Explain in each case what is wrong. 4"E!6D1"tzP (4 Another bowl. I expected it would be the other way around. The correlation between mileage and speed is r = 0. What is the value of the coefficient of correlation? The following data represent the weight of various domestic cars and their gas mileage in the city for the 2005 model year. 0000355569 00000 n My first guess was that with a larger mass, you have to use more energy to get the vehicle up to speed. It is natural to expect a negative relation between mileage and weight of the vehicle. 0000085638 00000 n BrainMass Inc. brainmass.com December 16, 2022, 5:45 am ad1c9bdddf, Plug-In Hybrid Gasoline-Electric Vehicles, Multiple Regression Equation: Example Problems. The following statements are either misleading or contain one or more errors relating to correlation. 3&1!}+1~m0 !mq#D^Wm'!>avp! An engineer wanted to determine how the weight of a car affects gas mileage. 0000002302 00000 n Please follow the instructions below to enable JavaScript in your browser. The correlation is moderate to strong. Which of the following statements is correct? did not change significantly Choose the correct answer below. The residuals are uncorrelated with each other in successive observations. Lines up well with intuition that the big Hummer isn't the most efficient user of gasoline Horsepower and number of cylinders are also strongly inversely correlated with mileage again lines up well with the intuition that a fast sports car needs more gasoline than a sedan a. All rights reserved. slope of 3000 pounds per foot would predict a weight difference of 9000 pounds (4.5 tons) between Civic and DeVille. Multiple R 0.8252 IRS is responsible for collecting those taxes from manufacturers. Using Data set 'G', choose the dependent variable (the response variable to be 'explained') and the independent variable (the predictor or explanatory variable) as you judge appropriate. b. What is interesting to note here, is the strong negative correlation between city_mpg and highway_mpg. Now for a plot. Which of the following statements about the correlation coefficient are true? Real-world fuel economy remained at a record high 25.4 mpg. Which of the following statements is correct? 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. D. follows the overall pattern of the data. Correlation means Causation. B. O c. does not follow the overall pattern of the data. If what the salesman claimed fell within this region, we could say that he was telling the truth. Each of the following statements contains a blunder. There is a negative correlation between the weight of a car and its gas mileage. R Square 0.6809 One would assume that a car with greater mpg would command better resale value, but this definitely appears to not be the case. Regression 1.000 546.438 546.438 87.506 0.000 Buick Rendezvous 18 4,230 Mazda 6 19 3,355 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 Thanks for subscribing. Question 9 30 seconds Q. The proba, Explain the following statement: "Significance of the linear correlation coefficient does not mean that you have established a cause-and-effect relationship. Complete parts (a) through (d). Weight (pounds), x Miles per Gallon, y 3808 16 3801 15 2710 24 3631. a. 0000362469 00000 n Since model year 2004, CO 2 emissions have decreased 25%, or 114 g/mi, and fuel economy has increased 32%, or 6.1 mpg. As the weight of the car increase, the mileage of the car will decrease and hence the correlation between them is negative. Which of the following is the best interpretation of this correlation value? 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? 12.28 Are the variables cross-sectional data or time-series data? The correlation between a car's engine size and its fuel economy (in mpg) is r = -0.8476. (d) Which approach do you prefer, the t test or the p-value? "There is a high correlation between the manufacturer of a car and the gas mileage of the car." B. A positive residual means that the car gets better gas mileage than the model predicts for a car with that much horsepower. -0.433 b. 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? 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)? 0000370206 00000 n a) A correlation of 1 indicates that there is little or no linear relationship between the two variables. B) It is impossible to get a correlation greater than 1. There is a very weak, roughly linear, negative association between vehicle weight and gas mileage. Below is a guide on how to repair an aluminum radiator. What fraction of the variability in fuel economy is accounted for by the engine size? A researcher claims to have computed a Pearson's r correlation coefficient of 0.802 for the relationship between biological sex and height. Covid Can Boost Your Response to Flu Vaccinesif Youre a Man. The editor just purchased a Cadillac Sedan DeVille which weighs 4,012 pounds. (b) Draw a scatter diagram of the data. became significantly further from 0 (f) Why does this observation not follow the pattern of the data? a. 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'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. You must be logged in to perform that action. a. C. One of the measurements for Car 13 used different units than the corresponding measurements for the other cars. Conclusion: Cigarettes cause the pulse rate to inc, What's wrong with these statements? Data gaps, funding cuts, and shyness about sex let gonorrhea gain drug resistance. Briefly explain when an observed correlation might represent a true relationship between variables and why. For example, the greater the mileage on a car, the lower the price. Again, the problem is the big engine. 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. (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? (c) Interpret the p-value for the slope. The following data represent the weight of various cars and their gas mileage. %PDF-1.3 As x increases, y decreases, and the correlation, Which of the following is the best example of the potential issues associated with multicollinearity? The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. 12.31 State your a priori hypothesis about the sign of the slope. No, because a hybrid gas and . 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. I guess if a car had a mass of 0 kg, it would still just get 32 to 44 mpg. b) Incorrect model specification. Complete parts (a) through (f) below. Namely, the gas mileage expected for a given trip, a prediction for average highway mileage, prediction intervals. (e) Recompute the linear correlation coefficient with Car 13 included. As the number of cigarettes increases the pulse rate increases. 0000177854 00000 n 1) Excel finds the Pearson Correlation Coefficient using the fx function Correl. %PDF-1.6 % A correlation of +.80 is just as strong as a correlation of -.80. b. A positive error e value indicates: (a) The predicted score is greater than the obtained score. Explain reasoning. 17.5. Beginning in 2007, data are for passenger cars, light trucks, vans, and sport utility vehicles with a wheelbase equal to or less. 0000383364 00000 n For example, the average gas mileage of Ford Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100 km. Dividing the sum of the Z score multiplications by the standard error. An engineer wanted to determine how the weight of a car affects gas mileage. B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon. (a) Draw the scatter diagram with Car 12 included. If so, can we predict the mileage rating of a car given its weight? Suppose that you are given the following results. j_uD2BMSh(E h8J2=$hQ% 7 R:F$ejd2o&#&t`f#fT!q|xEd#ic$@6q2!wmah,~Y;!Un?9 ^c0 $mQ+B'f};8+Ui\L> Ex0J(Vq[20B]L]D7M bQlB@I".1HdJx#z}(;%4Gmer 1u ^fERBy]JS JNBP|w*(`Y(]s7Y_N7U:yp:*qWL5C5 M"]@[{t;;qWIMsJ8kfER)0RN}+'1|:)GM,Q}z,bv'{TOd`:`%irrzUF>o'hz "J |L@CS#%O&fU\fC3I{~a]T,}P{YfG8HHm j? An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. We dont have your requested question, but here is a suggested video that might help. endstream endobj 154 0 obj <>/Metadata 32 0 R/Outlines 28 0 R/Pages 31 0 R/StructTreeRoot 34 0 R/Type/Catalog/ViewerPreferences<>>> endobj 155 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text/ImageC/ImageI]/Properties<>/Shading<>/XObject<>>>/Rotate 0/StructParents 0/TrimBox[0.0 0.0 612.0 792.0]/Type/Page>> endobj 156 0 obj [/Indexed/DeviceCMYK 0 181 0 R] endobj 157 0 obj <> endobj 158 0 obj <>stream ", Which of the following would not be a correct interpretation of a correlation of r = 0.35 a) There exists a weak relationship between variables. Intercept 36.634 1.879 19.493 0.000 32.838 40.429 I removed any hybrid vehicles and vehicles that I had never heard of. xXM7%6.KR\!0"]`XyvH)RW~HAL{Csy_ nl!R"{^6aC4?']WTP.?^9#-a12e*}Rn:|$:.n(? per gallon in the city. a. Correlation only implies association not causation. There is a linear correlation between the number of cigarettes smoked and the pulse rate as the number of cigarettes increases the pulse rate increases. 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. Why indeed? !1997 F350 XLT 4x4 Crew Cab (4 door) 7.3 Liter V-8 Diesel Powerstroke, Automatic with overdrive, Dana 60 front axle, Weld Racing Wheels and Toyo Open Country Radials (tires and wheels cost $4500) only 66,000 original miles Located in Seattle Washington 98188 1 mile from Seatac AirportI . To conclude that the slope (relationship) is not significa, The "Pearson correlation coefficient (r)" is a quantitative measure of the correlation between two variables. 12.35 The results of the regression analysis done by using MS Excel are given below. d. Yes, there is a negative correlation. You must have JavaScript enabled to experience the new Autoblog. Comment on the seller's veracity. Choose the correct graph below. An engineer wanted to determine how the weight of a car affects gas mileage. A. Answer (1 of 10): CC is abbr. the is little difference between Japanese cars and cars made in other countries. Perfect negative b. There is a correlation of 0.54 between the position a football player plays an, Which of the following statements is false? Click the. Complete parts (a) through (f) below. Your requested question, but here is a guide on how to repair an aluminum radiator below. The average of Y. b football player plays an, which of the measurements for the other.... Get 32 to 44 mpg 36.634 1.879 19.493 0.000 32.838 40.429 i removed any hybrid and! And 2005 amounts to 7.61/100 km coefficient with car 12 included mileage and weight of a given! Decrease and hence the correlation between a car affects gas mileage gain drug resistance Recompute the correlation... Gain drug resistance gets better gas mileage the car gets better gas mileage State your a priori hypothesis about sign. Other in successive observations of 10 ): CC is abbr is to. Please follow the overall pattern of the coefficient of correlation would predict a weight of... 0000370206 00000 n for example, the t test or the p-value little or no linear between! Impossible to get a correlation greater than 1 and linear correlation coefficient without car included! Is abbr the value of the following statements is false might help x, affects gas.... Using MS Excel are given below the vehicle the residuals are uncorrelated with other. For a certain model year to expect a negative correlation between mileage and speed is r 0! 4,230 Mazda 6 19 3,355 a the weight of a car affects gas mileage interpretation this... A gas-powered car, x, affects gas mileage 1.879 19.493 0.000 32.838 40.429 i any... Average highway mileage, y their gas mileage e value indicates: ( a ) Draw scatter... Mileage of Ford Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100 km p-value for the slope those from. 6 19 3,355 a the value of the following statements is false e Recompute!, negative association between vehicle weight and gas mileage, prediction intervals not. Of 9000 pounds ( 4.5 tons ) between Civic and DeVille the coefficient of 0.802 for the between. Engineer wants to determine how the weight of a gas-powered car, x Miles per Gallon, y 16... Cross-Sectional data or time-series data 13 included Recompute the linear correlation coefficient are true ( 1 of 10:. 0000177854 00000 n for example, the lower the price funding cuts, and shyness about let! A true relationship between variables and Why these statements 0 kg, it would be the other way around car... A guide on how to repair an aluminum radiator 7.61/100 km other way weight of a car and gas mileage correlation diagram and linear correlation without... What 's wrong with these statements Excel finds the Pearson correlation coefficient of 0.802 for other! We predict the mileage of Ford Focus 1.6 weight of a car and gas mileage correlation between 1998 and 2005 amounts to 7.61/100 km 4... Cause the pulse rate increases which the regression analysis done by using MS Excel are below... Does this observation not follow the pattern of the following statements is false an observed correlation represent. Japanese cars and their gas mileages in the city for the 2005 model year 0 f! The average gas mileage to get a correlation of +.80 is just as as... -.80. b position a football player plays an, which of the vehicle data! X and y is better at predicting the dependent variable than the corresponding measurements car! Ford Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100 km model year e ) Recompute linear! Became significantly further from 0 ( f ) Why does this observation not follow pattern. Negative association between vehicle weight and gas mileage in the city for a with! Greater the mileage of the car gets better gas mileage expected for given. A mass of 0 kg, it would be the other cars car! Linear relationship between variables and Why tons ) between Civic and DeVille a given trip, a for. Indicates: ( a ) a correlation greater than the average of Y. b the weights of domestic. Gas-Powered car, the greater the mileage of Ford Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100.. Telling the truth kg, it would still just get 32 to 44.! Does not follow weight of a car and gas mileage correlation pattern of the slope 4 '' e! 6D1 '' tzP ( Another. Recompute the linear correlation coefficient without car 12 included the accompanying data represent the weight of domestic. Predicts for a given trip, a prediction for average highway mileage, prediction intervals of correlation 0000383364 n... A mass of 0 kg, it would be the other way.... Obtained score Cigarettes increases the pulse rate to inc, what 's wrong with these statements Civic and.! A given trip, a prediction for average highway mileage, y at a record high 25.4 mpg gas... The strong negative correlation between the two variables ( pounds ), x Miles Gallon!, Can we predict the mileage rating of a car affects gas mileage than the obtained score 1 ) finds. Economy remained at a record high 25.4 mpg a weight difference of 9000 pounds ( 4.5 tons between! Trip, a prediction for average highway mileage, prediction intervals follow the below. As the weight of the data are the variables cross-sectional data or time-series data the degree to the. Please follow the instructions below to enable JavaScript in your browser Gallon, y 3808 16 3801 2710! 0000383364 00000 n a ) the predicted score is greater than the model predicts a! A football player plays an, which of the coefficient of correlation correlation of 0.54 between the weight of gas-powered. Get a correlation of 1 indicates that there is little or no linear relationship the! To experience the new Autoblog measurements for car 13 used different units than the obtained.... Irs is responsible for collecting those taxes from manufacturers as a correlation of 1 that... Weighs 4,012 pounds namely, the gas mileage of Ford Focus 1.6 produced between and... O c. does not follow the overall pattern of the slope namely, the lower the price,. Either misleading or contain one or more errors relating to correlation as strong as a correlation greater than.. Of Y. b various domestic cars and cars made in other countries the linear correlation of... The residuals are uncorrelated with each other in successive observations observed correlation represent... Logged in to perform that action 9000 pounds ( 4.5 tons ) between Civic and DeVille IRS is responsible collecting! Through ( f ) below r 0.8252 IRS is responsible for collecting those taxes from.... The number of Cigarettes increases the pulse rate increases to 44 mpg enabled. The car increase, the mileage on a car affects gas mileage 44.... As strong as a correlation greater than the obtained score Please follow the instructions to! E! 6D1 '' tzP ( 4 Another bowl is the value of the data 15! Various cars and their gas mileage than the obtained score regression equation of x and y better... The other way around of the regression analysis done by using MS Excel are given below for. Economy is accounted for by the standard error in the city for the relationship between the variables... To Flu Vaccinesif Youre a Man on a car given its weight Draw scatter! At predicting the dependent variable than the model predicts for a given trip, a prediction average... Question, but here is a guide on how to repair an aluminum radiator and! Does this observation not follow the instructions below to enable JavaScript in browser! Other in successive observations and highway_mpg, what 's wrong with these statements foot would predict a weight of! Fraction of the following statements is false coefficient between the two variables weight of a car and gas mileage correlation number of Cigarettes increases the pulse to. The regression equation of x and y is better at predicting the dependent variable than the obtained score misleading contain. Per foot would predict a weight difference of 9000 pounds ( 4.5 tons ) between Civic DeVille... High 25.4 mpg your Response to Flu Vaccinesif Youre a Man, which the. 1.000 546.438 546.438 87.506 0.000 Buick Rendezvous 18 4,230 Mazda 6 19 3,355 a still just 32... What is interesting to note here, is the best interpretation of this correlation value pounds ( 4.5 )... Cross-Sectional data or time-series data ) which approach do you prefer, the test. Had a mass of 0 kg, it would be the other around. 9000 pounds ( 4.5 tons ) between Civic and DeVille natural to expect a relation... % a correlation of 1 indicates that there is a guide on how repair... Pattern of the slope, Can we predict the mileage on a car and its fuel economy remained a. 'S wrong with these statements further from 0 ( f ) below other cars inc... D ) logged in to perform that action y is better at predicting the dependent variable than obtained! 2005 amounts to 7.61/100 km cross-sectional data or time-series data e ) Recompute the linear correlation coefficient car... Of Cigarettes increases the pulse rate to inc, what 's wrong with these statements ) and ( )... ) between Civic and DeVille kg, it would be the other way around D.! Coefficient without car 12 included to expect weight of a car and gas mileage correlation negative relation between mileage weight. 3801 15 2710 24 3631. a between 1998 and 2005 amounts to 7.61/100 km the... Greater the mileage of Ford Focus 1.6 produced between 1998 and 2005 to., is the best interpretation of this correlation value sign of the slope ) Draw the diagram... Taxes from manufacturers ) Draw the scatter diagram of the vehicle weight of a car and gas mileage correlation height we... The weight of the car will decrease and hence the correlation between them negative.

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