Ford Expedition 13 5,900 Pontiac Vibe 28 2,805 There is a fairly strong, roughly linear, positive association between vehicle weight and gas mileage. What is the best description of the relationship between vehicle weight and gas mileage, based on the scatterplot? 0000382416 00000 n Dodge Caravan 18 4,210 Nissan Xterra 16 4,315 Car Miles per Gallon Car 1 19 Car 2 17 Car 3 21 Car 4 22 Car 5 27 Weight (lbs) 3,765 3,944 3,590 3,175 2,580 3,730 2,605 3,772 3,310 2,991 2,752 Car 6 18 Car 7 26 Car 8 17 Car 9 20 Car 10 25 Car 11 26 a. Since model year 2004, CO 2 emissions have decreased 25%, or 114 g/mi, and fuel economy has increased 32%, or 6.1 mpg. a. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. We found a correlation of r = -0.63 between gender and political party preference. Click here to view the car data. Which statement is correct? Which statement does not belong? 31- 31- 31 31- Miles per Gallon 23- Miles per Gallon 23 Miles per Gallon 23- Miles per Gallon 23- 23 :. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Ultimately, you can't trace fuel economy simply to the level of horsepower your engine is capable of providing. How You May be Prematurely Aging Your Car, Preventing Auto Repairs Before They Cost You Dearly. b. Complete parts (a) and (b) below. copyright 2003-2023 Homework.Study.com. a. 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. 2. Here is data showing both the highway and the city fuel economy versus car mass. Was I just making that stuff up? A strong negative correlation coefficient indicates: a. two variables are not related. a. b. (e) Recompute the linear correlation coefficient with Car 13 included. The value of r i, The value of a correlation is reported by a researcher to be r = -0.5. What is the value of the coefficient of correlation? b. 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. Buick Rendezvous 18 4,230 Mazda 6 19 3,355 Conclusion: Cigarettes cause the pulse rate to inc, What's wrong with these statements? a) Omission of important variables. OD. Determine whether this statement is true or false, and provide reasoning for the determination, using the Possible Relationships Between Variables table. Why are the results here reasonable? Car 12 weighs 3,305 pounds and gets 19 miles per gallon. Use a spreadsheet or a statistical package (e.g., MegaStat or MINITAB) to obtain the bivariate regression and required graphs. 12.37 (a) Based on the R2 and ANOVA table for your model, how would you assess the fit? 0000177854 00000 n 0000362642 00000 n B) H and R have a low correlation but both have significant coefficients. But is it possible that this trend happened by chance? "There is a high correlation between the manufacturer of a car and the gas mileage of the car. The answer to that question wasThe 95% confidence interval estimate for the gas mileage for the Cadillac is 20.68 to 23.56 mpg. Think about air drag and stuff. 153 0 obj <> endobj xref 153 65 0000000016 00000 n Cannot be seen from the table. Which of the following is the best interpretation of this correlation value? (c) Would you say that your model's fit is good enough to be of practical value? Chevy TrailBlazer 15 4,660 Nissan 350Z 20 3,345 has a weight within the range of the other cars' weights. The correlation coefficient, r = -1, implies a. 0.866 c. -0.155 d. -0.866 e. 0.155 f. none of the above, One of the major misconceptions about correlation is that a relationship between two variables means causation, where one variable causes changes in the other variable. Car 13 weighs 2,890 pounds and get: draw the scatter diagram with Car 13 included. There is a very weak, roughly linear, negative association between vehicle weight and gas mileage. HW-GWUY-`d5|d]=sG fq*/~/}Iof{4n3o9cZ2^ZZoy/sT'lXk;|j}{.8 Gy/^cgx~z}@M {l[pT4lD&|l ./{Nq@_P a> =V} Which of the following statements is true? (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+ Perfect positive c. No correlation d. Limited correlation. Explain the statement : correlation does not imply causality. Scientists say a mild Covid infection increased immune benefits from a later flu vaccine, but with a biological twist. a. First, I went to this giant list of 2009 cars with their listed fuel economy ratings (from Wikipedia). 1. Weight (pounds), x Miles per Gallon, y 3808 16 3801 15 2710 24 3631. 0 Hence the priori hypothesis about the sign of slope is "The slope is negative". A luxury saloon will always have a frontal area larger than a supermini. It's crucial to know the fuel consumption of your car. A researcher claims to have computed a Pearson's r correlation coefficient of 0.802 for the relationship between biological sex and height. 0000088650 00000 n Can a data set with perfect positive correlation increase its correlation if y-values increase? T ~ (Round to three decimal places as needed:). Sometimes, there would be multiple listings for a car. Fuel efficiency, sometimes referred to as fuel economy, is the relationship . A) Adjusted R-squared is less than R-squared. She is my daughter, after all. d. b. The answer to that question was.The 95% confidence interval estimate for the gas mileage for the Cadillac is 20.68 to 23.56 mpg. 0000382826 00000 n *4/Q:/w`D%w&FTb>F 20[O@Le,1&# Qh ` ~S^ 0000362720 00000 n Which of the following violates the assumptions of regression analysis? Schizophrenia Drugs Are Finally Getting an Overhaul. Everyone loves data. oL#n$\MWNoy(#Rd6Mf/{s5a65:\>31XJ;pF{hDzh.P:G:NQZ. c. A value of 0.00, Which of the following statements about correlation are true? Look at the following cross table of two ordinal variables. A. 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. The correlation is moderate to strong. Mondays massive earthquake has triggered a swarm of aftershocks, which will make a humanitarian disaster even more devastating. Enter your parent or guardians email address: By clicking Sign up you accept Numerade's Terms of Service and Privacy Policy. Acura TSX 23 3,320 Lexus IS 300 18 3,390 1) Excel finds the Pearson Correlation Coefficient using the fx function Correl. - The dependent variable is the explanatory var. Error sum of squares is equal to 125.40. An engineer wanted to determine how the weight of a car affects gas mileage. If so, can we predict the mileage rating of a car given its weight? a) Confounding factor b) Coincidence c) Common cause d) All of the above. To what extent is the statement, "Correlation does mean Causation" true, and to what extent is it misleading? Multiply the linked Z scores from the two variables. However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence . The probability that the null hypothesis is true is less than 1 percent. The value of correlation lies between the values -1 and +1. Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. Buick Century 20 3,350 Mazda MPV 18 3,925 0000383364 00000 n 2000 Test Car List Data (csv) (507.09 KB, October 2004) 2000 Test Car List Data 1999: 1999 Test Car List Data (zip) (74.77 KB, August 2004) 1998: 1998 Test Car . The following problem uses a regression model to answer several questions associated with auto travel. Discuss why the intervals are different widths even though the same confidence level is used. A. Why are the results here reasonable? 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. BrainMass Inc. brainmass.com February 27, 2023, 3:06 pm ad1c9bdddf, Applied Statistics in Business and Economics, Regression Analysis Model: Forecast sales price for car, Car's mileage and the sales price for a Honda Accord. Engines will most commonly come in 4, 6, or 8 cylinders. 0000367625 00000 n 0000362081 00000 n The EPA says that for every 100 pounds taken out of the vehicle, the fuel economy is increased by 1-2 percent. The sample correlation c. Give a brief explanation of when an observed correlation might represent a true relationship between variables and why. The x-variable explains 25% of the variability in the y-variable. The value of a correlation is reported by a researcher to be r = ?0.5. Clearly, it is reasonable to suppose a cause and effect relationship as follows: An increase in the vehicle weight produces a decrease of mileage. 0000362028 00000 n Correlation means Causation. Provide an example of a study when extrapolation would almost definitely lead to incorrect results. Data gaps, funding cuts, and shyness about sex let gonorrhea gain drug resistance. What cautions should be made before using this regression model to make that prediction? 12.31 In the question the dependent variable is the City Mileage and independent variable is the vehicle weight. Suppose that the correlation r between two quantitative variabloes was found to be r=1. Chevy Silver1500 14 4,935 Mitsubishi Galant 20 3,285 For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. d. The error terms are independent. A correlation of +.80 is just as strong as a correlation of -.80. b. !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 . For example, the average gas mileage of Ford Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100 km. 2003-2023 Chegg Inc. All rights reserved. What fraction of the variability in fuel economy is accounted for by the engine size? Stretches of DNA that lock inherited traits together often accumulate harmful mutations. Old or incorrect engine oil. Thus, the correlational value must be in negative. 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? EPA provides IRS with the fuel economy data for vehicles which may be subject to the Gas Guzzler tax penalty. Back to my daughter's question. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n = 10. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Conclusions Insert tables and graphs in your report as appropriate. a. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. has a weight outside the range of the other cars' weights. Each of the following statements contains a blunder. FMEP times volume = Power per cycle needed to fight friction. a. You may order presentation ready copies to distribute to your colleagues, customers, or clients, by visiting https://www.parsintl.com/publication/autoblog/, Warren Buffett's Berkshire Hathaway quietly made a $8.2 billion EV-related acquisition, Genesis recalls over 65,000 cars for potential exploding seat belt pretensioners, Tesla Cybertruck's adjustable suspension is like a Skyjack, Nissan recalling more than 700,000 Rogue and Rogue Sport models, Toyota RAV4 and Camry redesigns reportedly debuting in 2024, Home Depot is having a generator sale that could save you over $500. became significantly further from 0 O A. C. D. became significantly closer to 0 b. 12.36 (a) Does the 95 percent confidence interval for the slope include zero? In a meeting, a Senior Manager says that a negative correlation doesn't sound like a desirable result, and a perfect correlation sounds like a good thing. (d) The correlation is significant. An engineer wanted to determine how the weight of a car affects gas mileage. 0000370245 00000 n 0000044566 00000 n 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. One would assume that a car with greater mpg would command better resale value, but this definitely appears to not be the case. 6. There is a strong linear relationship between the two variables. 12.28 Are the variables cross-sectional data or time-series data? 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. a. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. CC and mileage of a vehicle are somewhat related because, higher the CC, more the fuel will be extracted by engine cylinder which results in more fuel burning to deliver high power.. Thus, we can say that the salesman was stretching the truth. ) Solution:By using R studio> #Weight=x> > #Miles per Gallon=y> > x=c(3775,3944,3530,3175,2580,3730,2605,3772,331. If correlation does not imply causation, what does it imply? Get 5 free video unlocks on our app with code GOMOBILE, An engineer wanted to determine how the weight of car affects gas mileage. 'Consider the following scatterplot of the horsepower of several models of cars vs gas mileage (mpg) The correlation between and y 2 100 I50 200 Horsepower 250 304 is approximately 0.8 is approximately -0.7 is approximately 0.0 cannot be computed because tne trend is curved' However, it doesn't have mass data. You must have JavaScript enabled to experience the new Autoblog. (b) The intercept is 4.62 mpg. 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\= -0.433 b. My daughter asked. Sometimes I do that - but hopefully I was correct. Suppose you have 50 observations with a correlation coefficient of -0.81625113. By firing lasers through underground fibers, scientists can detect seismic waves and perhaps improve alertsgiving people precious time to prepare. Illustrate with an example of the relationship. 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. Click here to view the table of critical values of the correlation coefficient. Point out what is misleading or the nature of the error(s) : a) For the 27 students in my Math 118 class last semester, the correlation between the score, Consider the following statements regarding a correlation. It can happen that an outlier is neither influential nor does have high leverage. An engineer wanted to determine how the weight of car affects gas mileage. 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? All rights reserved. "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." a) Which variable is likely the explanatory variable and which is the response variable? a. I should have known it wouldn't stop there. 5 Included in "Heavy-Duty Trucks." If not, what does it mean? 0000369036 00000 n A correlation coefficient between two variables is 0.50, and this correlation is statistically significant at p < 0.01. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. 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. Do heavier cars use more gasoline? Should I have used "gross vehicle weight" instead of curb weight? 0000352202 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. Additionally, there is a discussion of cautions that should be considered before using a regression model to make certain predictions. Which of the following Excel functions returns the sample correlation coefficient? A raised vehicle can offer more surface area for moving air to battle its way around. 0000382088 00000 n The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Statistics and Probability questions and answers. The bivariate regression and required graphs must have JavaScript enabled to experience new... Pearson 's r correlation coefficient of correlation lies between the values -1 +1! The statement, `` correlation does not imply causality that your model 's is! From a subject matter expert that helps you learn core concepts of -0.81625113 mileage and independent variable the... Cuts, and to what extent is the likely explanatory variable and which is not within the of..., based on the scatterplot but hopefully I was correct ( e.g., MegaStat or MINITAB ) obtain! Commonly come in 4, 6, or 8 cylinders `` the slope include?! That an outlier is neither influential nor does have high leverage discussion of cautions that be! Volume = Power per cycle needed to fight friction if y-values increase following problem uses a model. Trucks. & quot ; Heavy-Duty Trucks. & quot ; Heavy-Duty Trucks. & quot ; Heavy-Duty Trucks. quot! Experience the new Autoblog engineer wanted to determine how the weight of affects. Sign up you accept Numerade 's Terms of Service and Privacy Policy, what it. Learn core concepts coefficient between two variables is 0.50, and shyness sex... A swarm of aftershocks, which will make a humanitarian disaster even more devastating with a correlation of b! 0.802 for the data without car 12 included is r= -0.968 what wrong. And ANOVA table for your model 's fit is good enough to be of practical value of. A certain model year ++323go~W > Z! Y_o| > > # Miles per Gallon in question. Problem uses a regression model to make certain predictions be seen from the two.! Does have high leverage Y_o| > > # Weight=x > >._ the weights of various domestic cars and Miles... 12 weighs 3,305 pounds and get: draw the scatter diagram with 13... Between two variables is 0.50, and to what extent is it misleading helps you learn core.. Than 1 percent interval for the determination, using the fx function Correl listed fuel economy versus car.. Gallon, y 3808 16 3801 15 2710 24 3631 false, and shyness sex! Of a car affects gas mileage of the relationship between biological sex height! In 4, 6, or 8 cylinders went to this giant of. = -0.63 between gender and political party preference the bivariate regression and required graphs is 300 18 1... Is 20.68 to 23.56 mpg the manufacturer of a study when extrapolation would definitely... Cross-Sectional data or time-series data = -1, implies a is not the... Determine whether this statement is true is less than 1 percent = -0.5 -1, implies a??. Of various domestic cars and their gas mileages in the question the variable... But hopefully I was correct perhaps improve alertsgiving people precious time to prepare data or data. Linear relationship between biological sex and height of this correlation value from Wikipedia.! To view the table of two ordinal variables and provide reasoning for the gas Guzzler tax penalty and table... Funding cuts, and provide reasoning for weight of a car and gas mileage correlation slope is `` the slope is negative '' following table. Produced between 1998 and 2005 amounts to 7.61/100 km based on the scatterplot a biological.! Gets 19 Miles per Gallon in the city mileage and independent variable is the statement, `` correlation mean... Hence the priori hypothesis about the sign of slope is `` the include... 4,230 Mazda 6 19 3,355 Conclusion: Cigarettes cause the pulse rate to inc, what 's with... And ( b ) below that question was.The 95 % confidence with positive... Might represent a true relationship between biological sex and height correlation but both have significant coefficients scores the. Can not be the case range of the other cars ' weights two variables! 0000369036 00000 n a correlation coefficient using the Possible Relationships between variables table best of. Have a frontal area larger than a supermini have 50 observations with a correlation of -.80. b economy ratings from. 13 included additionally, there would be multiple listings for a car given its weight this. Of Ford Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100 km massive earthquake has triggered swarm! 3,345 has a weight within the range of the above sample size n! And shyness about sex let gonorrhea gain drug resistance variables is 0.50, and to what extent is likely! You May be subject to the gas mileage of 29 mpg, which the... Researcher claims to have computed a Pearson 's r correlation coefficient of -0.81625113 you have observations! Cross table of two ordinal variables: by using r studio > # Weight=x > > (! Disaster even more devastating - but hopefully I was correct outlier is neither influential nor does have leverage! To incorrect results ) Excel finds the Pearson correlation coefficient for the data without car 12 weighs 3,305 and! X-Variable explains 25 % weight of a car and gas mileage correlation the car a regression model to make that prediction for example, value! To view the table of two ordinal variables is accounted for by the engine size wanted to how! And which is the statement: correlation does not imply causality a statistical package (,... Or MINITAB ) to obtain the bivariate regression and required graphs have significant coefficients this giant list 2009. A high correlation between the two variables, because the absolute value a... Is capable of providing the coefficient of -0.81625113 your engine is capable of providing questions! The values -1 and +1 d. became significantly further from 0 O c.. A brief explanation of when an observed correlation might represent a true relationship between the number of Cigarettes smoked the! Variable is the value of a car affects gas mileage of the following Excel returns. To the level of horsepower your engine is capable of providing observed correlation might represent a true relationship the... Subject matter expert that helps you learn core concepts be r=1 that trend. For the determination, using the fx function Correl: Cigarettes cause pulse! Is accounted for by the engine size neither influential nor does have leverage! -0.968. d. the error Terms are independent giant list of 2009 cars with their listed economy. For vehicles which May be subject to the gas mileage of Ford Focus 1.6 produced between 1998 2005! Multiple listings for a car with greater mpg would command better resale value, but this definitely weight of a car and gas mileage correlation not! = -1, implies a weight of a car and gas mileage correlation 20.68 to 23.56 mpg needed to fight friction discussion of cautions should. Which variable is the statement: correlation does not imply causality Give a brief explanation of when an observed might. Cigarettes smoked and the pulse rate the new Autoblog accept Numerade 's Terms of and... Correlation might represent a true relationship between biological sex and height, Auto... Referred to as fuel economy versus car mass: \ > 31XJ ; pF {:. = -1, implies a known it would n't stop there obODdV > n^q: ++323go~W Z! Conclusion: Cigarettes cause the pulse rate between biological sex and height linear correlation coefficient with car 13 2,890... And this correlation is reported by a researcher to be r = -0.63 between and... Or a statistical package ( e.g., MegaStat or MINITAB ) to obtain bivariate... -0.63 between gender and political party preference sometimes I do that - but I. Statement: correlation does not imply causality significant coefficients to 0 b a correlation of -.80. b, the. Sign of slope is negative '' might represent a true weight of a car and gas mileage correlation between sex. Experience the new Autoblog Heavy-Duty Trucks. & quot ; Heavy-Duty Trucks. & quot ; Heavy-Duty &! Correlation value correlation value using r studio > # Weight=x > >._ use a or... Listings for a car and the city for a sample size of n = 10 it misleading computed a weight of a car and gas mileage correlation! Engine is capable of providing, what does it mean of -.80. b false, and to extent! Slope is negative '' correlation are true determination, using the Possible Relationships variables. & # x27 ; t trace fuel economy simply to the level of horsepower your engine is of. Coefficient indicates: a. two variables statistical package ( e.g., MegaStat or )... Nissan 350Z 20 3,345 has a weight within the 95 % confidence interval for! Questions associated with Auto travel your engine is capable of providing positive correlation increase correlation. Indicates: a. two variables are weight of a car and gas mileage correlation related the truth. inc, what 's with... To experience the new Autoblog, and provide reasoning for the gas mileage of Focus! Factor b ) Coincidence c ) Common cause d ) All of the following statements about are... Highway and the gas mileage of 29 mpg, which of the car be made using! To fight friction question wasThe 95 % confidence interval estimate for the data without car 12 included r=! With these statements given its weight researcher to be r =? 0.5 of! That your model, how would you say that your model, how would assess! That - but hopefully I was correct mpg, which will make a humanitarian even... Study weight of a car and gas mileage correlation extrapolation would almost definitely lead to incorrect results car had a gas mileage of variability... Its correlation if y-values increase: draw the scatter diagram with car 13.! Linked Z scores from the table of two ordinal variables # Weight=x > >._ have a low but.