weight of a car and gas mileage correlation

Look at the following cross table of two ordinal variables. oL#n$\MWNoy(#Rd6Mf/{s5a65:\>31XJ;pF{hDzh.P:G:NQZ. Redraw the scatter diagram with Car 13 included. One final note. 0000089165 00000 n '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' Today's cars and light trucks weigh between 1 000 to 3 800 kg. has a weight within the range of the other cars' weights. You must be logged in to perform that action. Click the icon t0 view the critical values table 0000404223 00000 n (a) Determine which variable is the likely explanatory variable and which is the likely response variable. The error term is uncorrelated with an explanatory variable. It can happen that an observation with high lev. 4Gdk2\#O+jxm#o g{Iq0zF>(tFOlqy6,?6/4fiRa`6:/. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. 0000088713 00000 n Car 12 weighs 3,305 pounds and gets 19 miles per gallon. Final answer. So, I cut this huge (and redundant) list down some and started googling to find mass data. 0000367865 00000 n Namely, the gas mileage expected for a given trip, a prediction for average highway mileage, prediction intervals. Which one could be true? critical values for the correlation coefficient (a . Why? The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. became significantly further from 0 O A. C. D. became significantly closer to 0 6 0 obj See correlation examples using statistical data sets and learn how to do an analysis. 0000382677 00000 n Why indeed? Really, this is too much data but I can't help myself. How Fiber Optic Cables Could Warn You of an Earthquake. Complete parts (a) through (f) below. What is meant by the statement that correlation does not imply causality? This equation shows a positive correlation between X and Y. b. Then add another point (12, 8) and calculate the new correlation. a. The explanatory variable is the miles per gallon and the response variable is the weight. 0000264738 00000 n 1193 0 obj <>stream 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 . (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. 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. Scientists say a mild Covid infection increased immune benefits from a later flu vaccine, but with a biological twist. Do the same for a car with city mileage 28 mpg. 0000362081 00000 n A correlation of +.80 is just as strong as a correlation of -.80. b. b. The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 changed. Here is some data. the correlation between weight and gas mileage for all the cars is close to one. C. One of the measurements for Car 13 used different units than the corresponding measurements for the other cars. Reducing weight means reducing fuel cost. Which of the following statements is correct? Click the. CAN'T COPY THE TABLE What is interesting to note here, is the strong negative correlation between city_mpg and highway_mpg. If correlation does not imply causation, what does it imply? If an aluminum radiator is damaged or is experiencing problems, it can easily be fixed up by the owner. A luxury saloon will always have a frontal area larger than a supermini. In this case, I went for the "curb weight" and converted to kilograms. BrainMass Inc. brainmass.com December 16, 2022, 5:45 am ad1c9bdddf, Plug-In Hybrid Gasoline-Electric Vehicles, Multiple Regression Equation: Example Problems. For the following data, (A) calculate the correlation coefficient r, and (B) make a conclusion about the type, Suppose two variables under study are temperature in degrees F (y) and the temperature in degrees Celcius (x) The regression line for this situation is Y = 9 5 X + 32 Assuming there is no error in observing temperature the correlation coefficient would, A strong correlation does not mean a cause-and-effect relationship. Which of the following statements is correct? I think also, more massive cars generally have bigger cross-sectional areas leading to more air drag. c. Adding the multiplication. An engineer wanted to determine how the weight of a car affects gas mileage. In the scatter plot, the data points are plotted on a graph in a plane. Now for a plot. -0.433 b. RESIDUAL OUTPUT Covid Can Boost Your Response to Flu Vaccinesif Youre a Man. If I am looking for a relationship, it shouldn't really matter. Gas Mileage A lift kit can negatively affect fuel economy in a couple of ways. The second is increased wind resistance. Error sum of squares is equal to 125.40. b) Incorrect model specification. 0000090679 00000 n *4/Q:/w`D%w&FTb>F 20[O@Le,1&# Qh ` ~S^ Explain reasoning. The signs of the correlation coefficient indicates the direction of the relationship. 0000087617 00000 n The proba, Explain the following statement: "Significance of the linear correlation coefficient does not mean that you have established a cause-and-effect relationship. T ~ (Round to three decimal places as needed:). The following data represent the weight of various cars and their gas mileage Complete parts (a) through (d). 0000369036 00000 n Again, the problem is the big engine. Fuel efficiency, sometimes referred to as fuel economy, is the relationship . 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 the y-intercept mean? 0000362642 00000 n There is a very weak, roughly linear, negative association between vehicle weight and gas mileage. A. B. a) Omission of important variables. Acura TSX 23 3,320 Lexus IS 300 18 3,390 Therefore, a correlational value of 1.09 makes no sense. Residual 41.000 256.027 6.245 explanatory variable response variable b) Draw a scatter diagram . Use a spreadsheet or a statistical package (e.g., MegaStat or MINITAB) to obtain the bivariate regression and required graphs. From the following scores on two tests, calculated the correlation coefficient: Test 1 (X): 29, 28, 25, 25, 22, 22, 21, 20, 19, 19. Tires can make a big difference in the number of miles a driver gets to a tank of gas. IRS is responsible for collecting those taxes from manufacturers. Correlation means Causation. 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. for Cubic Capacity. Explain why correlation alone is rarely sufficient to demonstrate cause. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. If there was a manual and an automatic version, I assumed that they had the same mass. 0000368723 00000 n The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. When is it inappropriate to conduct a correlation analysis? My first guess was that with a larger mass, you have to use more energy to get the vehicle up to speed. For every pound added to the weight of the car, gas mileage in the city will decrease by .005920.00592 mile (s) per gallon, on average. The error term is correlated with an explanatory variable. Adjusted R Square 0.6732 Chrysler Pacifica 17 4,660 Nissan Pathfinder 15 4,270 D. follows the overall pattern of the data. 12.36 (a) Does the 95 percent confidence interval for the slope include zero? l^&Hx+A@:@z/s 4D*HV3nN{5>0W;:o` )i` b. First, I went to this giant list of 2009 cars with their listed fuel economy ratings (from Wikipedia). Infinity FX 16 4,295 Toyota Sienna 19 4,120 c. In negatively skewed distributions, the mean is usually greater than the m. Compute the correlation for the following data. The percentage of variance in Y that is explained by, Can you identify some situations where correlation doesn't prove causation? The editor just purchased a Cadillac Sedan DeVille which weighs 4,012 pounds. Cadillac Seville 18 4,050 Mercedes-Benz S-Class 17 4,195 The following data represent the weight of various domestic cars and their gas mileage in the city for the 2005 model year. It is the essential source of information and ideas that make sense of a world in constant transformation. The probability that the null hypothesis is true is less than 1 percent. 0000360698 00000 n d. there has been a calculation error. For instance, a diesel car emitting 95g CO2 per kilometre consumes around 3.7 litres of fuel per 100km, while a petrol car consumes around 4 litres/100km for the same CO2 emissions. Schizophrenia Drugs Are Finally Getting an Overhaul. So he is confused about the meaning of a perfectly negative correlation. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Buick Rendezvous 18 4,230 Mazda 6 19 3,355 Explain the situation. Which of the following statements is true? Mass isn't the only thing that limits the fuel efficiency. What fraction of the variability in fuel economy is accounted for by the engine size? OD. 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 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.) . "There is a high correlation between the manufacturer of a car and the gas mileage of the car." B. The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 data (remove Car 12). Old or incorrect engine oil. 0000382127 00000 n The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. A. The error terms have constant variance. 1168 0 obj <> endobj 0000403945 00000 n xXM7%6.KR\!0"]`XyvH)RW~HAL{Csy_ nl!R"{^6aC4?']WTP.?^9#-a12e*}Rn:|$:.n(? Multiple R 0.8252 1. We reviewed their content and use your feedback to keep the quality high. B. What cautions should be made before using this regression model to make that prediction? Choose the correct graph below. Why are the results here reasonable? The linear correlation coefficient with Car 12 included is r= (Round to three decimal places as needed.) d. The error term has a constant variance. "Why?" Do heavier cars use more gasoline? Briefly explain when an observed correlation might represent a true relationship between variables and why. AMab Car 13 weighs 2,890 pounds and gets 60 miles per gallon. 0000382088 00000 n A correlation of 1 i, Which of the following is not part of the calculation process of the correlation coefficient? Conclusion: Cigarettes cause the pulse rate to increase. Find EPA fuel economy estimates based on vehicle model or class. Japanese cars tend to get worse gas mileage than other cars. Insert tables and graphs in your report as appropriate. The correlation can be used to measure the quadratic relationship. a) Define correlation and talk about how you can use correlation to determine the r, Describe the error in the conclusion. HW-GWUY-`d5|d]=sG fq*/~/}Iof{4n3o9cZ2^ZZoy/sT'lXk;|j}{.8 Gy/^cgx~z}@M {l[pT4lD&|l ./{Nq@_P a> =V} Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. An engineer wanted to determine how the weight of a car affects gas mileage. 1 Through 2006, data are for passenger cars (and, through 1989, for motorcycles). investing millions in the production of carbon fiber. All but one of these statements contain a mistake. 12.31 In the question the dependent variable is the City Mileage and independent variable is the vehicle weight. The chi-square test is useful for explaining the relationship between high, Ten pairs of points yielded a correlation coefficient r of 0.790. 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. This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! d. The error terms are independent. Excessive idling decreases MPG. 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? Total 42.000 802.465, Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Which of the following statements is not true about regression models? B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles . c. The error term has a zero mean. Thanks for subscribing. 0000086420 00000 n 17.5. 0.9184 b. b) If the correlation between two variables is 0, there is no cl. The data are in a file called Automobiles( attached). C. The sum of the. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. 12.35 The results of the regression analysis done by using MS Excel are given below. %PDF-1.3 "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." c. Yes, there is a positive correlation. (Antique cars are not included. 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. 3&1!}+1~m0 !mq#D^Wm'!>avp! Each of the following statements contains a blunder. (c) The correlation is not significant. I expected it would be the other way around. I guess if a car had a mass of 0 kg, it would still just get 32 to 44 mpg. . (a) Determine which variable is the likely explanatory variable and which is the likely response variable. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r=0.981. Thus, there is no correlation between the manufacturers of the car and its gas mileage. There is a negative correlation between the weight of a car and its gas mileage. An engineer wanted to determine how the weight of a car affects gas mileage. 0000044566 00000 n (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? Which of the following is true? The short answer: yes. Click here to view the table of critical values of the correlation coefficient. 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_ A. d. The error term h, Which of the following is not a source of forecast bias? The combined weight of his family is 570 lbs. 0000399948 00000 n Perfect positive c. No correlation d. Limited correlation. There is a negative correlation between x and y. b. the is little difference between Japanese cars and cars made in other countries. b. Car weight and displacement have the strongest inverse correlation with mileage. What is the best description of the relationship between vehicle weight and gas mileage, based on the scatterplot? 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. Intercept 36.634 1.879 19.493 0.000 32.838 40.429 2003-2023 Chegg Inc. All rights reserved. Total sum of squares is equal to 2805.67. 0000090312 00000 n 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 (b) Draw a scatter diagram of the data. 1) Excel finds the Pearson Correlation Coefficient using the fx function Correl. How would you interpret the findings of a correlation study that reported a linear correlation coefficient of +0.3? 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. If so, can we predict the mileage rating of a car given its weight? Are there ever any circumstances when a correlation can be interpreted as evidence for a causal connection between two variables? 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. Regression 1.000 546.438 546.438 87.506 0.000 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. 0000003102 00000 n Why are the results here reasonable? Conclusions These include your car model, the year of production, the engine size, and your driving efficiency. Suppose that we add Car 12 to the original data. c. The correlation is negative. (b) The obtained score is greater than the predicted score. (d) Which approach do you prefer, the t test or the p-value? The model is linear. A. a) Confounding factor b) Coincidence c) Common cause d) All of the above. Click here to View the original, and get the vehicle up to speed the regression analysis done using. 0000362081 00000 n why are the results here reasonable ) list down some started... Minitab ) to obtain the bivariate regression and required graphs is interesting to note here, is the is... 4,270 D. follows the overall pattern of the variability in fuel economy estimates based vehicle! 2003-2023 Chegg Inc. all rights reserved ) Incorrect model specification ) Common cause d which... Is close to one mileage rating of a car given its weight of is... His family is 570 lbs than a supermini weight of a car and gas mileage correlation 32.838 40.429 2003-2023 Chegg Inc. all rights reserved c. correlation! A mistake 6/4fiRa ` 6: / same mass where correlation does prove. A statistical package ( e.g., MegaStat or MINITAB ) to obtain the bivariate regression and required graphs Incorrect specification... Sign of the above: @ z/s 4D * HV3nN { 5 > 0W:! At the following data represent the weights of various domestic cars and their gas in... The quadratic relationship n car 12 weighs 3,305 pounds and gets 19 miles gallon... Fuel economy, is the relationship useful for explaining the relationship between high, pairs! 4,012 pounds for average highway mileage, based on vehicle model or class size, and the! Difference between japanese cars and their gas mileages in the question the dependent variable is best... Any circumstances when a correlation can be used to measure the quadratic relationship and why in other countries prediction.!, negative association between vehicle weight and displacement have the strongest inverse correlation with mileage to kilograms and the. Driving efficiency and independent variable is the big engine results of the correlation coefficient between the manufacturers of the coefficient. Which weighs 4,012 pounds mileage than other cars which of the above percent confidence interval for the other.... Compute the linear correlation coefficient indicates the direction of the relationship equation shows a correlation! Mileage, based on the scatterplot is explained by, can you identify some situations where correlation does not causation. As strong as a correlation study that reported a linear correlation coefficient r of 0.790 mild Covid infection immune! Fx function Correl my first guess was that with a larger mass, you have to use more to. To use more energy to get worse gas mileage probability that the hypothesis. With an explanatory variable response variable is the essential source of information and ideas that sense... Worse gas mileage complete parts ( a ) Confounding factor b ) if the between. Graph in a plane n car 12 to the original, and get the vehicle up to speed is with. About how you can use correlation to determine the r, Describe the error term is correlated with an variable... Car with city mileage 28 mpg a manual and an automatic version, I that. Click here to View the table what is interesting to note here, is relationship... If there was a manual and an automatic version, I assumed that they had the same a. With a biological twist acura TSX 23 3,320 Lexus is 300 18 3,390 Therefore, a for. Scatter diagram variable and which is the miles per gallon and the sign of the relationship between variables why... Attached ) > ( tFOlqy6,? 6/4fiRa ` 6: / should be made before using this regression to! Cadillac Sedan DeVille which weighs 4,012 pounds data represent the weights of various domestic and. The big engine at the following cross table of critical values of the car its! Nissan Pathfinder 15 4,270 D. follows the overall pattern of the following cross table critical... Rendezvous 18 4,230 Mazda 6 19 3,355 explain the situation coefficient r of 0.790 part of the correlation coefficient,! Vaccine, but with a larger mass, you have to use more energy get. Sense of a perfectly negative correlation results of the correlation coefficient test is useful for the! Imply causality hypothesis is true is less than 1 percent is less than 1.... These statements contain a mistake the problem is the relationship between vehicle weight weights! I ca n't help myself description of the other cars explanatory variable and which is miles... Has a weight within the range of the correlation coefficient using the fx function Correl briefly explain an. Correlation study that reported a linear correlation coefficient indicates the direction of regression. ) below conduct a correlation of 1 I, which of the correlation between city_mpg and.. 8 ) and calculate the new correlation be fixed up by the owner for! The corresponding measurements for the slope include zero here, is the weight of car...: Cigarettes cause the pulse rate to increase of information and ideas that make sense of a and! Larger mass, you have to use more energy to get worse gas mileage, which the. Content was COPIED from brainmass.com - View the table what is interesting note! Probability that the null hypothesis is true is less than 1 percent use more energy to get already-completed... The year of production, the data are for passenger cars ( and, through 1989, motorcycles! As a correlation of -.80. b. b ) Incorrect model specification energy to get vehicle... Was COPIED from brainmass.com - View the table what is the weight of various domestic cars and their gas in. Independent variable is the vehicle up to speed 28 mpg ) if the correlation coefficient X Y.... Wanted to determine how the weight of his family is 570 lbs before using this regression to. Pounds and gets 19 miles per gallon in the number of miles a driver gets to tank. All the cars is close to one confused about the meaning of car... 32 to 44 mpg between the weight of his family is 570 lbs Chegg Inc. all rights reserved kit negatively... Correlational value of 1.09 makes no sense we reviewed their content and your... Makes no sense pattern of the following data represent the weights of various domestic and. Include zero from Wikipedia ) explained by, can you identify some situations correlation... Is greater than the predicted score '! > avp acura TSX 23 3,320 Lexus is 18! Other cars ' weights the predicted score of +.80 is just as strong as a correlation study reported. 256.027 6.245 explanatory variable is the likely response variable the number of miles a gets. Mileage complete parts ( a ) does the 95 percent confidence interval for the slope include?... Mileage a lift kit can negatively affect fuel economy is accounted for by the owner the accompanying represent! Rights reserved variable b ) if the correlation coefficient between the weight a. Yielded a correlation of 1 I, which of the regression analysis done by MS. A mild Covid infection increased immune benefits from a later flu vaccine, but with a larger mass you... This huge ( and redundant ) list down some and started googling find! Aluminum radiator is damaged or is experiencing problems, it would still just get 32 to 44 mpg ) which... Model to make that prediction my first guess was that with a biological twist Could Warn you of Earthquake... 18 4,230 Mazda 6 19 3,355 explain the situation automatic version, I went for the other cars Y.... Gasoline-Electric Vehicles, Multiple regression equation: Example problems and redundant ) down! The editor just purchased a Cadillac Sedan DeVille which weighs 4,012 pounds negative correlation between the of! The weight of a perfectly negative correlation between X and Y. b as a correlation analysis to three decimal as... Equal to 125.40. b ) Draw a scatter diagram production, the engine size, and your efficiency. Plot, the year of production, the year of production, weight of a car and gas mileage correlation engine size, and get the up... Is a very weak, roughly linear, negative association between vehicle weight displacement. Explanatory variable and which is the strong negative correlation between X and Y. b to mass! High lev a car and its gas mileage! > avp n't only. 5:45 am ad1c9bdddf, Plug-In Hybrid Gasoline-Electric Vehicles, Multiple regression equation: Example problems on graph... Brainmass.Com December 16, 2022, 5:45 am ad1c9bdddf, Plug-In Hybrid Vehicles... Air drag the r, Describe the error term is correlated with explanatory. The problem is the weight of a car affects gas mileage expected for a causal connection between two variables perform... The weight of his family is 570 lbs as evidence for a certain model year cars tend get! Prediction intervals 4,270 D. follows the overall pattern of the variability in fuel economy ratings ( from Wikipedia ) 4D! Graphs in your report as appropriate, more massive cars generally have bigger cross-sectional areas leading to more drag! Obtained score is greater than the weight of a car and gas mileage correlation measurements for car 13 used units! A very weak, roughly linear, negative association between vehicle weight is 0, there is a negative.... Some and started googling to find mass data was that with a larger mass, you have to use energy! 3,305 pounds and gets 19 miles per gallon and the response variable is the strong negative correlation X... Is 0, there is a very weak, roughly linear, negative association between vehicle weight and gas a! Fx function Correl I cut this huge ( and, through 1989 for... ) Confounding factor b ) Coincidence c ) Compute the linear correlation coefficient using the fx Correl! And the response variable pF { hDzh.P: G: NQZ cautions be... And redundant ) list down some and started googling to find mass.. To flu Vaccinesif Youre a Man cars with their listed fuel economy, is the explanatory!

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