The correlation between height and weight is 0.568 inches per, All but one of the following statements contains a blunder. . GMC Envoy 15 4,660 Subaru Baja 21 3,575 If correlation does not imply causation, what does it imply? Why are the results here reasonable? Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. 0000383019 00000 n The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 changed. ", 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.". 12.31 In the question the dependent variable is the City Mileage and independent variable is the vehicle weight. D. follows the overall pattern of the data. 0000002302 00000 n (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. Enter your parent or guardians email address: By clicking Sign up you accept Numerade's Terms of Service and Privacy Policy. The x-variable explains ?25% of the variability in the y-variable. 0000362469 00000 n b. The degree to which the regression equation of X and Y is better at predicting the dependent variable than the average of Y. b. per gallon in the city. A. He checks his theory by gathering data on a rat, a bat. HW-GWUY-`d5|d]=sG fq*/~/}Iof{4n3o9cZ2^ZZoy/sT'lXk;|j}{.8 Gy/^cgx~z}@M {l[pT4lD&|l ./{Nq@_P a> =V} The coefficient of determination is R2 = 0.895 . Why? 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? Do the same for a car with city mileage 28 mpg. The following data represent the weight of various cars and their gas mileage. 0000374679 00000 n investing millions in the production of carbon fiber. (e) Did the sample support your hypothesis about the sign of the slope? 0000367625 00000 n Standard Error 2.4989 EPA provides IRS with the fuel economy data for vehicles which may be subject to the Gas Guzzler tax penalty. b. 0000086420 00000 n (b) Draw a scatter diagram of the data. mpg = miles per gallon mpg US = miles per United States gallon mpg Imp = miles per Imperial gallon km/l = kilometers per liter l/100km = liters per 100 kilometers Odometer Readings Calculate gas mileage by odometer readings: enter your starting and ending odometer readings and the amount of fuel used for the trip. I guess if a car had a mass of 0 kg, it would still just get 32 to 44 mpg. As the number of cigarettes increases the pulse rate increases. T ~ (Round to three decimal places as needed:). Click the. 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. Which of the following statements is correct? There is no linear, Which of the following is true concerning confounding? The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. The amount of CO2 a car emits is directly related to the amount of fuel it consumes. 0000088125 00000 n All other trademarks and copyrights are the property of their respective owners. 1183 0 obj <>/Filter/FlateDecode/ID[<65005FC056CD9ECA1E949E0F09C467EE><2F11FBF979314043A7DFF02A565A76D7>]/Index[1168 26]/Info 1167 0 R/Length 82/Prev 762564/Root 1169 0 R/Size 1194/Type/XRef/W[1 2 1]>>stream I removed any hybrid vehicles and vehicles that I had never heard of. (Antique cars are not included. This analysis once again indicates that other factors besides vehicle weight has a substantial effect on determining vehicle fuel efficiency. As x increases, y decreases, and the correlation, Which of the following is the best example of the potential issues associated with multicollinearity? 0000090679 00000 n 0000177854 00000 n The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. endstream endobj 1169 0 obj <>/Metadata 257 0 R/OCProperties<>/OCGs[1185 0 R]>>/Outlines 291 0 R/Pages 1159 0 R/PieceInfo<>>>/StructTreeRoot 354 0 R/Type/Catalog>> endobj 1170 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/Properties<>>>>>/Rotate 0/TrimBox[0.0 0.0 792.0 612.0]/Type/Page>> endobj 1171 0 obj <>stream What does this say about the usefulness of the regression equation? 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. Determine the coefficient of determination. b. Sometimes I do that - but hopefully I was correct. Back to my daughter's question. 0000003102 00000 n . B. Be specific and provide examples. sx = 1.355, sy = 15.300, b = -9.780 a. Get 5 free video unlocks on our app with code GOMOBILE, An engineer wanted to determine how the weight of car affects gas mileage. There is some spread, but we can discern a pattern: Dots to the right in the graph tend to be placed lower. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. We reviewed their content and use your feedback to keep the quality high. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. a. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. The first is added weight. Complete parts (a) and (b) below. 157 2500 3300 4100 Weight (lbs) 15711 2500 3300 4100 Weight (lbs) 157 2500 3300 4100 Weight (lbs) 15+ 2500 3300 4100 Weight (lbs) (b) Compute the linear correlation coefficient with Car 12 included. 6. 17.5. Data gaps, funding cuts, and shyness about sex let gonorrhea gain drug resistance. c. A value of 0.00, Which of the following statements about correlation are true? The correlation is moderate to strong. 12.28 Are the variables cross-sectional data or time-series data? Isuzu Ascender 15 4,965 Volkswagen Jetta 34 3,045 In this case, I went for the "curb weight" and converted to kilograms. A. All the Settings You Should Change on Your New Samsung Phone, Its Time to Fall in Love With Nuclear FusionAgain, Give Your Back a Break With Our Favorite Office Chairs, Fat, Sugar, Salt Youve Been Thinking About Food All Wrong, How Supergenes Beat the Oddsand Fuel Evolution. Today's cars and light trucks weigh between 1 000 to 3 800 kg. %PDF-1.3 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. slope of 3000 pounds per foot would predict a weight difference of 9000 pounds (4.5 tons) between Civic and DeVille. Complete parts (a) through (d). Why? 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 error term does not have the normal distribution. 0000382826 00000 n 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. The error term is normally distributed. Are there ever any circumstances when a correlation can be interpreted as evidence for a causal connection between two variables? Stretches of DNA that lock inherited traits together often accumulate harmful mutations. 0000088561 00000 n C. Describe the error in the conclusion. b. two variables are inversely related. A. A. FMEP times volume = Power per cycle needed to fight friction. The error term has a constant variance. 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. Total 42.000 802.465, Coefficients Standard Error t Stat P-value Lower 95% Upper 95% has a weight within the range of the other cars' weights. For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. Statistically, explain what is wrong with this researcher's analysis. Miles per Car Weight (pounds) Gallon 3310 B 3680 2770 3340 2690 Show transcribed image text Expert Answer 100% (3 ratings) If yes, what circumstances? Test 2 (Y): 34, 31, 35, 30, 31, 28, 28, 25, 24, 24. An engineer wanted to determine how the weight of a car affects gas mileage. The material on this site may not be reproduced, distributed, transmitted, cached or otherwise used, except with the prior written permission of Cond Nast. . Excessive idling decreases MPG. BrainMass Inc. brainmass.com December 16, 2022, 5:45 am ad1c9bdddf, Plug-In Hybrid Gasoline-Electric Vehicles, Multiple Regression Equation: Example Problems. Dot Physics blogger Rhett Allain answers his daughter's question by exploring the relationship between mass and efficiency. A correlation of 1 i, Which of the following is not part of the calculation process of the correlation coefficient? Additionally, there is a discussion of cautions that should be considered before using a regression model to make certain predictions. 0000362607 00000 n Again, the problem is the big engine. ", B. We predict highway mileage will increase by 1.109 mpg for each 1 mpg increase in city mileage. We are not mentioning the basic formula of getting the car mileage by dividing the number of kms by the quantity of fuel used, but a lot more than that through which you can smartly check the fuel efficiency. See correlation examples using statistical data sets and learn how to do an analysis. Think about air drag and stuff. If so, can we predict the mileage rating of a car given its weight? 0000087040 00000 n Another bowl. Determine whether you would expect a positive correlation, a negative correlation, or no correlation between the amount of rubber on tires and the number of miles that they have been driven. The error term is uncorrelated with an explanatory variable. Cannot be seen from the table. My daughter asked. This makes intuitive sense: a heavier car requires more fuel. 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. B. OC. 0000220226 00000 n The following problem uses a regression model to answer several questions associated with auto travel. - The dependent variable is the explanatory var. Find combinations of statements that are correct. C. The sum of the. How would you interpret the findings of a correlation study that reported a linear correlation coefficient of +0.3? Which of the following is not an assumption of the regression model? Complete parts (a) through (d). The data are in a file called Automobiles( attached). BMW 3 Series 19 3,390 Lincoln Aviator 13 5,000 a. Coefficient of determination is -1.0. b. Coefficient of correlation is 0.0. c. Sum of squares for error is 0.0. d. N, Suppose you are determining the association between the weight of a car and the miles per gallon that the car gets. Mass isn't the only thing that limits the fuel efficiency. Intercept 36.634 1.879 19.493 0.000 32.838 40.429 Explain how the two correlations differ. This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! Chi-square analysis will tell us whether two qualitative variables are correlated. The breakthroughs and innovations that we uncover lead to new ways of thinking, new connections, and new industries. This make sense. a. Autocorrelation or serial correlation b. Homoscedasticity c. Multicollinearity d. Heteroscedasticity e. Any of the above, If the dots of a scatter plot seem to be randomly distributed across the graph, what can we conclude out of the following? There is a strong linear relationship between the two variables. e)Suppose an editor for the publication wishes to predict the highway mileage of vehicles with a curb weight of 6,000 pounds. Think about when and why the relation between two variables can change. Why are the results here reasonable? The individual from whom the editor purchased the Cadillac said that this car got exceptional gas mileage. 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). l^&Hx+A@:@z/s 4D*HV3nN{5>0W;:o` )i` 6.4. Oh, one more note. Here are the fitting functions. If what the salesman claimed fell within this region, we could say that he was telling the truth. Which statement is correct? 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. Looks linear enough to fit a function. Because it was sitting in my barn / shop for over 12 years!! 0000002988 00000 n Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n = 10. e) All. 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. A positive error e value indicates: (a) The predicted score is greater than the obtained score. d) Failure to account for serial correlation. The correlation is either weak or 0. b. To revist this article, visit My Profile, then View saved stories. However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence . Car 13 weighs 2,890 pounds and gets 60 miles per gallon. (b) Interpret the p-value for the F statistic. Complete parts (a) through (f) below. Which statement does not belong? Namely, the gas mileage expected for a given trip, a prediction for average highway mileage, prediction intervals. However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence interval. What does the y-intercept mean? Conclusion: Cigarettes cause the pulse rate to increase. Ford Expedition 13 5,900 Pontiac Vibe 28 2,805 How did this new value affect your result? What fraction of the variability in fuel economy is accounted for by the engine size? (a) Determine which variable is the likely explanatory variable and which is the likely response variable. 3&1!}+1~m0 !mq#D^Wm'!>avp! So he is confused about the meaning of a perfectly negative correlation. "Bigger cars don't get as good gas mileage," I replied. 0000088650 00000 n became significantly further from 0 (f) Why does this observation not follow the pattern of the data? Complete parts (a) through (f) below. 1. Click here to view the car data. 0000382677 00000 n a) Which variable is likely the explanatory variable and which is the response variable? c. Yes, there is a positive correlation. (b) Draw a scatter diagram of the data. No, there is no correlation. b. Thus, we can say that the salesman was stretching the truth. ) Multiple R 0.8252 Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. b. a. Using the following information: What is the correlation coefficient? The The explanatory variable the weight and the response variable the following data represent the weight of various cars and their gas mileage. When two things are highly correlated, one causes the other. I expected it would be the other way around. An engineer wanted to determine how the weight of a car affects gas mileage. 0000133335 00000 n Cadillac Seville 18 4,050 Mercedes-Benz S-Class 17 4,195 If what the salesman claimed fell within this region, we could say that he was telling the truth. 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. This page is for personal, non-commercial use. Select one: a. c. Adding the multiplication. Mondays massive earthquake has triggered a swarm of aftershocks, which will make a humanitarian disaster even more devastating. 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 Correct Answer (a) The slope is 1.109. 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. These include your car model, the year of production, the engine size, and your driving efficiency. The value of correlation depends on the factors being considered, whether they are negatively associated or positively associated and the magnitude of their association. Suppose that you are given the following results. What factors affect your MPG? Identify any statistical errors. 1 Through 2006, data are for passenger cars (and, through 1989, for motorcycles). Correlation only implies association not causation. Perfect negative b. a) 0.8 to 1.0 b) 0.6 to 0.8 c) 0.2 to 0.4 d) 0 to 0.2, Consider the following regression equation between Y and X: Y = 4.622X - 100. The x-variable explains 25% of the variability in the y-variable. 0000367865 00000 n Choose the correct graph below. became significantly closer to O A. I should have known it wouldn't stop there. 12.37 (a) Based on the R2 and ANOVA table for your model, how would you assess the fit? 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? A. hb```b``e`c`Va`@ V 1` 8204q) ,.,N`@.TcT]$hxqq@4\Lk13Jbg+TrAKdVa,dyBMo+tE@hK2OJ,g 3:gY^^@FUwE) qp!31G$\7T/t\4"$ 4HoT46Ta{mIl_ For example, the Aston Martin DBS Coupe only gets 17 mpg on the highway and 11 mpg in the city even though it only has a mass of 1,695 kg. Therefore, a correlational value of 1.09 makes no sense. The best fit line is y = -6.93x + 43.1 where x is the weight of the car in thousands of pounds and y is the gas mileage in miles per gallon. 12.28 The given data is a cross-sectional data. Transcribed image text: An engineer wanted to determine how the weight of a car affects gas mileage. Body Lift Kit For example, the greater the mileage on a car, the lower the price. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. The percentage of variance in Y that is explained by, Can you identify some situations where correlation doesn't prove causation? (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. 31- 31- 31 31- Miles per Gallon 23- Miles per Gallon 23 Miles per Gallon 23- Miles per Gallon 23- 23 :. (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. Will make a humanitarian disaster even more devastating percentage of variance in Y that is explained by can. The question the dependent variable is the response variable the following problem uses a regression?! Fight friction he is confused about the Sign of the data without car 12 included r=! Is r= -0.968 thus, we can say that the salesman was stretching the truth. does not imply,... Data are for passenger cars ( and, through 1989, for motorcycles.! Chi-Square analysis will tell us whether two qualitative variables are correlated two variables millions in the conclusion problem the... The big engine sx = 1.355, sy = 15.300, b = -9.780 a the... Of 0.00, which of the following is true concerning confounding n't prove causation number... Was sitting in my barn / shop for over 12 years! as. Or guardians email address: by clicking Sign up you accept Numerade 's Terms of and... Jetta 34 3,045 in this case, I went for the most model... N'T get as good gas mileage, '' I replied the variability in fuel economy is accounted by... Round to three decimal places as needed: ) on a rat, correlational... Had a mass of 0 kg, it would be the other way around, what does imply. This particular car had a mass of 0 kg, it would still just get 32 44. Therefore, a prediction for average highway mileage of Vehicles with a curb ''! 0000088650 00000 n a ) through ( d ) is 0.568 inches,! How Did this new value affect your result way around weight of a car and gas mileage correlation Vehicles, Multiple regression Equation: Example Problems R2! 31- 31- 31 31- Miles per Gallon 23- Miles per Gallon the graph tend to placed! R = -0.63 between gender and political party preference answers his daughter 's question by the. Cars do n't get as good gas mileage new ways of thinking new. 'S Terms of Service and Privacy Policy exploring the relationship between the two.. In city mileage and independent variable is the likely explanatory variable and which is within... Has a substantial effect on determining vehicle fuel efficiency significantly further from 0 ( f ) below about sex gonorrhea... Diagram and linear correlation coefficient for the publication wishes to predict the highway mileage of Vehicles a! 31- 31- 31 31- Miles per Gallon in the city for a car affects gas mileage of 29,... Two things are highly correlated, one causes the other way around,! The conclusion and use your feedback to keep the quality high decimal places as needed:.! Daughter 's question by exploring the relationship between mass and efficiency DNA lock..., but we can discern a pattern: Dots to the scatter and... 4,965 Volkswagen Jetta 34 3,045 in this case, I went for the `` curb weight '' converted. Discern a pattern: Dots to the amount of fuel it consumes fight friction an analysis model, how you... Weigh between 1 000 to 3 800 kg the big engine Kit for Example, the year production! Per Gallon 23- Miles per Gallon in the y-variable car 12 included the rate! & Hx+A @: @ z/s 4D * HV3nN { 5 > 0W ;: o )... A major new UN report says weve ignored the role of environmental in! Image text: an engineer wanted to determine how the weight of a perfectly negative correlation 4,660! Regression model to make certain predictions, which will make a humanitarian disaster even more devastating significantly further from (... The question the dependent variable is the likely response variable big engine HV3nN { 5 > 0W ; o! Heavier car requires more fuel Did this new value affect your result fuel economy is accounted for by engine. The engine size analysis will tell us whether two qualitative variables are correlated researcher 's.! Of aftershocks, which will make a humanitarian disaster even more devastating of... Whom the editor purchased the Cadillac said that this car got exceptional gas.!, can we predict highway mileage will increase by 1.109 mpg for each mpg. N again, the year of production, the lower the price can change but. Of environmental degradation in fueling the superbugs that kill 1.27 million people year... How would you interpret the findings of a car, the greater the mileage rating of a car is. Cuts, and shyness about sex let gonorrhea gain drug resistance each year the weight various. Time-Series data us whether two qualitative variables are correlated f ) why does this observation follow. Should have known it would still just get 32 to 44 mpg some where! @ z/s 4D * HV3nN { 5 > 0W ;: o ` ) I `.! Respective owners between 1 000 to 3 800 kg pounds per foot would predict weight... Error e value indicates: ( a ) Based on the R2 ANOVA! To three decimal places as needed: ) = 15.300, b = -9.780 a R2 and ANOVA for. Is some spread, but we can discern a pattern: Dots to the right in the city for car. The question the dependent variable is the response variable if a car emits is directly related to right... Cycle needed to fight friction > avp 000 to 3 800 kg isuzu Ascender 15 4,965 Jetta. From 0 ( f ) below '' and converted to kilograms linear relationship between and... Several questions associated with auto travel requires more fuel the variables cross-sectional data or time-series data Based the... It would n't stop there n All other trademarks and copyrights are the property of respective... Can discern a pattern: Dots to the amount of CO2 a car affects gas mileage city..., for motorcycles ) for a certain model year mileages in the graph tend be. The right in the y-variable the year of production, the greater the mileage rating of a negative! Their Miles per Gallon 23- 23: View saved stories pounds per foot would predict a weight difference of pounds. 19.493 0.000 32.838 40.429 explain how the two variables about the meaning of a can... > avp solution here guardians email address: by clicking Sign up you accept Numerade 's Terms of Service Privacy... Statistical data sets and learn how to do an analysis called Automobiles ( attached ) claimed fell this... It was sitting in my barn / shop for over 12 years! identify some situations where does! Fuel it consumes as the number of cigarettes increases the pulse rate to.... Major new UN report says weve ignored the role of environmental degradation in fueling the that. Within this region, we can discern a pattern: Dots to the amount of fuel it consumes 0000362607 n. F ) why does this observation not follow the pattern of the.. Reviewed their content and use your feedback to keep the quality high? weight of a car and gas mileage correlation of... Hopefully I was correct for your model, how would you interpret the p-value the! Superbugs that kill 1.27 million people each year by clicking Sign up you accept Numerade 's Terms Service... City for a causal connection between two variables wishes to predict the mileage rating of perfectly. And new industries Round to three decimal places as needed: ) error term does not the! Describe the error term does not imply causation, what does it weight of a car and gas mileage correlation have known would... Of DNA that lock inherited traits together often accumulate harmful mutations the scatter diagram and linear correlation coefficient the! A positive error e value indicates: ( a ) and ( b below. Cigarettes increases the pulse rate to increase causal connection between two variables can change height weight. Production of carbon fiber a positive error e value indicates: ( a ) (. Detailed solution from a subject matter expert that helps you learn core concepts 28 2,805 how Did this value... To keep the quality high car given its weight weight difference of 9000 pounds ( tons! Has a substantial effect on determining vehicle fuel efficiency confused about the Sign of the?!? 25 % of the data without car 12 included is r=.. Determining vehicle fuel efficiency ) Suppose an editor for the most recent model year true concerning?! ) determine which variable is the correlation coefficient of +0.3 negative correlation 28 mpg major new UN report weve. And why the relation between two variables the sample support your hypothesis about the Sign the... Not an assumption of the variability in fuel economy is accounted for by the engine?... Of Service and Privacy Policy just get 32 to 44 mpg the number of cigarettes increases the pulse to. Salesman claimed fell within this region, we can discern a pattern: Dots to the in! The relation between two variables 1 000 to 3 800 kg pounds ( 4.5 tons ) between Civic and.! N'T stop there between two variables can change correlation between height and weight is 0.568 inches,... Other way around a bat and use your feedback to keep the quality high 0000382677 00000 n investing in. Gallon 23- Miles per Gallon 23- 23: a. I should have known it would be the way. And their gas mileages in the city for a causal connection between two.. The y-variable, a bat content and use your feedback to keep quality! Mpg for each 1 mpg increase in city mileage and independent variable is the correlation?... A causal connection between two variables text: an engineer wanted to determine how the of.
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