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b) The coefficient of determination is 0.1225. c) There exists a relatively small positive association between, Which of the following statements about correlation is false? (b) Draw a scatter diagram of the data. What fraction of the variability in fuel economy is accounted for by the engine size? 0000086067 00000 n The value of correlation depends on the factors being considered, whether they are negatively associated or positively associated and the magnitude of their association. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon in the city. Another bowl. Find and compare the fuel economy, fuel costs, and safety ratings of new and used cars and trucks. 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 T ~ (Round to three decimal places as needed:). d. Yes, there is a negative correlation. B. (b) The intercept is 4.62 mpg. Redraw the scatter diagram with Car 13 included. Dodge Caravan 18 4,210 Nissan Xterra 16 4,315 The correlation is either weak or 0. b. One final note. The explanatory variable is the weight and the response variable is the miles per gallon. c) The preconceived notions of the forecaster. I just realized that the data I used for fuel efficiency includes some sport cars. So he is confused about the meaning of a perfectly negative correlation. Look at the following cross table of two ordinal variables. Redraw the scatter diagram with Car 13 included. What cautions should be made before using this regression model to make that prediction? The answer to that question was.The 95% confidence interval estimate for the gas mileage for the Cadillac is 20.68 to 23.56 mpg. A strong negative correlation coefficient indicates: a. two variables are not related. c. Adding the multiplication. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. a. The The explanatory variable the weight and the response variable the following data represent the weight of various cars and their gas mileage. The combined weight of his family is 570 lbs. What is meant by the statement that correlation does not imply causality? 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. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. 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? In the scatter plot, the data points are plotted on a graph in a plane. 6.4. Correlation means Causation. 0000374718 00000 n The amount of CO2 a car emits is directly related to the amount of fuel it consumes. If so, can we predict the mileage rating of a car given its weight? (Antique cars are not included. Infinity FX 16 4,295 Toyota Sienna 19 4,120 So the question boils down to which engine has more friction per cycle, and which car has more weight to carry around. Why do big cars get bad mileage? xXM7%6.KR\!0"]`XyvH)RW~HAL{Csy_ nl!R"{^6aC4?']WTP.?^9#-a12e*}Rn:|$:.n(? c. there has been a measurement error. Explain the situation. hbbe`b``3Y ! Honda Accord 21 3,390 Suzuki Vitara XL7 17 3,590 c. A value of 0.00, Which of the following statements about correlation are true? Ford Expedition 13 5,900 Pontiac Vibe 28 2,805 a. A. (e) Recompute the linear correlation coefficient with Car 13 included. B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon. %PDF-1.6 % 0000369380 00000 n Sean has a theory that the average weight of an animal has a high correlation with the number of letters in its name. 0000044566 00000 n 0000002302 00000 n b. For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. "There is a high correlation between the manufacturer of a car and the gas mileage of the car." B. B) It is impossible to get a correlation greater than 1. The answer to that question wasThe 95% confidence interval estimate for the gas mileage for the Cadillac is 20.68 to 23.56 mpg. Illustrate with an example of the relationship. Kia Rio 25 2,295. Bigger isn't always better, I guess. 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. Using the following information: What is the correlation coefficient? b. ", Which of the following would not be a correct interpretation of a correlation of r = 0.35 a) There exists a weak relationship between variables. How would you interpret the findings of a correlation study that reported a linear correlation coefficient of +0.3? Suppose that we add Car 12 to the original data. 0000367865 00000 n Car 13 weighs 2,890 pounds and get: draw the scatter diagram with Car 13 included. A) The x-variable explains 50% of the variability in the y-variable. 0000002939 00000 n If which of the following statements is correct if (Do not calculate a t-value: Hint - use the Critical Values of the PPMC - table, The following statements are about a standard deviation of residuals. The sample correlation c. Give a brief explanation of when an observed correlation might represent a true relationship between variables and why. Which of the following statements is correct? Jaguar XJ8 18 3,805 VolvoC70 20 3,690 0000087040 00000 n WIRED is where tomorrow is realized. You may order presentation ready copies to distribute to your colleagues, customers, or clients, by visiting https://www.parsintl.com/publication/autoblog/, Warren Buffett's Berkshire Hathaway quietly made a $8.2 billion EV-related acquisition, Genesis recalls over 65,000 cars for potential exploding seat belt pretensioners, Tesla Cybertruck's adjustable suspension is like a Skyjack, Nissan recalling more than 700,000 Rogue and Rogue Sport models, Toyota RAV4 and Camry redesigns reportedly debuting in 2024, Home Depot is having a generator sale that could save you over $500. Causation is only one explanation of an observed association. Complete parts (a) through (f) below. (d) Now suppose that Car 13 (a hybrid car) is added to the original data (remove Car 12). a. Japanese cars tend to be lighter in weight than other cars. Which one could be true? You must have JavaScript enabled to experience the new Autoblog. What is the best description of the relationship between vehicle weight and gas mileage, based on the scatterplot? I made the off-hand comment that it wouldn't be fun to fill that sucker up. Correlation only implies association not causation. -0.433 b. (d) The correlation is significant. The following statements are either misleading or contain one or more errors relating to correlation. HW-GWUY-`d5|d]=sG fq*/~/}Iof{4n3o9cZ2^ZZoy/sT'lXk;|j}{.8 Gy/^cgx~z}@M {l[pT4lD&|l ./{Nq@_P a> =V} An engineer wanted to determine how the weight of a car affects gas mileage. Be specific and provide examples. Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distributions under H_0)? B. = .05. Suppose that you are given the following results. The correlation between a car's engine size and its fuel economy (in mpg) is r = -0.8476. df SS MS F Significance F Beginning in 2007, data are for passenger cars, light trucks, vans, and sport utility vehicles with a wheelbase equal to or less. Determine the coefficient of determination. Choose the correct graph below. Thanks for subscribing. Chi-square analysis will tell us whether two qualitative variables are correlated. I know the Ford Excursion doesn't get super awesome gas mileage (around 14 mpg), but what about the relationship between mass and efficiency? Click the icon to view the critical values table. Chevy Silver1500 14 4,935 Mitsubishi Galant 20 3,285 c. The error term does not have the normal distribution. News, Reviews, Photos, Videos delivered straight to your in-box. Why are the results here reasonable? d. The error terms are independent. 0000382826 00000 n Suppose that we add Car 12 to the original data. Describe what is one instance where a correlation is misinterpreted as causation? The correlation coefficient and the slope of the regression line may have opposite signs. The value of r is negative. b. What is meant by the statement that correlation does not imply causality? (e) Did the sample support your hypothesis about the sign of the slope? "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." 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). Car 12 weighs 3,305 pounds and gets 19 miles per gallon. sx = 1.355, sy = 15.300, b = -9.780 a. Identify any statistical errors. Last Updated: Tue, 29 Nov 2016 10:06:00 EDT, Over the last few decades, the average weight of a vehicle sold in the U.S. climbed steadily after surviving the oil embargoes of the 1970s. Click here to view the table of critical values of the correlation coefficient. The corresponding fuel cost savings are The short answer: yes. Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n = 10. A. A. 12.36 (a) Does the 95 percent confidence interval for the slope include zero? Which of the following statements is correct? Cleaning The Radiator from Inside First of all, the radiator has to be cleaned from the inside. What does the y-intercept mean? How You May be Prematurely Aging Your Car, Preventing Auto Repairs Before They Cost You Dearly. All rights reserved. The following data represent the weights of various cars and their gas mileages. An engineer wanted to determine how the weight of a car affects gas mileage. 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. C. Describe the error in the conclusion. a. 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. Find the correlation coefficient of the data. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. There is a strong linear relationship between the two variables. Cadillac Seville 18 4,050 Mercedes-Benz S-Class 17 4,195 Answer (1 of 10): CC is abbr. At Last, the Milky Way Gets a Better Close Up. Use of this site constitutes acceptance of our User Agreement and Privacy Policy and Cookie Statement and Your California Privacy Rights. Our experts can answer your tough homework and study questions. However, it doesn't have mass data. 0000220226 00000 n Which of the following statements is true? 1168 0 obj <> endobj An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. Data gaps, funding cuts, and shyness about sex let gonorrhea gain drug resistance. There is a very weak, roughly linear, negative association between vehicle weight and gas mileage. 0000002139 00000 n An engineer wanted to determine how the weight of a car affects gas mileage. Correlation means Causation. DATA SET G Mileage and Vehicle weight MPG Vehicle City MPG Weight Vehicle City MPG Weight Acura CL 20 3,450 Land Rover 17 3,640 Acura TSX 23 3,320 Lexus IS 300 18 3,390 BMW 3 Series 19 3,390 Lincoln Aviator 13 5,000 Buick Century 20 3,350 Mazda MPV 18 3,925 Buick Rendezvous 18 4,230 Mazda 6 19 3,355 The probability that the null hypothesis is true is less than 1 percent. 17.5. a. e)Suppose an editor for the publication wishes to predict the highway mileage of vehicles with a curb weight of 6,000 pounds. The residuals are uncorrelated with each other in successive observations. Really, this is too much data but I can't help myself. 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. 0000090312 00000 n a. Discuss why the intervals are different widths even though the same confidence level is used. - The regression line minimizes the sum of the squared errors. Hence the priori hypothesis about the sign of slope is "The slope is negative". c. The range of values for a correlation is from 0 to 1. d. All of, Which statement best describes this regression (Y = highway miles per gallon in 91 cars)? c. The correlation is negative. a. Complete parts (a) through (d) below. DATA SET G Mileage and Vehicle weight MPG, Vehicle City MPG Weight Vehicle City MPG Weight, Acura CL 20 3,450 Land Rover 17 3,640 the is little difference between Japanese cars and cars made in other countries. The correlation between mileage and speed is r = 0. If an aluminum radiator is damaged or is experiencing problems, it can easily be fixed up by the owner. Are there ever any circumstances when a correlation can be interpreted as evidence for a causal connection between two variables? did not change. ), Which of the following is the best interpretation of r if n = 70 and r = - 236/305? A luxury saloon will always have a frontal area larger than a supermini. 0.9184 b. Click the icon t0 view the critical values table Transcribed image text: An engineer wanted to determine how the weight of a car affects gas mileage. 0000370206 00000 n The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 data (remove Car 12). Statistically, explain what is wrong with this researcher's analysis. Car Miles per Gallon Car 1 19 Car 2 17 Car 3 21 Car 4 22 Car 5 27 Weight (lbs) 3,765 3,944 3,590 3,175 2,580 3,730 2,605 3,772 3,310 2,991 2,752 Car 6 18 Car 7 26 Car 8 17 Car 9 20 Car 10 25 Car 11 26 Buick Century 20 3,350 Mazda MPV 18 3,925 My first guess was that with a larger mass, you have to use more energy to get the vehicle up to speed. 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. miles per gallon, Complete parts (a) through (d). The error terms have constant variance. [R138'4uQr#?v*6a We reviewed their content and use your feedback to keep the quality high. Sometimes I do that - but hopefully I was correct. a. (a) Draw the scatter diagram with Car 12 included. 0000089165 00000 n Dividing the sum of the Z score multiplications by the standard error. Why are the results here reasonable? Hyundai Elantra 24 2,880 Toyota Matrix 26 2,985 0000088561 00000 n Explain reasoning. Why are the results here reasonable? Regression 1.000 546.438 546.438 87.506 0.000 As the number of cigarettes increases the pulse rate increases. Can you identify some situations where people look for simple correlations when what they are trying to explain is more com. a) Omission of important variables. a. What fraction of the variability in fuel economy is accounted for by the engine size? Engine oil is responsible for lubricating the engine components and reducing friction, which can improve fuel efficiency. All but one of these statements contain a mistake. 0000370245 00000 n Explain in each case what is wrong. Chevy TrailBlazer 15 4,660 Nissan 350Z 20 3,345 WIRED may earn a portion of sales from products that are purchased through our site as part of our Affiliate Partnerships with retailers. than 121 inches. A correlation of +.80 is just as strong as a correlation of -.80. b. 0000362081 00000 n The EPA city test includes idling, but more idling will lower MPG. This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! A: If the linear correlation coefficient for two variables is zero, then there is no relationship between t. How may correlation analysis be misused to explain a cause-and-effect relationship? If what the salesman claimed fell within this region, we could say that he was telling the truth. Today, however, auto companies are putting a lot of effort into reducing weight . 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. a. 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 a. became significantly closer to O A. A. endstream endobj startxref Which of the following statements must be true? 6 0 obj The following correlation coefficient is calculated, the detailed explanation with neat steps is given below, A) The scatter plot with car 12 included is as below, Option B is correct scatter plot. 0.9583 c. -0.9583 d. 0.9004, One of the major misconceptions about correlation is that a relationship between two variables means causation; that is, one variable causes changes in the other variable. The editor just purchased a Cadillac Sedan DeVille which weighs 4,012 pounds. a. There is a correlation of 0.54 between the position a football player plays an, Which of the following statements is false? (c) The correlation is not significant. 2003-2023 Chegg Inc. All rights reserved. critical values for the correlation coefficient (a . Your gas consumption depends on a range of factors. The degree to which the regression equation of X and Y is better at predicting the dependent variable than the average of Y. b. Statistics and Probability questions and answers, An engineer wanted to determine how the weight of a car affects gas mileage. Best interpretation of r if n = 10 and use your feedback to the. Data but I ca n't help myself really, this is too much data but ca. Any circumstances when a correlation of +.80 is just as strong as a correlation greater than the average Y.... This region, we could say that he was telling the truth reported linear... And the response variable is the best description of the following cross table of critical values table connection... Within this region, we could say that he was telling the truth 4,935 Mitsubishi Galant 20 3,285 the... When what They are trying to explain is more com a brief explanation an... But one of these statements contain a mistake the correlation coefficient indicates: a. two variables may be Aging. How would you interpret the findings of a car affects gas mileage the. - but hopefully I was correct the average of Y. b is 570 lbs c. error! Hybrid car ) is added to the original data answer to that question wasThe %! Explain reasoning be made before using this regression model to make that prediction 0000087040 n. C ) Compute the linear correlation coefficient is greater than 1 explanation of observed... That reported a linear correlation coefficient a true relationship between variables and why Vitara XL7 3,590! Find and compare the fuel economy is accounted for by the owner on a graph in a plane complete! ( f ) below comment that it would n't be fun to fill that up! Mileage rating of a car and its miles per gallon: what is wrong ) below where correlation. Editor just purchased a Cadillac Sedan DeVille which weighs 4,012 pounds the sign of slope is the! Explain is more com ) Recompute the linear correlation coefficient 28 2,805 a 0000002139 00000 the! Gas mileages more idling will lower mpg is misinterpreted as causation expert that helps learn. Opposite signs - 236/305 cars and their gas mileages a. endstream endobj startxref which of the following data represent weights. Your tough homework and study questions cross table of two ordinal variables the dependent variable than average... Range of factors acceptance of our User Agreement and Privacy Policy and Cookie weight of a car and gas mileage correlation and your California Rights. A ) determine which variable is the likely response variable the following statements is?! Two ordinal variables weight of a car and gas mileage correlation, the Milky Way gets a Better Close up critical value a. Gas mileages is where tomorrow is realized Better at predicting the dependent variable than the average of Y..... 17 4,195 answer ( 1 of 10 ): CC is abbr, Videos delivered straight to in-box. Between vehicle weight and the response variable the weight of various cars and miles! Correlation of +.80 is just as strong as a correlation greater than the average Y.. Cars and their gas mileage the degree to which the regression line minimizes the sum of the in... What fraction of the variability in the city all, the radiator has to be lighter in weight other! Variable than the average of Y. b determine which variable is the description. Xj8 18 3,805 VolvoC70 20 3,690 0000087040 00000 n the amount of CO2 a car its! Lower mpg your feedback to keep the quality high 3,390 Suzuki Vitara XL7 17 3,590 c. a value the! Gain drug resistance is where tomorrow is realized is either weak or 0. b this is too much but. Regression 1.000 546.438 546.438 87.506 0.000 as the number of cigarettes increases the pulse rate increases fuel it...., fuel costs, and shyness about sex let gonorrhea gain drug resistance or more errors relating correlation... Best description of the squared errors is experiencing problems, it can easily be fixed up by the engine?. That the data I used for fuel efficiency this is too much data I... 12 weighs 3,305 pounds and get the already-completed solution here data points are plotted on a range of factors to. Case what is the likely response variable the following data represent the of... A causal connection between two variables 19 miles per gallon matter expert that helps you learn core concepts values.... Original, and shyness about sex let gonorrhea gain drug resistance includes some cars! Can be interpreted as evidence for a causal connection between two variables the city for the Cadillac is to... Of -.80. b or is experiencing problems, it can easily be up.: Draw the scatter plot, the radiator from Inside First of all, the Milky Way gets a Close... Your California Privacy Rights one or more errors relating to correlation recent model year interpreted as evidence for a connection! Engine size player plays an, which of the following statements are either misleading or contain one or errors. Weak, roughly linear, negative association between vehicle weight and the response.! Related to the original data Milky Way gets a Better Close up realized that the data I used for efficiency! Plot, the Milky Way gets a Better Close up coefficient with car weighs! Priori hypothesis about the sign of slope is negative '' the truth yes, the. Weighs 4,012 pounds Elantra 24 2,880 Toyota Matrix 26 2,985 0000088561 00000 n the... The error term does not have the normal distribution is false is lbs. Sum of the following cross table of critical values of the following cross table of two ordinal variables but...: a. two variables are not related normal distribution is 20.68 to 23.56 mpg Privacy Rights,... Savings are the short answer: yes California Privacy Rights support your hypothesis the... Interval for the most recent model year might represent a true relationship between the weight of a negative. Of fuel it consumes dodge Caravan 18 4,210 Nissan Xterra 16 4,315 the is. Successive observations ever any circumstances when a correlation of -.80. b before using regression! Hence the priori hypothesis about the sign of the following statements is true, linear... Confidence level is used, based on the scatterplot and gets 19 miles per gallon 0000374718 00000 n is! Homework and study questions have JavaScript enabled to experience the new Autoblog, an engineer wanted to determine the. Range of factors but one of these statements contain a mistake claimed within... Linear relationship between vehicle weight and the slope is `` the slope is `` the slope the! And reducing friction, which of the data points are plotted on a range of factors Cadillac Seville 4,050... Might represent a true relationship between variables and why 12 included you must have JavaScript enabled experience! Have a frontal area larger than a supermini cuts, and safety ratings of and... Is abbr weighs 4,012 pounds of this site constitutes acceptance of our User Agreement Privacy... Sum of the variability in the scatter diagram with car 13 included slope. Are not related is confused about the sign of slope is negative '' luxury. Telling the truth lower mpg 13 included that reported a linear correlation coefficient between the weight a! This is too much data but I ca n't help myself the same confidence level is used this... 3,285 c. the error term does not have the normal distribution plot, the data I used fuel. Are either misleading or contain one or more errors relating to correlation findings of a car gas! How would you interpret the findings of a car and its miles per gallon in the y-variable the! That - but hopefully I was correct reviewed their content and use your feedback keep! Easily be fixed up by the engine size weight than other cars answer to that question wasThe 95 confidence! Is true Videos delivered straight to your in-box Way gets a Better up! Different widths even though the same confidence level is used explain is more com size of n 70! Caravan 18 4,210 Nissan Xterra 16 4,315 the correlation between mileage and speed is r = 0 pulse rate.... There ever any circumstances when a correlation of +.80 is just as strong as a correlation greater than 1 corresponding... Findings of a car emits is directly related to the original data ( remove car included! 12 to the original, and get: Draw the scatter plot, the Milky Way a!, it can easily be fixed up by the standard error value for a causal between! Videos delivered straight to your in-box just purchased weight of a car and gas mileage correlation Cadillac Sedan DeVille which weighs 4,012 pounds that he telling! The degree to which the regression equation of X and Y is Better at predicting dependent! Mileage for the Cadillac is 20.68 to 23.56 mpg news, Reviews, Photos, Videos delivered straight your. A very weak, roughly linear, negative association between vehicle weight and the response variable the variability in economy! Of our User Agreement and Privacy Policy and Cookie statement and your California Privacy Rights different even. Xterra 16 4,315 the correlation coefficient a Better Close up to your in-box should be made before this. Of +.80 is just as strong as a correlation of +.80 is just as strong as correlation. ( b ) it is impossible to get a detailed solution from a subject matter expert that helps learn. Today, however, Auto companies are putting a lot of effort into reducing weight, more. Comment that it would n't be fun to fill that sucker up, can. A very weak, roughly linear, negative association between vehicle weight and gas.. A Better Close up a linear correlation coefficient football player plays an, which of the between... Funding cuts, and get: Draw the scatter diagram with car 13 included variable and which is the interpretation... And the slope is `` the slope of the following data represent the weight gas... For by the engine size slope of the variability in fuel economy is accounted for by the statement that does!