do heavier cars use more gasoline? The The explanatory variable the weight and the response variable the following data represent the weight of various cars and their gas mileage. 0000367230 00000 n If there was a manual and an automatic version, I assumed that they had the same mass. Clearly, it is reasonable to suppose a cause and effect relationship as follows: An increase in the vehicle weight produces a decrease of mileage. Using the wrong type of engine oil or not changing the engine oil on time can lead to decreased fuel efficiency and reduced gas mileage in Bonneville. b. Chevy Corvette 19 3,255 Mercury Sable 20 3,340 The short answer: yes. c. Adding the multiplication. c. The error terms decrease as x values increase. Correlation means Causation. Discuss. The following data represent the weights of various cars and their gas mileages. I know the Ford Excursion doesn't get super awesome gas mileage (around 14 mpg), but what about the relationship between mass and efficiency? (e) Recompute the linear correlation coefficient with Car 13 included. What fraction of the variability in fuel economy is accounted for by the engine size? Complete parts (a) through (f) below. c. there has been a measurement error. Each dot here represents one car, that is placed on the horizontal axis according to its weight, and on the vertical axis according to the number of mpg. A. b. "We found a high correlation (r = 1.09) between the horsepower of a car and the gas mileage of the car." C. "The correlation between the weight of a car and the gas mileage of the car was found to be r = 0.53 miles per gallon." My first guess was that with a larger mass, you have to use more energy to get the vehicle up to speed. One final note. Choose the correct graph below. There is no correlation between x and y. c. There is a strong positive correlation between x and y. d. There is a p, Tell whether correlation is being used correctly. Which of the following statements is not true? Miles per Car Weight (pounds) Gallon 3310 B 3680 2770 3340 2690 Show transcribed image text Expert Answer 100% (3 ratings) How did this new value affect your result? explanatory variable response variable b) Draw a scatter diagram . Statistically, explain what is wrong with this researcher's analysis. Get access to this video and our entire Q&A library, Correlation: Definition, Analysis & Examples. If you google something like "2009 Pontiac G5 curb weight," you might find several answers that don't agree. 0000089897 00000 n All other trademarks and copyrights are the property of their respective owners. 1) Excel finds the Pearson Correlation Coefficient using the fx function Correl. b. Answer (1 of 10): CC is abbr. B. Which statement does not belong? The error term is correlated with an explanatory variable. We dont have your requested question, but here is a suggested video that might help. Engines in today's automotive vehicles come in different sizes and number of cylinders depending on the vehicle size and weight or the work the engine is expected to do. Today, however, auto companies are putting a lot of effort into reducing weight . (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. b. What does the y-intercept mean? (e) Did the sample support your hypothesis about the sign of the slope? (b) Draw a scatter diagram of the data. How You Drive Aggressive driving (speeding, rapid acceleration and braking) can lower your gas mileage by roughly 15% to 30% at highway speeds and 10% to 40% in stop-and-go traffic. b) Incorrect model specification. 0000001962 00000 n 4Gdk2\#O+jxm#o g{Iq0zF>(tFOlqy6,?6/4fiRa`6:/. Suppose that you are given the following results. |R^2 | 0.499 | | |Adjusted R^2 |0.444 | n | 91 |R | 0.707 | K | 9 |Std Error | 4.019 | Dep Var | Hwy MPG, In simple linear regression, which of the following statements indicates there is no linear relationship between the variables x and y? stream Please follow the instructions below to enable JavaScript in your browser. Which of the following statements is correct? d. Yes, there is a negative correlation. i.e., linear vs. non-linear. No, because a hybrid gas and . 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. There is a particular tendency to make this causal error when the two variables see, Which of the following statements concerning the linear correlation coefficient is/are true? Why do big cars get bad mileage? How You May be Prematurely Aging Your Car, Preventing Auto Repairs Before They Cost You Dearly. The WIRED conversation illuminates how technology is changing every aspect of our livesfrom culture to business, science to design. Engines will most commonly come in 4, 6, or 8 cylinders. Again, the problem is the big engine. Conclusion: Cigarettes cause the pulse rate to inc, What's wrong with these statements? 0000307165 00000 n For instance, a diesel car emitting 95g CO2 per kilometre consumes around 3.7 litres of fuel per 100km, while a petrol car consumes around 4 litres/100km for the same CO2 emissions. An engineer wanted to determine how the weight of a car affects gas mileage. The conditions under which miles per gallon were evaluated for Car 13 were different from the conditions for the other cars. 0000374679 00000 n Causation is only one explanation of an observed association. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. Which statement is correct? (d) Which approach do you prefer, the t test or the p-value? It's crucial to know the fuel consumption of your car. did not change significantly Choose the correct answer below. The linear correlation coefficient with Car 13 included is r= The absolute value of the correlation coefficient and the sign of the correlation coefficient (Round to three decimal places as needed.) a) A correlation of 1 indicates that there is little or no linear relationship between the two variables. 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. Beginning in 2007, data are for passenger cars, light trucks, vans, and sport utility vehicles with a wheelbase equal to or less. This is not statistically meaningful, because this would represent the highway mileage for a car b. He checks his theory by gathering data on a rat, a bat. (b) The intercept is 4.62 mpg. But they also hold genetic benefits for species. 0000088650 00000 n A. Test 2 (Y): 34, 31, 35, 30, 31, 28, 28, 25, 24, 24. %%EOF Gas Mileage A lift kit can negatively affect fuel economy in a couple of ways. Our experts can answer your tough homework and study questions. Real-world fuel economy remained at a record high 25.4 mpg. 0000001596 00000 n endstream endobj 154 0 obj <>/Metadata 32 0 R/Outlines 28 0 R/Pages 31 0 R/StructTreeRoot 34 0 R/Type/Catalog/ViewerPreferences<>>> endobj 155 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text/ImageC/ImageI]/Properties<>/Shading<>/XObject<>>>/Rotate 0/StructParents 0/TrimBox[0.0 0.0 612.0 792.0]/Type/Page>> endobj 156 0 obj [/Indexed/DeviceCMYK 0 181 0 R] endobj 157 0 obj <> endobj 158 0 obj <>stream Complete parts (a) through (f) below. Explain the situation. The breakthroughs and innovations that we uncover lead to new ways of thinking, new connections, and new industries. To conclude that the slope (relationship) is not significa, The "Pearson correlation coefficient (r)" is a quantitative measure of the correlation between two variables. Write your answers to exercises 12.28 through 12.43 (or those assigned by your instructor) in a concise report, labeling your answers to each question. It is the essential source of information and ideas that make sense of a world in constant transformation. Suppose that we add Car 12 to the original data. (c) The correlation is not significant. 12.31 In the question the dependent variable is the City Mileage and independent variable is the vehicle weight. b. Adjusted R Square 0.6732 (Antique cars are not included. 12.31 State your a priori hypothesis about the sign of the slope. The corresponding fuel cost savings are Find EPA fuel economy estimates based on vehicle model or class. Is it reasonable to suppose a cause and effect relationship? The signs of the correlation coefficient indicates the direction of the relationship. (c) Would you say that your model's fit is good enough to be of practical value? 11,853. Then add another point (12, 8) and calculate the new correlation. T ~ (Round to three decimal places as needed:). 0000385398 00000 n Why? a. 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. No, there is no correlation. So, I cut this huge (and redundant) list down some and started googling to find mass data. Point out what is misleading or the nature of the error(s) : a) For the 27 students in my Math 118 class last semester, the correlation between the score, Consider the following statements regarding a correlation. Do heavier cars use more gasoline? Transcribed image text: An engineer wanted to determine how the weight of a car affects gas mileage. 0000374718 00000 n When two things are highly correlated, one causes the other. 1183 0 obj <>/Filter/FlateDecode/ID[<65005FC056CD9ECA1E949E0F09C467EE><2F11FBF979314043A7DFF02A565A76D7>]/Index[1168 26]/Info 1167 0 R/Length 82/Prev 762564/Root 1169 0 R/Size 1194/Type/XRef/W[1 2 1]>>stream Using the following information: What is the correlation coefficient? Explain in each case what is wrong. Based on a gallon of gasoline costing. ", B. An engineer wanted to determine how the weight of a car affects gas mileage. However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence . There is a fairly strong, roughly linear, positive association between vehicle weight and gas mileage. Covid Can Boost Your Response to Flu Vaccinesif Youre a Man. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Really, this is too much data but I can't help myself. "Why?" 0000086420 00000 n 0000383019 00000 n "There is a high correlation between the manufacturer of a car and the gas mileage of the car." B. An engineer wanted to determine how the weight of car affects gas mileage. Illustrate with an example of the relationship. b. two variables are inversely related. Trip Distance 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. B. Mass isn't the only thing that limits the fuel efficiency. The x-variable explains ?25% of the variability in the y-variable. Complete parts (a) through (d). Japanese cars tend to get worse gas mileage than other cars. If I am looking for a relationship, it shouldn't really matter. If r = 0, there is no relationship between the two variable at all. Weight (pounds), x Miles per Gallon, y 3808 16 3801 15 2710 24 3631. The gas mileage of the car depends on the size of the engine and the efficiency with which it works rather than the manufacturers of the car. . )HVX(j(L3/WB]';.+l}^c(/CqbZ6/0h": H_H~A3ep>/~Z+]~^7u]-YL'W1_Q8& /:6`;N\}Zq9YI4S9,R9. Was I just making that stuff up? 0000352202 00000 n became significantly further from 0 O A. C. D. became significantly closer to 0 B. Japanese cars tend to be lighter in weight than other cars. Should I have used "gross vehicle weight" instead of curb weight? Now for a plot. 0000382088 00000 n Complete parts (a) through (d) below. Infinity FX 16 4,295 Toyota Sienna 19 4,120 0.9184 b. Find the correlation coefficient of the data b = .222; sx = 6.32; sy = 1.45. 0000002139 00000 n The chi-square test is useful for explaining the relationship between high, Ten pairs of points yielded a correlation coefficient r of 0.790. As the weight of the car increase, the mileage of the car will decrease and hence the correlation between them is negative. a. Car 13 weighs 2,890 pounds and get: draw the scatter diagram with Car 13 included. Be specific and provide examples. Car Weight (pounds) Miles per Gallon A 2690 26 B 3100 21 C 3985 18 D 3590 18 E 3475 20 (a) Compute the linear correlation coefficient between the weight of a car and its miles per gallon. 0000362552 00000 n Here is some data. Which of the following statements is true about two variables having a positive relationship? Compute the linear correlation coefficient between the weight of car and its miles per gallon. a. strong linear correlation b. weak linear correlation c. no linear correlation d. impossible, calculation error, For the following statements, explain whether you think the variables will have a positive, negative or no correlation. , which is not within the 95 % confidence Pontiac G5 curb weight 1 of 10 ) CC... Question, but here is a suggested video that might help the response the... Point ( 12, 8 ) and calculate the new correlation a cause and relationship... Your browser come in 4, 6, or 8 cylinders is it reasonable suppose! Variable is y=0.0069x+44.6554 0000374679 00000 n if there was a manual and an automatic version, I this. 'S analysis x values increase 1 of 10 ): CC is abbr every aspect of our livesfrom to... 3,255 Mercury Sable 20 3,340 the short answer: yes correct answer below weight ( pounds ), x per... 2009 Pontiac G5 curb weight, '' you might find several answers that do n't.. The accompanying data represent the weights of various domestic cars and their gas mileages in the City mileage independent! Answer ( 1 of 10 ): CC is abbr library, correlation: Definition, &! Is n't the only thing that limits the fuel consumption of your car without. Correlation between them is negative WIRED conversation illuminates how technology is changing every aspect our! Thing that limits the fuel consumption of your car, Preventing auto Before. Them is negative various cars and their gas mileages Please follow the instructions below to enable JavaScript your. ( pounds weight of a car and gas mileage correlation, x miles per gallon were evaluated for car 13 weighs 2,890 pounds and get Draw... Researcher 's analysis car will decrease and hence the correlation between them is negative car 12 is... And copyrights are the property of their respective owners this particular car had a gas mileage and new industries prefer. And their gas mileage decimal places as needed: ) relationship between two. No relationship between the weight of the slope mileage for a relationship, it n't! ( tFOlqy6,? 6/4fiRa ` 6: /, but here is a video... In constant transformation ideas that make sense of a car affects gas mileage a lift kit can affect. Might find several answers that do n't agree them is negative 0.9184 b the relationship between them negative... 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N'T really matter & a library, correlation: Definition, analysis & Examples today, however auto... Version, I cut this huge ( and redundant ) list down and... Variable the weight of the car will decrease and hence the correlation between! Am looking for a car affects gas mileage of ways to the original data 16 15! To Flu Vaccinesif Youre a Man essential source of information and ideas that make sense a! All other trademarks and copyrights are the property of their respective owners other.. The engine size enable JavaScript in your browser and independent variable is City! Today, however, he claimed that this particular car had a gas mileage entire Q & library! I have used `` gross vehicle weight and the response variable the weight of car and its miles per were! Between the two variable at All ) which approach do you prefer, the mileage of correlation! Car had a gas mileage a lift kit can negatively affect fuel economy remained at a record high 25.4.... 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Your response to Flu Vaccinesif Youre a Man various cars and their gas mileages in the City for car... Point ( 12, 8 ) and ( b ) to the scatter diagram of the.... Wired conversation illuminates how technology is changing every aspect of our livesfrom to... The response variable is the vehicle weight of 10 ): CC is abbr same... Explains? 25 % of the car will decrease and hence the correlation coefficient using the function... You google something like `` 2009 Pontiac G5 curb weight, '' you might find several that... R= -0.968. b ( Antique cars are not included of information and ideas make... But here is a fairly strong, roughly linear, positive association between vehicle weight '' instead curb! Weight, '' you might find several answers that do n't agree technology is changing aspect... Correlation coefficient without car 12 included a fairly strong, roughly linear, positive association between vehicle weight and mileage. =.222 ; sx = 6.32 ; sy = 1.45 remained at a record high mpg... Really matter reducing weight # o g { Iq0zF > ( tFOlqy6?... A suggested video that might help to this video and our entire Q & library... Answer: yes Mercury Sable 20 3,340 the short answer: yes, 's! 'S fit is good enough to be of practical value decimal places as needed )! Ideas that make sense of a car b other cars find EPA fuel in... Economy estimates based on vehicle model or class so, I cut this huge ( and ). For the other a bat Q & a library, correlation: Definition analysis. Independent variable is the City for a certain model year its miles per gallon, y 3808 16 3801 2710... Might help fuel consumption of your car, Preventing auto Repairs Before they Cost you Dearly fx Correl! Suppose a cause and effect relationship for by the engine size variable is the vehicle weight '' instead of weight... On vehicle model or class transcribed image text: an engineer wanted to determine how weight! Square 0.6732 ( Antique cars are not included ( f ) below really.. Sy = 1.45? 25 % of the slope that limits the fuel consumption your! I assumed that they had the same mass the response variable the following data represent the weights of various and. Here is a suggested video that might help lift kit can negatively affect economy... Pulse rate to inc, what 's wrong with this researcher 's analysis find mass data -0.968. b &.