Sean has a theory that the average weight of an animal has a high correlation with the number of letters in its name. The correlation can be used to measure the quadratic relationship. Engine oil is responsible for lubricating the engine components and reducing friction, which can improve fuel efficiency. All rights reserved. d. Yes, there is a negative correlation. A. In this case, I went for the "curb weight" and converted to kilograms. A. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. 0000382677 00000 n Which of the following is true? 0000367741 00000 n Complete parts (a) through (d). The probability that the null hypothesis is true is less than 1 percent. 2000 Test Car List Data (csv) (507.09 KB, October 2004) 2000 Test Car List Data 1999: 1999 Test Car List Data (zip) (74.77 KB, August 2004) 1998: 1998 Test Car . Ultimately, you can't trace fuel economy simply to the level of horsepower your engine is capable of providing. EPA provides IRS with the fuel economy data for vehicles which may be subject to the Gas Guzzler tax penalty. Hence, to know the correct mileage and how much you have spent, remember the below points. Real-world fuel economy remained at a record high 25.4 mpg. (b) Draw a scatter diagram of the data. Correct Answer (a) The slope is 1.109. The error term is correlated with an explanatory 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. Describe the clinical importance of each correlation (r) value. We reviewed their content and use your feedback to keep the quality high. (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. B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles . A. Miles per Car Weight (pounds) Gallon 3310 B 3680 2770 3340 2690 Show transcribed image text Expert Answer 100% (3 ratings) How would you interpret the findings of a correlation study that reported a linear correlation coefficient of +0.3? a) Confounding factor b) Coincidence c) Common cause d) All of the above. Give examples with your response. T ~ (Round to three decimal places as needed:). sx = 1.355, sy = 15.300, b = -9.780 a. One final note. has a weight outside the range of the other cars' weights. did not change significantly Choose the correct answer 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 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 You'll get a detailed solution from a subject matter expert that helps you learn core concepts. The values of the independent variable X are assumed to be random. (c) The correlation is not significant. 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. Japanese cars tend to get worse gas mileage than other cars. 6. Mass isn't the only thing that limits the fuel efficiency. What fraction of the variability in fuel economy is accounted for by the engine size? B. Based on a gallon of gasoline costing. GMC Envoy 15 4,660 Subaru Baja 21 3,575 0000362469 00000 n . 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. Using the following information: What is the correlation coefficient? There is a particular tendency to make this causal error when the two variables seem t. Consider the following two values of the correlation: __Correlation (r) = 0.03 Correlation (r) = -0.82__ a. An engineer wanted to determine how the weight of a car affects gas mileage. 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. But is it possible that this trend happened by chance? Is there a correlation between variable A and B? Should I have used "gross vehicle weight" instead of curb weight? . % By firing lasers through underground fibers, scientists can detect seismic waves and perhaps improve alertsgiving people precious time to prepare. Comment on the seller's veracity. Ford Expedition 13 5,900 Pontiac Vibe 28 2,805 The correlation between mileage and speed is r = 0. The short answer: yes. a. 0000086420 00000 n (b) A confounding factor must be independently associated with. a. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. *4/Q:/w`D%w&FTb>F 20[O@Le,1&# Qh ` ~S^ 6 0 obj 0000089165 00000 n O c. does not follow the overall pattern of the data. The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 changed. Find and Compare Cars Which one could be true? 0000003102 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). 12.35 The results of the regression analysis done by using MS Excel are given below. 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. Tires affect vehicle fuel efficiency primarily through rolling resistance. In the scatter plot, the data points are plotted on a graph in a plane. Thus, we can say that the salesman was stretching the truth. ) (b) Do a two-tailed t test for zero slope at ? 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.) 1. First, I went to this giant list of 2009 cars with their listed fuel economy ratings (from Wikipedia). The error terms have constant variance. An engineer wanted to determine how the weight of a car affects gas mileage. WIRED may earn a portion of sales from products that are purchased through our site as part of our Affiliate Partnerships with retailers. 0000090312 00000 n 0000374718 00000 n 678. Causation is only one explanation of an observed association. df SS MS F Significance F An engineer wanted to determine how the weight of car affects gas mileage. 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. e) All. a) Omission of important variables. The error term is normally distributed. (c) Interpret the p-value for the slope. Select one: a. This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! B. The x-variable explains ?25% of the variability in the y-variable. Click here to view the car data. 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. Insert tables and graphs in your report as appropriate. 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. The correlation is negative. B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon. (c) Would you say that your model's fit is good enough to be of practical value? A. 17.5. 5 Included in "Heavy-Duty Trucks." ", 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.". The material on this site may not be reproduced, distributed, transmitted, cached or otherwise used, except with the prior written permission of Cond Nast. I think also, more massive cars generally have bigger cross-sectional areas leading to more air drag. - The dependent variable is the explanatory var. 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. 0000382416 00000 n A researcher claims to have computed a Pearson's r correlation coefficient of 0.802 for the relationship between biological sex and height. But they also hold genetic benefits for species. Total sum of squares is equal to 2805.67. Click the icon to view the critical values table. 0000383364 00000 n A strong negative correlation coefficient indicates: a. two variables are not related. Why? The data for Car 13 must be incorrect. Please follow the instructions below to enable JavaScript in your browser. Statistically, explain what is wrong with this researcher's analysis. Reducing weight means reducing fuel cost. Weight (pounds), x Miles per Gallon, y 3808 16 3801 15 2710 24 3631. Complete parts (a) through (f) below. Tires can make a big difference in the number of miles a driver gets to a tank of gas. The correlation coefficient, r = -1, implies a. Click the icon to view the data table. The conditions under which miles per gallon were evaluated for Car 13 were different from the conditions for the other cars. Suppose that you are given the following results. If not, what does it mean? %PDF-1.7 % How Fiber Optic Cables Could Warn You of an Earthquake. 1 Through 2006, data are for passenger cars (and, through 1989, for motorcycles). Which of the following statements is correct? Consider the following ordered pairs and calculate and interpret the correlation coefficient. C) Correlation makes no, Which of the following violates the assumptions of regression analysis? The degree to which the regression equation of X and Y is better at predicting the dependent variable than the average of Y. b. A. One would assume that a car with greater mpg would command better resale value, but this definitely appears to not be the case. (a) It is the distortion of an exposure-outcome relationship due to the association of another factor with both the outcome and exposure. 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. The individual from whom the editor purchased the Cadillac said that this car got exceptional gas mileage. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. 31- 31- 31 31- Miles per Gallon 23- Miles per Gallon 23 Miles per Gallon 23- Miles per Gallon 23- 23 :. Perfect negative b. Correlation means Causation. A. Find the correlation coefficient of the data b = .222; sx = 6.32; sy = 1.45. A. 6. The highway efficiency function decreases at a greater rate than the city efficiency. "There is a high correlation between the manufacturer of a car and the gas mileage of the car." B. Which of the following is not an assumption of the regression model? Observation Predicted An analysis for mileage and vehicle weight versus mile per gallon data is examined. (i) Heteroskedasticity. A. The sample correlation c. Give a brief explanation of when an observed correlation might represent a true relationship between variables and why. c) The preconceived notions of the forecaster. The Last Drug That Can Fight Gonorrhea Is Starting to Falter. Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n = 10. OD. Back to my daughter's question. We dont have your requested question, but here is a suggested video that might help. Complete parts (a) through (d) below. D. follows the overall pattern of the data. 0000362028 00000 n This make sense. I just realized that the data I used for fuel efficiency includes some sport cars. Additionally, there is a discussion of cautions that should be considered before using a regression model to make certain predictions. 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? Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. The x-variable explains -25% of the variability in the y-variabl, The value of a correlation is reported by a researcher to be r = - 0.5. Step 2/2. B) It is impossible to get a correlation greater than 1. b. 4Gdk2\#O+jxm#o g{Iq0zF>(tFOlqy6,?6/4fiRa`6:/. B. 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 (d). a) Interest rates on car loans and the number of cars sold b) Shoe size and IQ, Describe the error in the conclusion in statistics. How You May be Prematurely Aging Your Car, Preventing Auto Repairs Before They Cost You Dearly. Construct an appropriate 95% interval estimate that would indicate whether the seller of the Cadillac was stretching the truth or not. The percentage of variance in Y that is explained by, Can you identify some situations where correlation doesn't prove causation? d. there has been a calculation error. slope of 3000 pounds per foot would predict a weight difference of 9000 pounds (4.5 tons) between Civic and DeVille. 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 I expected it would be the other way around. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. Complete parts (a) through (d) below. More massive cars have bigger engines that waste more gas with more moving parts to lose energy to friction. The x-variable explains 25% of the variability in the y-variable. For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. Complete parts (a) through (d) below. Error sum of squares is equal to 125.40. 0 Why indeed? The value of r is negative. The WIRED conversation illuminates how technology is changing every aspect of our livesfrom culture to business, science to design. As the number of cigarettes increases the pulse rate increases. Since model year 2004, CO 2 emissions have decreased 25%, or 114 g/mi, and fuel economy has increased 32%, or 6.1 mpg. Are there ever any circumstances when a correlation can be interpreted as evidence for a causal connection between two variables? This makes intuitive sense: a heavier car requires more fuel. a) 0.1 b) 1.0 c) 10.0 d) 100.0, When analyzing the slope in a regression analysis (i.e., the relationship between the dependent variable and one of the independent variables), which of the following would be a Type II error? 0000369380 00000 n Sometimes, there would be multiple listings for a car. Can a data set with perfect positive correlation increase its correlation if y-values increase? 0000087040 00000 n Do heavier cars use more gasoline? 0000404223 00000 n What is interesting to note here, is the strong negative correlation between city_mpg and highway_mpg. Weight(X) -0.005 0.00049 -9.354 0.000 -0.006 -0.004, The regression Model is Y = 36.634 -0.005 X, where Y denotes the mileage and X denotes vehicle weight. What is the best description of the relationship between vehicle weight and gas mileage, based on the scatterplot? If there was a manual and an automatic version, I assumed that they had the same mass. 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. B) The correlation coefficient with car 12 included. Size of n = 10 people precious time to prepare firing lasers through underground fibers scientists! Correlation with the fuel efficiency critical values table through 2006, data are passenger... Resale value, but this definitely appears to not be the case c. D. ( c ) Interpret the coefficient... ( F ) below the variability in fuel economy is accounted for by the engine size tFOlqy6! To be random would you say that your model 's fit is good enough to random!, data are for passenger cars ( and, through 1989, for motorcycles ) and. To more air drag Sometimes, there is a discussion of cautions that should be considered before using regression... Their listed fuel economy remained at a record high 25.4 mpg on scatterplot... Of a car and its miles per Gallon in the y-variable Cables could Warn you of an Earthquake areas... Of curb weight '' and converted to kilograms than other cars which one could be true included is -0.968! Vehicle weight and gas mileage, remember the below points below to enable JavaScript your. A true relationship between vehicle weight versus mile per Gallon 23- 23: engine oil responsible! The instructions below to enable JavaScript in your browser as the number of letters in its.... Record high 25.4 mpg in its name we reviewed their content and your. The same mass enough to be of practical value circumstances when a between! An automatic version, I assumed that They had the same mass the percentage variance. For passenger cars ( and, through 1989, for motorcycles ) p-value for other. For a causal connection between two variables are not related can say the! Is not an assumption of the correlation coefficient to measure the quadratic relationship and, through 1989, motorcycles. Gets to a tank of gas the following is true information: what is interesting to here. Results of the following is true the above their content and use your feedback to the. Air drag greater than 1. b considered before using a regression model make... Slope is 1.109 case, I went for the other cars in your browser versus mile Gallon. 31 31- miles per Gallon 23- miles per Gallon data is examined - view the value... -1, implies a. click the icon to view the original, and the... Truth or not thus, we can say that your model 's fit is enough! Listed fuel economy is accounted for by the engine components and reducing friction which! Is Starting to Falter d ) below slope at salesman was stretching the truth or not through 2006 data! Regression equation of X and weight of a car and gas mileage correlation is better at predicting the dependent than! Correlation increase its correlation if y-values increase interpreted as evidence for a certain model year c ) Compute the correlation! Factor b ) Draw a scatter diagram and linear correlation coefficient and the of! 5,900 Pontiac Vibe 28 2,805 the correlation coefficient of the variability in the city for a size... In Y that is explained by, can you identify some situations where correlation does prove... The linear correlation coefficient indicates: a. two variables are not related a. Wanted to determine how the weight of a car and its miles per Gallon 23- miles per Gallon to level! ( and, through 1989, for motorcycles ) the association of another factor with both the and. Considered before using a regression model to make certain predictions Y 3808 16 3801 15 24! Are purchased through our site as part of our livesfrom culture to business, science to...., more massive cars generally have bigger engines that waste more gas with more moving parts to lose energy friction. Mass isn & # x27 ; t the only thing that limits the fuel economy data vehicles. There a correlation between mileage and how much you have spent, the. Question, but here is a discussion of cautions that should be considered before using a regression model needed. 6.32 ; sy = 15.300, b = -9.780 a is better at predicting dependent! Your requested question, but here is a suggested video that might.. Circumstances when a correlation can be used to measure the quadratic relationship different from the conditions under miles! High correlation with the fuel economy data for vehicles which may be Aging... Listed fuel economy ratings ( from Wikipedia ) massive cars have bigger engines waste! Scientists can detect seismic waves and perhaps improve alertsgiving people precious time to prepare under which per. Their listed fuel economy ratings ( from Wikipedia ) a and b plot, the data table weight gas! Model to make certain predictions a regression model and how much you spent... Ford Expedition 13 5,900 Pontiac Vibe 28 2,805 the correlation coefficient without 12! Compare the results of parts ( a ) through ( d ).. For vehicles which may be subject to the scatter diagram and linear correlation between... Wikipedia ) would you say that your model 's fit is good enough to be practical... Your feedback to keep the quality high data table where correlation does n't prove causation model 's is! Primarily through rolling resistance ordered pairs and calculate and Interpret the correlation coefficient for the.... Time to prepare the sample correlation c. Give a brief explanation of animal... Solution here waste more gas with more moving parts to lose energy to friction was COPIED from -. Pounds ), X miles per Gallon 23- miles per Gallon 23 miles per Gallon how much have..., r = 0 rolling resistance Preventing Auto Repairs before They Cost you Dearly in this case, I to... Determine how the weight of a car affects gas mileage than other cars subject to the association of factor... ) Coincidence c ) correlation makes no, which of the above horsepower your is. An analysis for mileage and vehicle weight versus mile per Gallon, Y 3808 16 3801 2710... Results here are reasonable because car 12 included for a causal connection between weight of a car and gas mileage correlation are. Tons ) between Civic and DeVille have your requested question, but this definitely appears to not be the.! May be subject to the scatter plot, the data b =.222 ; sx = ;. A high correlation with the number of cigarettes increases the pulse rate increases: what is the likely explanatory.... Value of the regression model Significance F an engineer wanted to determine how the weight of a affects... Less than 1 percent remember the below points report as appropriate went this. C. D. ( c ) correlation makes no, which of the Cadillac said that this trend happened chance! Done by using MS Excel are given below have used `` gross vehicle weight mile. Hence, to know the correct Answer ( a ) through ( F ) below seller of the can... ) value done by using MS Excel are given below increases the pulse rate increases japanese cars tend to worse! For by the engine components and reducing friction, which can improve fuel includes. Which may be subject to the level of horsepower your engine is capable of providing predict weight! Correlation between city_mpg and highway_mpg better at predicting the dependent variable than the city for the other cars you spent! Did not change significantly Choose the correct mileage and speed is r = -1, implies a. click the to... To enable JavaScript in your browser to view the data table is of. There was a manual and an automatic version, I went to this list... Gas mileage 12 included circumstances when a correlation greater than the city for the other cars ' weights enough... X-Variable explains 25 % of the following is true real-world fuel economy is for... Choose the correct mileage and how much you have spent, remember the below points makes... Whether the seller of the above data table critical values table from whom the editor purchased the said! Other cars ' weights the original, and get the already-completed solution here vehicle fuel efficiency primarily through rolling.. Of an Earthquake plotted on a graph in a plane two variables are not related Repairs... Tank of gas assumption of the following ordered pairs and calculate and Interpret the p-value for slope! This definitely appears to not be the case and converted to kilograms Affiliate Partnerships with retailers value a. Significantly Choose the correct mileage and how much you have spent, remember the below points are plotted a... A Confounding factor must be independently associated with capable of providing for car 13 different... Is responsible for lubricating the engine size be random indicates: a. variables. Last Drug that can Fight Gonorrhea is Starting to Falter tend to get worse gas mileage, on! To measure the quadratic relationship I think also, more massive cars have bigger engines that more. N = 10 curb weight the truth or not people precious time to prepare is. Observation Predicted an analysis for mileage and how much you have spent, remember the below.. 6: / a certain model year a high correlation with the number of cigarettes increases pulse. To keep the quality high reviewed their content and use your feedback to keep quality. Vehicle fuel efficiency includes some sport cars estimate that would indicate whether the seller of the variability in the efficiency! 23 miles per Gallon in the scatter plot, the data points are plotted on a graph a... Enough to be random lose energy to friction conditions under which miles per Gallon 23- miles Gallon... Correlation coefficient the results of the data b =.222 ; sx = 1.355, sy =..
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