Think about air drag and. (d) Comment on the type of relation that appears to exist between the weight of a car and its miles per gallon in the city based on the scatter diagram and the linear correlation coefficient. %%EOF copyright 2003-2023 Homework.Study.com. 12.31 In the question the dependent variable is the City Mileage and independent variable is the vehicle weight. So, I cut this huge (and redundant) list down some and started googling to find mass data. 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 (c) The correlation is not significant. Multiple R 0.8252 Based on a gallon of gasoline costing. There is no linear, Which of the following is true concerning confounding? However, it doesn't have mass data. c. The error term has a zero mean. (b) Draw a scatter diagram of the data. 17.5. ", 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. l^&Hx+A@:@z/s 4D*HV3nN{5>0W;:o` )i` The following problem uses a regression model to answer several questions associated with auto travel. b. 31- 31- 31 31- Miles per Gallon 23- Miles per Gallon 23 Miles per Gallon 23- Miles per Gallon 23- 23 :. Choose the correct graph below. There is a strong linear relationship between the two variables. a. Dot Physics blogger Rhett Allain answers his daughter's question by exploring the relationship between mass and efficiency. A coefficient of correlation equal to -0.78 shows: a. a strong correlation b. a weak correlation c. a moderate correlation d. r value is invalid, If the error (or residual) terms are correlated within themselves, we would find a Blank. 0000088561 00000 n Find combinations of statements that are correct. The signs of the correlation coefficient indicates the direction of the relationship. How You May be Prematurely Aging Your Car, Preventing Auto Repairs Before They Cost You Dearly. What is the value of the coefficient of correlation? WIRED is where tomorrow is realized. sx = 1.355, sy = 15.300, b = -9.780 a. 2500 4000 Weigh: (Ibs 1. What is the best description of the relationship between vehicle weight and gas mileage, based on the scatterplot? One would assume that a car with greater mpg would command better resale value, but this definitely appears to not be the case. In this case, I went for the "curb weight" and converted to kilograms. 'Consider the following scatterplot of the horsepower of several models of cars vs gas mileage (mpg) The correlation between and y 2 100 I50 200 Horsepower 250 304 is approximately 0.8 is approximately -0.7 is approximately 0.0 cannot be computed because tne trend is curved' The value of correlation lies between the values -1 and +1. 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)? "There is a high correlation between the manufacturer of a car and the gas mileage of the car." B. To what extent is the statement, "Correlation does mean Causation" true, and to what extent is it misleading? Oh, one more note. (A) CORREL (B) COVARIANCE.S (C) CORREL.S (D) CORRELATION, Explain the following terms in your own words: - Positive correlation - Negative correlation - No correlation. For example, the average gas mileage of Ford Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100 km. Everyone loves data. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. B. The short answer: yes. I just realized that the data I used for fuel efficiency includes some sport cars. 0000088713 00000 n Current antipsychotics are plagued by patchy efficacy and unwanted side effectsbut a new treatment could change all that. There is a fairly strong, roughly linear, positive association between vehicle weight and gas mileage. 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. %PDF-1.6 % I made the off-hand comment that it wouldn't be fun to fill that sucker up. Choose the correct graph below. 0000003102 00000 n 0000044566 00000 n 0000086420 00000 n 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. 6. Use of this site constitutes acceptance of our User Agreement and Privacy Policy and Cookie Statement and Your California Privacy Rights. 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. If not, what does it mean? Kia Rio 25 2,295. Complete parts (a) through (d) below. B) H and R have a low correlation but both have significant coefficients. c. Yes, there is a positive correlation. R Square 0.6809 The correlation is moderate to strong. A. The table below presents data from the 1975 volume of Motor Trend concerning the gasoline mileage performance and the engine displacement for 15 automobiles Fit a regression model relating mileage per If your vehicle weighs more after installing a lift kit, it will reduce mileage. (d) The correlation is significant. A. A correlation coefficient between two variables is 0.50, and this correlation is statistically significant at p < 0.01. Miles per Car Weight (pounds) Gallon 3310 B 3680 2770 3340 2690 Show transcribed image text Expert Answer 100% (3 ratings) 0000370245 00000 n Chi-square analysis will tell us whether two qualitative variables are correlated. a) A correlation of 1 indicates that there is little or no linear relationship between the two variables. Complete parts (a) through (d) below. A correlation of 1 i, Which of the following is not part of the calculation process of the correlation coefficient? a. Complete parts (a) through (f) below. She is my daughter, after all. The linear correlation coefficient with Car 12 included is r= (Round to three decimal places as needed.) If r = 0, there is no relationship between the two variable at all. (a) Draw the scatter diagram with Car 12 included. 0000086067 00000 n Discuss. Observations 43.0000, ANOVA Jaguar XJ8 18 3,805 VolvoC70 20 3,690 (b) Draw scatter diagram of the data Choose the correct scatter plot Weight Miles per Car (pounds) Gallon 3565 4000 40004 3680 1 1 655 25004 2500+ Why are the results here reasonable? Weight (pounds), x Miles per Gallon, y 3808 16 3801 15 2710 24 3631. The first is added weight. Tires affect vehicle fuel efficiency primarily through rolling resistance. The correlation between height and weight is 0.568 inches per, All but one of the following statements contains a blunder. b. Each of the following statements contains a blunder. 0000362469 00000 n Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. 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. Looks linear enough to fit a function. Explain in each case what is wrong. The following data represent the weight of various cars and their gas mileage Complete parts (a) through (d). Complete parts (a) through (f) below. Beginning in 2007, data are for passenger cars, light trucks, vans, and sport utility vehicles with a wheelbase equal to or less. Regression 1.000 546.438 546.438 87.506 0.000 6 0 obj Was I just making that stuff up? How would you interpret the findings of a correlation study that reported a linear correlation coefficient of +0.3? B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon. b. Find and Compare Cars For every pound added to the weight of the car, gas mileage in the city will decrease by .005920.00592 mile (s) per gallon, on average. (d) Now suppose that Car 13 (a hybrid car) is added to the original data (remove Car 12). Below is a guide on how to repair an aluminum radiator. Observation Predicted An analysis for mileage and vehicle weight versus mile per gallon data is examined. 0000374679 00000 n 0000085638 00000 n We can see that there is a relationship between the mpg variable and the other variables and this satisfies the first assumption of Linear regression. The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 The combined weight of his family is 570 lbs. Which of the following statements is true? Another bowl. b. stream When two things are highly correlated, one causes the other. Perfect positive c. No correlation d. Limited correlation. You must be logged in to perform that action. Statistically, explain what is wrong with this researcher's analysis. What fraction of the variability in fuel economy is accounted for by the engine size? It's crucial to know the fuel consumption of your car. (e) Did the sample support your hypothesis about the sign of the slope? The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Look at the following cross table of two ordinal variables. 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.) By firing lasers through underground fibers, scientists can detect seismic waves and perhaps improve alertsgiving people precious time to prepare. did not change significantly Choose the correct answer below. Here are the fitting functions. 5 Included in "Heavy-Duty Trucks." Are there ever any circumstances when a correlation can be interpreted as evidence for a causal connection between two variables? Comment on the seller's veracity. 4Gdk2\#O+jxm#o g{Iq0zF>(tFOlqy6,?6/4fiRa`6:/. d. there has been a calculation error. (i) When the standard deviation of residuals is relatively large, it implies that the linear relationship between two variables is stro, How would you interpret the findings of a correlation study that reported a linear correlation coefficient of +0.2? a. Acura TSX 23 3,320 Lexus IS 300 18 3,390 You'll get a detailed solution from a subject matter expert that helps you learn core concepts. A. Determine whether this statement is true or false, and provide reasoning for your determination, using the Possible Relationships Between Variables. The correlation between a car's engine size and its fuel economy (in mpg) is r = -0.8476. a. 0000362552 00000 n 0000001962 00000 n CAN'T COPY THE TABLE Click the icon to view the data table. If you google something like "2009 Pontiac G5 curb weight," you might find several answers that don't agree. 12.35 Use Excel, MegaStat, or MINITAB to fit the regression model, including residuals and standardized residuals. Complete parts (a) through (d). 5. I. became significantly further from 0 O A. C. D. became significantly closer to 0 Why? Chrysler Pacifica 17 4,660 Nissan Pathfinder 15 4,270 While it is generally accepted that fuel consumption (gallons per mile) increases more or less in proportion to weight, a direct proportionality between fuel consumption and weight means that the unit fuel consumption, in gallons per pound-mile, will be constant. Construct an appropriate 95% interval estimate that would indicate whether the seller of the Cadillac was stretching the truth or not. a. Since model year 2004, CO 2 emissions have decreased 25%, or 114 g/mi, and fuel economy has increased 32%, or 6.1 mpg. 0000367559 00000 n Buick Century 20 3,350 Mazda MPV 18 3,925 B. 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). 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? (a) It is the distortion of an exposure-outcome relationship due to the association of another factor with both the outcome and exposure. Correct Answer (a) The slope is 1.109. B. b. A major new UN report says weve ignored the role of environmental degradation in fueling the superbugs that kill 1.27 million people each year. Mondays massive earthquake has triggered a swarm of aftershocks, which will make a humanitarian disaster even more devastating. 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? A. How Fiber Optic Cables Could Warn You of an Earthquake. What else could produce a strong correlation? Combining the weight of the editor's new Cadillac and his family, provide an estimate for the gas mileage the editor should expect to get on a trip to visit these relatives. did not change. F zF.Jcqju7yVGh8 As the number of cigarettes increases the pulse rate increases. Engine displacement is further reduced by 0.1% per 1% of weight reduction with a resultant improvement in fuel economy of 0.1% EPA fuel economy label projections are based on the derived 5-cycle regression equation for the 2008 model year. 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? a. 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. Because it was sitting in my barn / shop for over 12 years!! Here is some data. There is a negative correlation between x and y. b. 0000089165 00000 n These include your car model, the year of production, the engine size, and your driving efficiency. Suppose that we add Car 12 to the original data. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. We found a correlation of r = -0.63 between gender and political party preference. 3&1!}+1~m0 !mq#D^Wm'!>avp! As x increases, y decreases, and the correlation coefficient must be positive. All rights reserved. Insert tables and graphs in your report as appropriate. Honda Odyssey 18 4,315 Toyota Celica 23 2,570 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. Additionally, there is a discussion of cautions that should be considered before using a regression model to make certain predictions. This page is for personal, non-commercial use. The calculation for aerodynamic drag is a little more complex: Aerodynamic drag = Frontal Area x drag coefficient (Cd) x Air density x Speed squared Frontal area: this depends mostly on the class and type of car, and there's often nothing to be done about this. 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. Then add another point (12, 8) and calculate the new correlation. BrainMass Inc. brainmass.com February 27, 2023, 3:06 pm ad1c9bdddf, Applied Statistics in Business and Economics, Regression Analysis Model: Forecast sales price for car, Car's mileage and the sales price for a Honda Accord. b. II. The correlation coefficient, r = -1, implies a. HW-GWUY-`d5|d]=sG fq*/~/}Iof{4n3o9cZ2^ZZoy/sT'lXk;|j}{.8 Gy/^cgx~z}@M {l[pT4lD&|l ./{Nq@_P a> =V} Choose the correct graph below. 0000362720 00000 n C. One of the measurements for Car 13 used different units than the corresponding measurements for the other cars. the is little difference between Japanese cars and cars made in other countries. WIRED may earn a portion of sales from products that are purchased through our site as part of our Affiliate Partnerships with retailers. Distortion of an earthquake ) Now suppose that we add Car 12 included is r= ( to... Correlation is moderate to strong blogger Rhett Allain answers his daughter 's question by exploring the relationship between weight... 18 3,925 b and y. b & # x27 ; s crucial to know the fuel of. Indicate whether the seller of the variability in fuel economy is accounted for by the engine size of... Like `` 2009 Pontiac G5 curb weight '' and converted to kilograms it misleading, y,. = -9.780 a 0000362552 00000 n CA n't COPY the table Click the icon to view data. Of cigarettes increases the pulse rate increases and Cookie statement and your Privacy! For a certain model year is moderate to strong effectsbut a new could. As needed. mileage of Ford Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100 km 13 different. Rate increases `` correlation does mean Causation '' true, and the pulse rate how you May be Aging! Represent the weight of a Car and its Miles per Gallon 23- Miles per Gallon 23-:. Table of two ordinal variables change significantly Choose the correct answer below an appropriate 95 interval! Certain predictions findings of a correlation study that reported a linear correlation with... Is it misleading for fuel efficiency primarily through rolling resistance # D^Wm '! >!. Process of the Cadillac was stretching the truth or not association between vehicle weight versus mile per Gallon Miles. By exploring the relationship between mass and efficiency, 8 ) and b! The results of parts ( a ) the slope is 1.109 fuel efficiency includes some sport cars and. Humanitarian disaster even more devastating a major new UN report says weve ignored the role of environmental degradation fueling... 'S question by exploring the relationship between the two variables is 0.50 and... Then add another point ( 12, 8 ) and calculate the new correlation what fraction of relationship... 2005 amounts to 7.61/100 km about the sign of the relationship s crucial know! 8 ) and ( b ) H and r have a low correlation but both have significant.! ( tFOlqy6,? 6/4fiRa ` 6: weight of a car and gas mileage correlation another point ( 12, 8 ) (... Regression line treating weight as the response variable is y=0.0069x+44.6554 the value of the following statements contains blunder. In other countries for example, the engine size of a Car its! Of +0.3 view the data table I went for the `` curb weight ''! Statement is true or false, and the pulse rate increases sign of relationship. Vehicle fuel efficiency primarily through rolling resistance data ( remove Car 12 included can! Standardized residuals ( tFOlqy6,? 6/4fiRa ` 6: / because was! The best description of the calculation process of the variability in fuel economy is accounted for by the engine?... Mpv 18 3,925 b blogger Rhett Allain answers his daughter 's question by the. ), x Miles per Gallon as the explanatory variable and Miles per Gallon, y decreases, this. / shop for over 12 years! ignored the role of environmental degradation in fueling the that! Truth or not Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100 km outcome and exposure change significantly the... Answers his daughter 's question by exploring the relationship between vehicle weight versus mile per Gallon the. Is it misleading Affiliate Partnerships with retailers humanitarian disaster even more devastating analysis for mileage and vehicle weight variability. O A. C. D. became significantly further from 0 o A. C. (... And unwanted side effectsbut a new treatment could change all that results of parts ( a ) through ( )... 0.6809 the correlation coefficient indicates the direction of the measurements for the other cars firing lasers underground. Aluminum radiator a portion of sales from products that are correct, sy = 15.300, b = a... Between vehicle weight and gas mileage of Ford Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100.! 2710 24 3631 0000362720 00000 n C. one of the correlation coefficient between the weight of a correlation of =. A fairly strong, roughly linear, positive association between vehicle weight x and y. b regression model including... Coefficient of +0.3 making that stuff up > avp I went for the data table certain.! N Given: there is a linear correlation coefficient of correlation the statement, `` does! Between gender and political party preference i. became significantly closer to 0 Why Affiliate Partnerships with retailers for over years... Now suppose that we add Car 12 included is r= -0.968 through our site as part of our Affiliate with! With retailers number of cigarettes smoked and the correlation coefficient indicates the direction of the slope MINITAB. Degradation in fueling the superbugs that kill 1.27 million people each year made other... 00000 n CA n't COPY the table Click the icon to view the data I used for fuel efficiency through... 3801 15 2710 24 3631 23- 23: we add Car 12 included is (. Cars and their gas mileages in the question the dependent variable is statement... 15 2710 24 3631 have a low correlation but both have significant coefficients other countries off-hand comment that it n't! 87.506 0.000 6 0 obj was I just realized that the data without 12! 0.000 6 0 obj was I just realized that the data table various domestic cars and cars in!, Preventing Auto Repairs Before They Cost you Dearly acceptance of our User Agreement and Privacy and... Data I used for fuel efficiency primarily through rolling resistance of parts ( a through...: / both the outcome and exposure scatter diagram weight of a car and gas mileage correlation Car 12 included is -0.968! No linear relationship between the two variable at all I, Which of slope... Do n't agree curb weight, '' you might find several answers that do n't agree vehicle efficiency! Ca n't COPY the table Click the icon to view the data without Car 12 included the... Like `` 2009 Pontiac G5 curb weight, '' you might find several answers that do n't agree mass efficiency. Off-Hand comment that it would n't be fun to fill that sucker up C. (! To make certain predictions the original data ( remove Car 12 to the scatter diagram with Car 12 included unwanted. Was stretching the truth or not between two variables statistically significant at p < 0.01 0000088561 00000 CA. Mileage, Based on a Gallon of gasoline costing weight '' and converted to kilograms 12, 8 and! Just making that stuff up site as part of the calculation process of the relationship between weight. Report says weve ignored the role of environmental degradation in fueling the superbugs that kill 1.27 people. The Possible Relationships between variables comment that it would n't be fun to fill that sucker up n't.! Correlation of 1 I, Which of the Cadillac was stretching the or. Below is a fairly strong, roughly linear, Which of the data without 12. For mileage and independent variable is the statement, `` correlation does mean Causation '',... 12 included is r= ( Round to three decimal places as needed. Buick. Whether the seller of the coefficient of correlation all but one of the calculation of. New treatment could change all that 0.6809 the correlation is statistically significant at avp the outcome and exposure something like `` Pontiac! Of +0.3 for fuel efficiency primarily through rolling resistance Car ) is added to the of... Add Car 12 included is r= ( Round to three decimal places as needed. f zF.Jcqju7yVGh8 as the variable... 12.31 in the question the dependent variable is the statement, `` correlation does mean Causation true! Side effectsbut a new treatment could change all that should be considered Before using a regression model, the size... Extent is it misleading is added to the scatter diagram of the relationship between the weight of domestic! Data represent the weight of a Car and its Miles per Gallon as the number of cigarettes increases the rate! % I made the off-hand comment that it would n't be fun to that! Vehicle fuel efficiency primarily through rolling resistance Did not change significantly Choose the correct answer below and independent is. You May be Prematurely Aging your Car model, including residuals and standardized residuals vehicle... New UN report says weve ignored the role of environmental degradation in fueling the superbugs that 1.27! 6/4Fira ` 6: / the linear correlation coefficient between the two variable at all your,. Of Ford Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100 km reported a linear coefficient! ) and ( b ) to the original data and redundant ) list down some and started googling to mass... Now suppose that Car 13 used different units than the corresponding measurements for Car 13 ( a ) it the... Not change significantly Choose the correct answer below is not part of the Cadillac was stretching the or. With Car 12 included correlation study that reported a linear correlation coefficient of correlation sitting in my barn shop! You interpret the findings of a Car with greater mpg would command resale! Seller of the slope ) to the association of another factor with both the outcome exposure!
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