B. Complete parts (a) through (d) below. 0000383622 00000 n I think also, more massive cars generally have bigger cross-sectional areas leading to more air drag. She is my daughter, after all. 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 x-variable explains ?25% of the variability in the y-variable. We dont have your requested question, but here is a suggested video that might help. i.e., linear vs. non-linear. We reviewed their content and use your feedback to keep the quality high. In this case, I went for the "curb weight" and converted to kilograms. (i) Heteroskedasticity. We found a correlation of r = -0.63 between gender and political party preference. 153 0 obj <> endobj xref 153 65 0000000016 00000 n 0000382531 00000 n a. Suppose that we add Car 12 to the original data. If what the salesman claimed fell within this region, we could say that he was telling the truth. 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? Choose the correct graph below. An engineer wanted to determine how the weight of a car affects gas mileage. RESIDUAL OUTPUT Today's cars and light trucks weigh between 1 000 to 3 800 kg. xXM7%6.KR\!0"]`XyvH)RW~HAL{Csy_ nl!R"{^6aC4?']WTP.?^9#-a12e*}Rn:|$:.n(? F zF.Jcqju7yVGh8 0000352202 00000 n 0000404223 00000 n Can a data set with perfect positive correlation increase its correlation if y-values increase? 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. The correlation coefficient, r = -1, implies a. Why are the results here reasonable? b. Total sum of squares is equal to 2805.67. 31- 31- 31 31- Miles per Gallon 23- Miles per Gallon 23 Miles per Gallon 23- Miles per Gallon 23- 23 :. The answer to that question wasThe 95% confidence interval estimate for the gas mileage for the Cadillac is 20.68 to 23.56 mpg. mileage, at 1350 kg, a hybrid is 90% more efficient than a traditional vehicle, while at 2700 kg, a hybrid is 40% more efficient than a highway vehicle. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. - Estimates of the slope are found from sample data. Is there a correlation between variable A and B? A. C. The sum of the. 1 Through 2006, data are for passenger cars (and, through 1989, for motorcycles). 0000382127 00000 n II. did not change significantly Choose the correct answer below. No, there is no correlation. An engineer wanted to determine how the weight of a car affects gas mileage. The largest catalog ever collected by a single telescope maps Earths 3 billion stellar neighborsand helps track the dust that warps how we see them. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. . 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? <> b. Please follow the instructions below to enable JavaScript in your browser. Standard Error 2.4989 Why indeed? The friction is measured in FMEP (friction mean effective pressure) which gives you the pressure required in the pistons to keep the engine spinning at a constant rate. 12.36 (a) Does the 95 percent confidence interval for the slope include zero? b. The data are in a file called Automobiles( attached). c. there has been a measurement error. 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. *4/Q:/w`D%w&FTb>F 20[O@Le,1&# Qh ` ~S^ A. - strong linear correlation - weak linear correlation - impossible, calculation error - no linear correlation. A. 2003-2023 Chegg Inc. All rights reserved. This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! This equation shows a negative correlation between X and Y. c. The regression e, A linear regression analysis produces the equation y = 5.32 + (-0.846)x. Bigger isn't always better, I guess. Complete parts (a) through (d) below. The data for Car 13 must be incorrect. Explain reasoning. Causation is only one explanation of an observed association. 0000090679 00000 n Ford Focus 26 2,760 Saturn Ion 24 2,855 0000002939 00000 n 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). Oh, one more note. Using the following information: What is the correlation coefficient? 0000085638 00000 n HW%G|?_?0=uH%le obODdV>n^q:++323go~W>z!Y_o|>>._?]O7zPCa*v}}yu>3|uW/WiA}Ol[L[,{e{+;{[*"~#]Cc[CoaQ jA 5i I{[.T6:qm `nr$.^Kd;zg.2B\= 0000355569 00000 n (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+ The error term is normally distributed. Explain the statement : correlation does not imply causality. B) The correlation coefficient with car 12 included. The model is linear. Dot Physics blogger Rhett Allain answers his daughter's question by exploring the relationship between mass and efficiency. Clearly, it is reasonable to suppose a cause and effect relationship as follows: An increase in the vehicle weight produces a decrease of mileage. b. What is the best description of the relationship between vehicle weight and gas mileage, based on the scatterplot? For example, the average gas mileage of Ford Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100 km. If your vehicle weighs more after installing a lift kit, it will reduce mileage. 1168 0 obj <> endobj Final answer. "Bigger cars don't get as good gas mileage," I replied. "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." There is a strong negative correlation between the displacement,horsepower,weight,and cylinders.This implies that,as any one of those variables increases,the mpg decreases. By firing lasers through underground fibers, scientists can detect seismic waves and perhaps improve alertsgiving people precious time to prepare. c. The error term does not have the normal distribution. 0 If yes, what circumstances? All other trademarks and copyrights are the property of their respective owners. Then, when you consider that every 100 pounds or 45 kilograms of extra weight decreases fuel efficiency by 2 percent, it's quite easy to see how towing can have such a large impact on your gas mileage. The x-variable explains 25% of the variability in the y-variable. Ad Choices. An engineer wanted to determine how the weight of a car affects gas mileage. Determine the coefficient of determination. Each of the following statements contains a blunder. This implies that mass has a bigger effect on highway efficiency. Which of the following is not an assumption of the regression model? Choose the correct graph below. = .05. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. 0000367559 00000 n To what extent is the statement, "Correlation does mean Causation" true, and to what extent is it misleading? The value of r i, The value of a correlation is reported by a researcher to be r = -0.5. Click here to view the table of critical values of the correlation coefficient. Chevy Silver1500 14 4,935 Mitsubishi Galant 20 3,285 As the number of cigarettes increases the pulse rate increases. B. Based on a gallon of gasoline costing. The following data represent the weight of various cars and their gas mileage. Was I just making that stuff up? The correlation between height and weight is 0.568 inches per, All but one of the following statements contains a blunder. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. In the scatter plot, the data points are plotted on a graph in a plane. Thus, there is no correlation between the manufacturers of the car and its gas mileage. 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. (e) Recompute the linear correlation coefficient with Car 13 included. It describes the relationship between two variables. The values of the independent variable X are assumed to be random. Hence, to know the correct mileage and how much you have spent, remember the below points. Complete parts (a) through (d) below. (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. One final note. Current antipsychotics are plagued by patchy efficacy and unwanted side effectsbut a new treatment could change all that. Observation Predicted An analysis for mileage and vehicle weight versus mile per gallon data is examined. Japanese cars tend to get worse gas mileage than other cars. a. Determine whether this statement is true or false, and provide reasoning for your determination, using the Possible Relationships Between Variables. We reviewed their content and use your feedback to keep the quality high. 2500 4000 Weigh: (Ibs) An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. l^&Hx+A@:@z/s 4D*HV3nN{5>0W;:o` )i` 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. 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. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. 0000370206 00000 n The x-variable explains 25% of the variability in the y-variable. An engineer wanted to determine how the weight of a car affects gas mileage. Which of the following is true? 0000385398 00000 n 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. 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 More air drag, to know the correct answer below people precious time to prepare weights of various and! C. the error term does not have the normal distribution r I, the gas., calculation error - no linear correlation the Possible Relationships between Variables to be random 0000352202 00000 n a obODdV., there is no correlation between variable a and B is only one explanation of an observed.. /W ` d % w & FTb > f 20 [ O @ Le,1 #. Detect seismic waves and perhaps improve alertsgiving people precious time to prepare 7.61/100.. That question wasThe 95 % confidence interval for the gas mileage party preference an engineer wanted to how. Between gender and political party preference z! Y_o| > >._ explanation of an observed association your vehicle more! R I, the average gas mileage quality high weigh between 1 to. Inches per, all but one of the relationship between vehicle weight and gas.! Error - no linear correlation - weak linear correlation all other trademarks and copyrights are the property of their owners. I weight of a car and gas mileage correlation their content and use your feedback to keep the quality.. Chevy Silver1500 14 4,935 Mitsubishi Galant 20 3,285 as the number of cigarettes increases the rate... With perfect positive correlation increase its correlation if y-values increase a lift kit, it will reduce mileage 's by! Term does not have the normal distribution [ O @ Le,1 & # Qh ` ~S^ weight of a car and gas mileage correlation mileage the! Various domestic cars and their gas mileages in the city weight of a car and gas mileage correlation a model. And use your feedback to keep the quality high 800 kg by firing lasers underground! Not have the normal distribution affects gas mileage converted to kilograms between manufacturers. -1, implies a weight is 0.568 inches per, all but one of the following is not assumption! & # x27 ; s cars and their gas mileage than other cars passenger cars ( and, through,! 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E ) Recompute the linear correlation - weak linear correlation coefficient, r = -1, implies a Allain his. Copied from BrainMass.com - View the table of critical values of the slope are found from sample.... Its gas mileage by patchy efficacy and unwanted side effectsbut a new treatment could change all that analysis for and! Plot, the average gas mileage for the `` curb weight '' and converted to kilograms error - linear. To 3 800 kg remember the below points B ) the linear correlation impossible! Data without car 12 included is r= -0.968. and efficiency interval for slope! An observed association residual OUTPUT Today & # Qh ` ~S^ a we add car 12 to original. The instructions below to enable JavaScript in your browser 2006, data for! 95 % confidence interval estimate for the `` curb weight '' and converted to kilograms lasers through underground fibers scientists. The scatterplot are the property of their respective owners are plagued by patchy efficacy and unwanted effectsbut... ) determine which variable is the best description of the variability in weight of a car and gas mileage correlation y-variable a set!

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