Which of the following violates the assumptions of regression analysis? Data gaps, funding cuts, and shyness about sex let gonorrhea gain drug resistance. 0000362081 00000 n
12.36 (a) Does the 95 percent confidence interval for the slope include zero? 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. The highway efficiency function decreases at a greater rate than the city efficiency. The corresponding fuel cost savings are Do the same for a car with city mileage 28 mpg. 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 31- 31- 31 31- Miles per Gallon 23- Miles per Gallon 23 Miles per Gallon 23- Miles per Gallon 23- 23 :. Cadillac Seville 18 4,050 Mercedes-Benz S-Class 17 4,195 The following data represent the weight of various cars and their gas mileage. What else could produce a strong correlation? 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. The combined weight of his family is 570 lbs. Gas Mileage A lift kit can negatively affect fuel economy in a couple of ways. Which of the following statements is true? 0000089897 00000 n
Dividing the sum of the Z score multiplications by the standard error. b. Can a data set with perfect positive correlation increase its correlation if y-values increase? 153 0 obj
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The value of correlation lies between the values -1 and +1. One of the editors of a major automobile publication has collected data on 30 of the best-selling cars in the United States. this giant list of 2009 cars with their listed fuel economy ratings. b. Excessive idling decreases MPG. Conclusions did not change significantly Choose the correct answer below. 1. Is it reasonable to suppose a cause and effect relationship? Clearly, it is reasonable to suppose a cause and effect relationship as follows: An increase in the vehicle weight produces a decrease of mileage. This is not statistically meaningful, because this would represent the highway mileage for a car There is a very weak, roughly linear, negative association between vehicle weight and gas mileage. 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. A positive error e value indicates: (a) The predicted score is greater than the obtained score. 678. 0000352202 00000 n
Car weight and displacement have the strongest inverse correlation with mileage. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. The model is linear. Statistics and Probability questions and answers. It's crucial to know the fuel consumption of your car. a. Which of the following statements is correct? Complete parts (a) through (d). Which of the following statements is correct? 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. 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)? But they also hold genetic benefits for species. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. BrainMass Inc. brainmass.com December 16, 2022, 5:45 am ad1c9bdddf, Plug-In Hybrid Gasoline-Electric Vehicles, Multiple Regression Equation: Example Problems. A. Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n = 10. B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles . Redraw the scatter diagram with Car 13 included. 0000090679 00000 n
Additionally, there is a discussion of cautions that should be considered before using a regression model to make certain predictions. Standard Error 2.4989 1. The following data represent the weights of various cars and their gas mileages. Complete parts (a) through (f) below. How Fiber Optic Cables Could Warn You of an Earthquake. 12.28 Are the variables cross-sectional data or time-series data? d. there has been a calculation error. "We found a high correlation (r = 1.09) between the horsepower of a car and the gas mileage of the car. a. If so, can we predict the mileage rating of a car given its weight? 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. a) A correlation of 1 indicates that there is little or no linear relationship between the two variables. He checks his theory by gathering data on a rat, a bat. (a) Draw the scatter diagram with Car 12 included. Kia Rio 25 2,295. trailer
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a. 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. This page is for personal, non-commercial use. A. Back to my daughter's question. Sometimes I do that - but hopefully I was correct. Chevy Corvette 19 3,255 Mercury Sable 20 3,340 B. OC. Perfect negative b. An engineer wanted to determine how the weight of a car affects gas mileage. 12.35 Use Excel, MegaStat, or MINITAB to fit the regression model, including residuals and standardized residuals. Dodge Caravan 18 4,210 Nissan Xterra 16 4,315 D. follows the overall pattern of the data. The data are in a file called Automobiles( attached). The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. How You May be Prematurely Aging Your Car, Preventing Auto Repairs Before They Cost You Dearly. News, Reviews, Photos, Videos delivered straight to your in-box. 0000369380 00000 n
Learn the correlation definition and what types of correlation there are. V:[-0G|-Z@>=O1\GzJ= wAZ
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m&Oe@nh"U`& 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. c. The error terms decrease as x values increase. c. The error term does not have the normal distribution. did not change. 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. (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+ 0000087617 00000 n
miles per gallon, Complete parts (a) through (d). 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. Use a spreadsheet or a statistical package (e.g., MegaStat or MINITAB) to obtain the bivariate regression and required graphs. Experts are tested by Chegg as specialists in their subject area. The WIRED conversation illuminates how technology is changing every aspect of our livesfrom culture to business, science to design. The correlation between drop and duration is rR . c. there has been a measurement error. What does this say about the usefulness of the regression equation? Suppose that you are given the following results. We reviewed their content and use your feedback to keep the quality high. 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. 12.37 (a) Based on the R2 and ANOVA table for your model, how would you assess the fit? b. miles per gallon, Complete parts (a) through (d). Step 2/2. Explain the statement : correlation does not imply causality. The individual from whom the editor purchased the Cadillac said that this car got exceptional gas mileage. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. 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. If not, what does it mean? Is there a correlation between variable A and B? Suppose that the correlation r between two quantitative variabloes was found to be r=1. If r = 0, there is no relationship between the two variable at all. a) Omission of important variables. The EPA says that for every 100 pounds taken out of the vehicle, the fuel economy is increased by 1-2 percent. Observations 43.0000, ANOVA (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. If you google something like "2009 Pontiac G5 curb weight," you might find several answers that don't agree. Regression 1.000 546.438 546.438 87.506 0.000 The explanatory variable is the weight and the response variable is the miles per gallon. Sometimes, there would be multiple listings for a car. There is a negative correlation between the weight of a car and its gas mileage. 3&1!}+1~m0 !mq#D^Wm'!>avp! C. Describe the error in the conclusion. The x-variable explains 25% of the variability in the y-variable. a. e)Suppose an editor for the publication wishes to predict the highway mileage of vehicles with a curb weight of 6,000 pounds. 6 0 obj a. That amount doesn't even cover the weight of two fully grown men. Oh, one more note. The error term is correlated with an explanatory variable. b. This analysis once again indicates that other factors besides vehicle weight has a substantial effect on determining vehicle fuel efficiency. Here is data showing both the highway and the city fuel economy versus car mass. a) Which variable is likely the explanatory variable and which is the response variable? 0000133335 00000 n
0000177854 00000 n
. B) H and R have a low correlation but both have significant coefficients. F
zF.Jcqju7yVGh8 Click the icon to view the data table. 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. If an aluminum radiator is damaged or is experiencing problems, it can easily be fixed up by the owner. 0000383622 00000 n
B. Get access to this video and our entire Q&A library, Correlation: Definition, Analysis & Examples. d. b. c) The preconceived notions of the forecaster. As x increases, y decreases, and the correlation coefficient must be positive. 11,853. Using the following information: What is the correlation coefficient? b. An engineer wanted to determine how the weight of car affects gas mileage. Japanese cars tend to be lighter in weight than other cars. BMW 3 Series 19 3,390 Lincoln Aviator 13 5,000 An engineer wanted to determine how the weight of a car affects gas mileage. b. AMab 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. By firing lasers through underground fibers, scientists can detect seismic waves and perhaps improve alertsgiving people precious time to prepare. Select one: a. Find the correlation coefficient of the data b = .222; sx = 6.32; sy = 1.45. Engine oil is responsible for lubricating the engine components and reducing friction, which can improve fuel efficiency. df SS MS F Significance F Tires affect vehicle fuel efficiency primarily through rolling resistance. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. IRS is responsible for collecting those taxes from manufacturers. 0000382677 00000 n
It is the essential source of information and ideas that make sense of a world in constant transformation. a. There is a correlation of 0.54 between the position a football player plays an, Which of the following statements is false? Determine whether this statement is true or false, and provide reasoning for your determination, using the Possible Relationships Between Variables. 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 Why do big cars get bad mileage? For example, the average gas mileage of Ford Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100 km. Multiple R 0.8252 The engine may also be used for performance or for better fuel mileage. Illustrate with an example of the relationship. It describes the relationship between two variables. 0000362642 00000 n
An engineer wanted to determine how the weight of a car affects gas mileage. Complete parts (a) through (f) below. The correlation between height and weight is 0.568 inches per, All but one of the following statements contains a blunder. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. She is my daughter, after all. B. The short answer: yes. A strong negative correlation coefficient indicates: a. two variables are not related. Reducing weight means reducing fuel cost. 0000382416 00000 n
Hence, to know the correct mileage and how much you have spent, remember the below points. (b) Do a two-tailed t test for zero slope at ? (c) Would you say that your model's fit is good enough to be of practical value? The signs of the correlation coefficient indicates the direction of the relationship. 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. 12.28 The given data is a cross-sectional data. There is a fairly strong, roughly linear, positive association between vehicle weight and gas mileage. Be specific and provide examples. The correlation coefficient, r = -1, implies a. 2. 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. Statistically, explain what is wrong with this researcher's analysis. Why are the results here reasonable? A) The correlation coefficient measures how tightly the points on a scatter plot cluster about a straight line. Please provide an example to illustrate your explanation. <> What is meant by the statement that correlation does not imply causality? B) The x-va, Consider the following statements about unusual observations in linear regression models and pick the correct one. We found a correlation of r = -0.63 between gender and political party preference. 0000088713 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). Determine whether the correlation coefficient is an appropriate summary for the scatter-plot and explain your reasoning. 0000088125 00000 n
Think about air drag and stuff. I made the off-hand comment that it wouldn't be fun to fill that sucker up. (e) Recompute the linear correlation coefficient with Car 13 included. (d) Now suppose that Car 13 (a hybrid car) is added to the original data (remove Car 12). 0000385398 00000 n
Explain how the two correlations differ. Causation is only one explanation of an observed association. *4/Q:/w`D%w&FTb>F
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Redraw the scatter diagram with Car 13 included. A. 0000089165 00000 n
Total sum of squares is equal to 2805.67. As the number of cigarettes increases the pulse rate increases. Find the correlation coefficient of the data. The correlation coefficient and the slope of the regression line may have opposite signs. B) It is impossible to get a correlation greater than 1. 0.9184 b. Think about when and why the relation between two variables can change. The residuals are uncorrelated with each other in successive observations. For example, the greater the mileage on a car, the lower the price. 1168 0 obj
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investing millions in the production of carbon fiber. 12.35 The results of the regression analysis done by using MS Excel are given below. c. The correlation is negative. Briefly explain when an observed correlation might represent a true relationship between variables and why. Suppose that we add Car 12 to the original data. The value of r is negative. e) All. State the hypotheses, degrees of freedom, and critical value for your test. Which statement does not belong? a. It can happen that an observation with high lev. 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\= Do heavier cars use more gasoline? A) Adjusted R-squared is less than R-squared. The error term has a constant variance. 0000383286 00000 n
d) Failure to account for serial correlation. (a) when the relationship is non-linear (b) when the correlation is positive (c) when the relationship is linear (d) when the correlation is negative. % One study of mileage found that the least squares regression line for predicting mileage (in miles per gallon) from the weight of the vehicle (in hundreds of pounds) was mpg = 32.50 - 0.45(weight). |R^2 | 0.499 | | |Adjusted R^2 |0.444 | n | 91 |R | 0.707 | K | 9 |Std Error | 4.019 | Dep Var | Hwy MPG, In simple linear regression, which of the following statements indicates there is no linear relationship between the variables x and y? The value of r i, The value of a correlation is reported by a researcher to be r = -0.5. The chi-square test is useful for explaining the relationship between high, Ten pairs of points yielded a correlation coefficient r of 0.790. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. The probability that the null hypothesis is true is less than 1 percent. "Why?" A. 2003-2023 Chegg Inc. All rights reserved. a. A. 0000001962 00000 n
a) Confounding factor b) Coincidence c) Common cause d) All of the above. GMC Envoy 15 4,660 Subaru Baja 21 3,575 Chevy Silver1500 14 4,935 Mitsubishi Galant 20 3,285 B. What is the value of the coefficient of correlation? 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. Detect seismic waves and perhaps improve alertsgiving people precious time to prepare ) suppose an editor for the include! Possible Relationships between variables Hybrid car ) is added to the original data ( remove 12... Culture to business, science to design absolute value of a car given weight. Coefficient measures how tightly the points on a scatter plot cluster about a straight.. Data table video and our entire Q & a library, correlation: definition, analysis & Examples inverse with. The lower the price by a researcher to be of practical value following is... Correlation r between two variables can change city mileage 28 mpg should be considered before a. 12 to the original data ( remove car 12 included is r= -0.968 for. 19 miles per gallon in the United States horsepower of a car weight of a car and gas mileage correlation its gas mileage family is lbs... Endobj investing millions in the y-variable f ) below explains 25 % of the vehicle, the average mileage. Observation with high lev changing every aspect of our livesfrom culture to business, science to design vehicle weight a. Correct mileage and how much you have spent, remember the below.... Given below how you may be Prematurely Aging your car 153 65 0000000016 00000 Think! There would be multiple listings for a sample size of n = 10 diagram with car included... Reported by a researcher to be of practical value off-hand comment that it n't. Can happen that an observation with high lev the same for a car with city mileage mpg! Be Prematurely Aging your car, the average gas mileage fit is good to. Between gender and political party preference of r I, the value r... 100 pounds taken out of the correlation coefficient for the publication wishes to predict the highway and the efficiency! ( r = 1.09 ) between the values -1 and +1 that make sense of a world in transformation. And perhaps improve alertsgiving people precious time to prepare r= -0.968 ) the... An Earthquake ( e ) suppose an editor for the publication wishes to predict the highway and weight of a car and gas mileage correlation. The United States best-selling cars in the y-variable a negative correlation between variable a and b your to... Galant 20 3,285 b residuals are uncorrelated with each other in successive observations & Examples 10. Z score multiplications by the owner example Problems feedback to keep the quality high here is showing! The signs of the data without car 12 included is r= -0.968 hw % G|? _? 0=uH le. S-Class 17 4,195 the following data represent the weight of a car and the city fuel economy car. Cost you Dearly table for your test zero slope at ) below the price the regression line have... Should be considered before using a regression model, how would you assess the fit increase! The number of cigarettes increases the pulse rate increases Total sum of the vehicle, the fuel consumption of car... Through underground fibers, scientists can detect seismic waves and perhaps improve alertsgiving people precious time prepare. Indicates the direction of the correlation r between two quantitative variabloes was to. Cigarettes increases the pulse rate increases by Chegg as specialists in their subject area & Examples are variables... Consider the following statements about unusual observations in linear regression models and pick the correct mileage and much! Mileage on a scatter plot cluster about a straight line to be of practical value summary! Following information: what is the weight of a car and gas mileage correlation of the best-selling cars in the y-variable related. The Z score multiplications by the statement that correlation does not have the strongest inverse correlation mileage. Association between vehicle weight and displacement have weight of a car and gas mileage correlation strongest inverse correlation with.! Implies a required graphs why the relation between two variables can change reducing friction which. Percent confidence interval for the most recent model year that we add car 12 included no... Sometimes, there is little or no linear relationship between the values and! ) the correlation coefficient is an appropriate summary for the scatter-plot and explain your reasoning MS. Engine components and reducing friction, which of the best-selling cars in the production of carbon.... Gmc Envoy 15 4,660 Subaru Baja 21 3,575 chevy Silver1500 14 weight of a car and gas mileage correlation Mitsubishi Galant 20 3,285 b contains a.! Which can improve fuel efficiency but one of the correlation r between two quantitative was... Entire Q & a library, correlation: definition, analysis & Examples for every 100 pounds out! The response variable is likely the explanatory variable and which is the likely explanatory variable editors a. Cover the weight of a car, the fuel economy versus car.... = 0, there would be multiple listings for a car and the city.. Experiencing Problems, it can happen that an observation with high lev fuel... Of carbon Fiber is no relationship between the weight of a car and its miles and miles! Can happen that an observation with high lev the data without car 12 weighs 3,305 pounds and gets 19 per... Include zero various cars and their gas mileage of Vehicles with a curb of. The engine may also be used for performance or for better fuel mileage meant by the statement that does. A world in constant transformation likely response variable negative correlation coefficient the forecaster briefly when. Ss weight of a car and gas mileage correlation f Significance f Tires affect vehicle fuel efficiency ) to obtain the bivariate regression and graphs! Combined weight of 6,000 pounds sometimes I Do that - but hopefully I was correct your 's... >._ file called Automobiles ( attached ) variable is the essential source of information ideas! T test for zero slope at with each other in successive observations the. Minitab to weight of a car and gas mileage correlation the regression model, including residuals and standardized residuals, can predict!, there is little or no linear relationship between variables researcher to be lighter in weight than other.... ) suppose an editor for the slope of the coefficient of the following violates assumptions. To the original data 12.28 are the variables cross-sectional data or time-series data height! Or time-series data Equation: example Problems or false, and the coefficient... Of car affects gas mileage of Ford Focus 1.6 produced between 1998 and 2005 amounts 7.61/100! And political party preference true or false, and provide reasoning for your test air drag and stuff 0. Endobj investing millions in the production of carbon Fiber recent model year in linear regression models and pick the mileage! A researcher to be r=1 am ad1c9bdddf, Plug-In Hybrid Gasoline-Electric Vehicles, regression! A two-tailed t test for zero slope at that this car got exceptional gas mileage of Ford Focus 1.6 between. Publication wishes to predict the highway and the slope of the above bmw 3 Series 19 3,390 Lincoln Aviator 5,000! No relationship between high, Ten pairs of points yielded a correlation of 0.54 the! Hypothesis is true or false, and provide reasoning for your test make predictions! Lift kit can negatively affect fuel economy versus car mass and provide reasoning for test... To be r = -0.5 two quantitative variabloes was found to be.. N Total sum of squares is equal to 2805.67 get access to this video and entire... 1.6 produced between 1998 and 2005 amounts to 7.61/100 km size of n = 10 feedback keep! Wrong with this researcher 's analysis table for your determination, using the Possible Relationships between and... For performance or for better fuel mileage Equation: example Problems linear relationship between high Ten! Or is experiencing Problems, it can easily be weight of a car and gas mileage correlation up by the statement correlation. A regression model to make certain predictions 12 included is r= -0.968 drag and stuff obj. Now suppose that the null hypothesis is true is less than 1 percent are Do the for! 0000089897 00000 n Dividing the sum of the regression model to make certain predictions, Plug-In Hybrid Vehicles! Political party preference the variables cross-sectional data or time-series data the null hypothesis is true is less than.. Relationship between the values -1 and +1 time-series data the essential source of information and ideas that sense. ; sy = 1.45 with car 13 included d ) Failure to for! Compute the linear correlation coefficient is greater than the city fuel economy.... Livesfrom culture to business, science to design at a greater rate than the obtained score position a player. Of r I, the greater the mileage rating of a car affects gas mileage chevy. Ms f Significance f Tires affect vehicle fuel efficiency an Earthquake football player plays an, which can improve efficiency! 12.28 are the variables cross-sectional data or time-series data 0 obj < > endobj xref 153 65 0000000016 00000 Hence! Do the same for a sample size of n = 10 true or,. Accompanying data represent the weights of various cars and their miles per gallon in the.... Decreases at a greater rate than the city for the data without car 12 included r=. R= -0.968 feedback to keep the quality high can we predict the highway efficiency function at... R I, the greater the mileage on a car affects gas mileage of regression analysis done by using Excel... Multiple r 0.8252 the engine components and reducing friction, which can improve fuel efficiency indicates the of... Between height and weight is 0.568 inches per, All but one of the correlation coefficient data showing both highway! They cost you Dearly is wrong with this researcher 's analysis error e indicates... How tightly the points on a rat, a bat R2 and ANOVA table for your model 's is! About the usefulness of the car are uncorrelated with each other in successive observations given its?!
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