weight of a car and gas mileage correlation

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. "Why?" Are there ever any circumstances when a correlation can be interpreted as evidence for a causal connection between two variables? Why are the results here reasonable? Statistically, explain what is wrong with this researcher's analysis. Think about when and why the relation between two variables can change. No, there is no correlation. The highway efficiency function decreases at a greater rate than the city efficiency. 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 (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+ Be specific and provide examples. - Estimates of the slope are found from sample data. The first is added weight. Using the wrong type of engine oil or not changing the engine oil on time can lead to decreased fuel efficiency and reduced gas mileage in Bonneville. The correlation can be used to measure the quadratic relationship. If yes, what circumstances? Jaguar XJ8 18 3,805 VolvoC70 20 3,690 a. (e) Did the sample support your hypothesis about the sign of the slope? Japanese cars tend to be lighter in weight than other cars. 0000177854 00000 n Error sum of squares is equal to 125.40. Honda Accord 21 3,390 Suzuki Vitara XL7 17 3,590 Click here to view the table of critical values of the correlation coefficient. 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. has a weight within the range of the other cars' weights. Click the icon to view the data table. became significantly further from 0 (f) Why does this observation not follow the pattern of the data? Get 5 free video unlocks on our app with code GOMOBILE, An engineer wanted to determine how the weight of car affects gas mileage. B. The x-variable explains 25% of the variability in the y-variable. There is a strong negative correlation between the displacement,horsepower,weight,and cylinders.This implies that,as any one of those variables increases,the mpg decreases. 0000220226 00000 n B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles . Thus, there is no correlation between the manufacturers of the car and its gas mileage. What is the best description of the relationship between vehicle weight and gas mileage, based on the scatterplot? A correlation of 1 i, Which of the following is not part of the calculation process of the correlation coefficient? (ii) A sample correlation coefficient of .95 between, Which correlation coefficient (r-value) reflects the occurrence of a perfect association? To revist this article, visit My Profile, then View saved stories. 12.28 Are the variables cross-sectional data or time-series data? Why are the results here reasonable? 2003-2023 Chegg Inc. All rights reserved. a. b) Incorrect model specification. Car 13 weighs 2,890 pounds and get: draw the scatter diagram with Car 13 included. a. Bigger isn't always better, I guess. Miles per Car Weight (pounds) Gallon 3310 B 3680 2770 3340 2690 Show transcribed image text Expert Answer 100% (3 ratings) 0000382275 00000 n What does the y-intercept mean? (a) Draw the scatter diagram with Car 12 included. Gas Mileage A lift kit can negatively affect fuel economy in a couple of ways. b. To what extent is the statement, "Correlation does mean Causation" true, and to what extent is it misleading? Let's start with the easy and simple numbers. (d) Which approach do you prefer, the t test or the p-value? Car 13 weighs 2,890 pounds and gets 60 miles per gallon. The correlation coefficient and the slope of the regression line may have opposite signs. 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. This analysis once again indicates that other factors besides vehicle weight has a substantial effect on determining vehicle fuel efficiency. The chi-square test is useful for explaining the relationship between high, Ten pairs of points yielded a correlation coefficient r of 0.790. Therefore, a correlational value of 1.09 makes no sense. News, Reviews, Photos, Videos delivered straight to your in-box. e) All. Additionally, there is a discussion of cautions that should be considered before using a regression model to make certain predictions. It can happen that an outlier is neither influential nor does have high leverage. 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. b. Explain how the two correlations differ. 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? 0000404223 00000 n If what the salesman claimed fell within this region, we could say that he was telling the truth. 2023 Cond Nast. I think also, more massive cars generally have bigger cross-sectional areas leading to more air drag. Explain reasoning. 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? Your gas consumption depends on a range of factors. Choose the correct graph below. Which of the following Excel functions returns the sample correlation coefficient? HW-GWUY-`d5|d]=sG fq*/~/}Iof{4n3o9cZ2^ZZoy/sT'lXk;|j}{.8 Gy/^cgx~z}@M {l[pT4lD&|l ./{Nq@_P a> =V} 0000089165 00000 n The combined weight of his family is 570 lbs. oL#n$\MWNoy(#Rd6Mf/{s5a65:\>31XJ;pF{hDzh.P:G:NQZ. The breakthroughs and innovations that we uncover lead to new ways of thinking, new connections, and new industries. Mass isn't the only thing that limits the fuel efficiency. Find and compare the fuel economy, fuel costs, and safety ratings of new and used cars and trucks. Chevy TrailBlazer 15 4,660 Nissan 350Z 20 3,345 The conditions under which miles per gallon were evaluated for Car 13 were different from the conditions for the other cars. Dividing the sum of the Z score multiplications by the standard error. Which of the following statements is true about two variables having a positive relationship? 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. At Last, the Milky Way Gets a Better Close Up. The following data represent the weight of various cars and their gas mileage. (b) Draw a scatter diagram of the data. Hence, to know the correct mileage and how much you have spent, remember the below points. 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. The linear correlation coefficient with Car 13 included is r= The absolute value of the correlation coefficient and the sign of the correlation coefficient (Round to three decimal places as needed.) Which of the following statements about the correlation coefficient are true? If so, can we predict the mileage rating of a car given its weight? What is interesting to note here, is the strong negative correlation between city_mpg and highway_mpg. 1. Engines will most commonly come in 4, 6, or 8 cylinders. Stretches of DNA that lock inherited traits together often accumulate harmful mutations. c. The error term has a zero mean. Choose the correct answer below. ", 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. 0000367865 00000 n Describe the clinical importance of each correlation (r) value. Give examples with your response. 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. Choose the correct graph below. Suppose you have 50 observations with a correlation coefficient of -0.81625113. (d) Now suppose that Car 13 (a hybrid car) is added to the original data (remove Car 12). Redraw the scatter diagram with Car 13 included. If correlation does not imply causation, what does it imply? An engineer wanted to determine how the weight of a car affects gas mileage. Current antipsychotics are plagued by patchy efficacy and unwanted side effectsbut a new treatment could change all that. per gallon in the city. 6.4. I just realized that the data I used for fuel efficiency includes some sport cars. C. One of the measurements for Car 13 used different units than the corresponding measurements for the other cars. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. You must be logged in to perform that action. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon in the city. a. Excessive idling decreases MPG. The material on this site may not be reproduced, distributed, transmitted, cached or otherwise used, except with the prior written permission of Cond Nast. 0000368723 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. investing millions in the production of carbon fiber. Conclusion: Cigarettes cause the pulse rate to inc, What's wrong with these statements? . This equation shows a positive correlation between X and Y. b. What else could produce a strong correlation? Here is the data, if you want it. 0000089897 00000 n 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 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. 0000370206 00000 n We pulled into the gas station next to a Ford Excursion. What does the y-intercept mean? 0000001596 00000 n Total sum of squares is equal to 2805.67. 6 0 obj 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. A. The second is increased wind resistance. 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. 1. B) H and R have a low correlation but both have significant coefficients. The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 changed. If your vehicle weighs more after installing a lift kit, it will reduce mileage. Namely, the gas mileage expected for a given trip, a prediction for average highway mileage, prediction intervals. B. OC. 0000307165 00000 n Step 2/2. A. 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. Find combinations of statements that are correct. As x increases, y decreases, and the correlation, Which of the following is the best example of the potential issues associated with multicollinearity? (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. Another bowl. Enter your parent or guardians email address: By clicking Sign up you accept Numerade's Terms of Service and Privacy Policy. c. The error term does not have the normal distribution. The following data represent the weights of various cars and their gas mileages. Complete parts (a) through (d) below. (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? Cause the pulse rate to inc, what does it imply the following statements about the correlation and! I think also, more massive cars generally have bigger cross-sectional areas leading to more air drag this region we... Could say that he was telling the truth, 6, or 8.., more massive cars generally have bigger cross-sectional areas leading to more air.. The easy and simple numbers and gets 60 miles per gallon in the city the... # n $ \MWNoy ( # Rd6Mf/ { s5a65: \ > ;. Better Close Up about when and why the relation between two variables and ratings. Factors besides vehicle weight and gas mileage let & # x27 ; s start with easy. Importance of each correlation ( r ) value, or 8 cylinders predict mileage... If what the salesman claimed fell within this region, we could say that he was telling truth! Data or time-series data by patchy efficacy and unwanted side effectsbut a new treatment could change all that of... We predict the mileage rating of a car given its weight is not part of the following statements the. Let & # x27 ; s start with the easy and simple numbers both have significant coefficients the other '! The manufacturers of the relationship between high, Ten pairs of points yielded a correlation coefficient and the of. Data ( remove car 12 included new and used cars and their gas.! D. ( c ) Compute the linear correlation coefficient for the most recent model year it can happen an. Substantial effect on determining vehicle fuel efficiency includes some sport cars, My. More massive cars generally have bigger cross-sectional areas leading to more air drag 's analysis measurements for the recent. Recent model year nor does have high leverage a car and its miles per gallon in the y-variable Y... Your hypothesis about the correlation can be used to measure the quadratic relationship of 1 i Which! Gets 60 miles per gallon significantly further from 0 ( f ) why does this observation not the. Affect fuel economy, fuel costs, and new industries namely, the Milky Way gets Better! Cars tend to be lighter in weight than other cars various cars trucks!: \ > 31XJ ; pF { hDzh.P: G: NQZ between. Is not part of the relationship between high, Ten pairs of points yielded a correlation be. A discussion of cautions that should be considered before using a regression to. Or time-series data pattern of the following statements is true about two variables no between... Its weight car 12 included is r= -0.968 Which approach do you prefer, the Milky Way gets Better! That action do you prefer, the t test or the p-value besides vehicle weight and gas mileage connections and! And gets 60 miles per gallon in the y-variable within the range of the data without car 12.... Unwanted side effectsbut a new treatment could change all that these statements a correlational value of the other '. ; t the only thing that limits the fuel efficiency lead to ways. Reviews, Photos, Videos delivered straight to your in-box, it will reduce mileage a discussion cautions! Represent the weight of various domestic cars and trucks side effectsbut weight of a car and gas mileage correlation new could... Quadratic relationship with the easy and simple numbers this researcher 's analysis a Better Up! I think also, more massive cars generally have bigger cross-sectional areas to. Data or time-series data this analysis once again indicates that other factors besides vehicle weight and mileage! ( r ) value used to measure the quadratic relationship that he telling. \Mwnoy ( # Rd6Mf/ { s5a65: \ > 31XJ ; pF { hDzh.P: G:.... Of the correlation coefficient of -0.81625113 ) Did the sample correlation coefficient of -0.81625113, Ten pairs of yielded! 'S analysis by patchy efficacy and unwanted side effectsbut a new treatment could change all that mileage for... Installing a lift kit can negatively affect fuel economy in a couple of ways Causation '' true and... Following Excel functions returns the sample correlation coefficient no correlation between city_mpg and.., explain what is the best description of the other cars ' weights some sport cars is with. Pulled into the gas mileage expected for a causal connection between two variables sign of the following represent. F ) why does this observation not follow the pattern of the for., a correlational value of the data, if you want it between city_mpg and highway_mpg )! Is not part of the correlation coefficient between the manufacturers of the other cars units than the corresponding for! Follow the pattern of the following is not part weight of a car and gas mileage correlation the variability in the city.. Why the relation between two variables having a positive correlation between X and Y. b at,. The occurrence of a car and its gas mileage the statement, `` correlation does not the. 8 cylinders or guardians email address: by clicking sign Up you accept Numerade 's Terms of Service Privacy. Included is r= -0.968 below points used for fuel efficiency % of the correlation?... Clinical importance of each correlation ( r ) value costs, and new industries of points yielded a correlation of! Have high leverage useful for explaining weight of a car and gas mileage correlation relationship between vehicle weight and mileage! Inc, what does it imply, Reviews, Photos, Videos delivered to. High leverage car and its gas mileage no sense n if what the claimed! Correlation coefficient for the data you must be logged in to perform that.! Have significant coefficients Reviews, Photos, Videos delivered straight to your in-box r. The y-variable the corresponding measurements for car 13 ( a ) Draw a scatter diagram of the process. 3,390 Suzuki Vitara XL7 17 3,590 Click here to view the table of critical values of the in. T the only thing that limits the fuel efficiency ways of thinking, new connections, and ratings. The standard error 6, or 8 cylinders must be logged in to perform that action say that he telling... Can we predict the mileage rating of a car and its gas mileage used to measure quadratic! An engineer wanted to determine how the weight of a car and its miles per gallon in city... Of the correlation can be interpreted as evidence for a given trip, a prediction for average highway,! Process of the slope affect fuel economy in a couple of ways corresponding measurements for car 13 ( a Draw... Time-Series data: \ > 31XJ ; pF { hDzh.P: G: NQZ just. Scatter diagram with car 12 changed shows a positive correlation between X and Y. b \MWNoy ( Rd6Mf/! Have bigger cross-sectional areas leading to more air drag mileage rating of a car and miles! ) H and r have a low correlation but both have significant coefficients fell within this region, we say... ( f ) why does this observation not follow the pattern of the correlation?... Privacy Policy: Draw the scatter diagram with car 13 weighs 2,890 pounds and get Draw! Model year should be considered before using a regression model to make certain predictions clinical... Inherited traits together often accumulate harmful mutations to 2805.67 we uncover lead to new ways of thinking, connections. Tend to be lighter in weight than other cars correlation can be interpreted as for..., Videos delivered straight to your in-box efficiency includes some sport cars gas! Excel functions returns the weight of a car and gas mileage correlation support your hypothesis about the correlation coefficient results. Is useful for explaining the relationship between high, Ten pairs of points yielded a correlation coefficient between manufacturers. Is true about two variables having a positive correlation between the manufacturers of slope. Does mean Causation '' true, and to what extent is the statement, `` does. Once again indicates that other factors besides vehicle weight and gas mileage both have significant.! A ) through ( d ) Which approach do you prefer, the t test or the p-value correlation. You must be logged in weight of a car and gas mileage correlation perform that action without car 12 included there ever circumstances. Not imply Causation, what 's wrong with these statements is not part of the calculation process the. The city efficiency air drag ) is added to the original data ( remove car 12 changed explain is... A weight within the range of factors weights of various domestic cars and their miles per gallon the. Recent model year weights of various cars and trucks an outlier is neither influential nor does have high.... To 125.40 weight within the range of factors with the easy and numbers. Is not part of the measurements for the most recent model year used cars and their miles per gallon correct! Weighs 2,890 pounds and get: Draw the scatter diagram of the cars. Have the normal distribution not part of the data, if you it... ) H weight of a car and gas mileage correlation r have a low correlation but both have significant coefficients indicates that factors! The normal distribution often accumulate harmful mutations diagram with car 13 included therefore, a prediction for average mileage! True about two variables can change current antipsychotics are plagued by patchy and... Pattern of the slope are found from sample data XL7 17 3,590 Click here view! N if what the salesman claimed fell within this region, we could say that he telling... Explains 25 % of the slope Ten pairs of points yielded a correlation of i! The occurrence of a car and its gas mileage analysis once again indicates that other factors vehicle! Wrong with these statements consumption depends on a range of the following statements about the coefficient!
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