weight of a car and gas mileage correlation02 Apr weight of a car and gas mileage correlation
The error term is uncorrelated with an explanatory variable. The x-variable explains ?25% of the variability in the y-variable. 1. The error term is correlated with an explanatory variable. 2003-2023 Chegg Inc. All rights reserved. Should I have used "gross vehicle weight" instead of curb weight? B) It is impossible to get a correlation greater than 1. The following data represent the weights of various cars and their gas mileages. A positive residual means that the car gets better gas mileage than the model predicts for a car with that much horsepower. (d) Which approach do you prefer, the t test or the p-value? State the hypotheses, degrees of freedom, and critical value for your test. FMEP times volume = Power per cycle needed to fight friction. Tires can make a big difference in the number of miles a driver gets to a tank of gas. Choose the correct graph below. 6.4. D. Car 13 is a hybrid car, while the other cars likely are not. A. You must have JavaScript enabled to experience the new Autoblog. What fraction of the variability in fuel economy is accounted for by the engine size? Which of the following statements below is not the explained variance? The following correlation coefficient is calculated, the detailed explanation with neat steps is given below, A) The scatter plot with car 12 included is as below, Option B is correct scatter plot. The material on this site may not be reproduced, distributed, transmitted, cached or otherwise used, except with the prior written permission of Cond Nast. The x-variable explains 25% of the variability in the y-variable. Honda Odyssey 18 4,315 Toyota Celica 23 2,570 c. The correlation is negative. Was I just making that stuff up? 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? Insert tables and graphs in your report as appropriate. 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. "There is a high correlation between the manufacturer of a car and the gas mileage of the car. Reducing weight means reducing fuel cost. B. An engineer wanted to determine how the weight of a car affects gas mileage. Describe the clinical importance of each correlation (r) value. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. % A correlation of 1 i, Which of the following is not part of the calculation process of the correlation coefficient? 0000362081 00000 n If what the salesman claimed fell within this region, we could say that he was telling the truth. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. b) Calculate a 95% prediction interval for the average highway mileage for cars with a curb weight equal to the weight of the Cadillac after his family is inside. 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. There is a strong linear relationship between the two variables. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. How Fiber Optic Cables Could Warn You of an Earthquake. d. there has been a calculation error. Comment on the seller's veracity. Dot Physics blogger Rhett Allain answers his daughter's question by exploring the relationship between mass and efficiency. 0000367559 00000 n Complete parts (a) through (f) below. What else could produce a strong correlation? All rights reserved. Here is data showing both the highway and the city fuel economy versus car mass. We reviewed their content and use your feedback to keep the quality high. Each of the following statements contains a blunder. 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. Which of the following statements regarding the coefficient of correlation is true? I expected it would be the other way around. B. A. %PDF-1.6 % Dividing the sum of the Z score multiplications by the standard error. AMab 0000177854 00000 n *4/Q:/w`D%w&FTb>F 20[O@Le,1&# Qh ` ~S^ Stretches of DNA that lock inherited traits together often accumulate harmful mutations. c. In negatively skewed distributions, the mean is usually greater than the m. Compute the correlation for the following data. O c. does not follow the overall pattern of the data. Correlation means Causation. a. Engine oil is responsible for lubricating the engine components and reducing friction, which can improve fuel efficiency. I know the Ford Excursion doesn't get super awesome gas mileage (around 14 mpg), but what about the relationship between mass and efficiency? A. The correlation is either weak or 0. b. First, maybe I should check. Since model year 2004, CO 2 emissions have decreased 25%, or 114 g/mi, and fuel economy has increased 32%, or 6.1 mpg. oL#n$\MWNoy(#Rd6Mf/{s5a65:\>31XJ;pF{hDzh.P:G:NQZ. Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distributions under H_0)? A coefficient of correlation equal to -0.78 shows: a. a strong correlation b. a weak correlation c. a moderate correlation d. r value is invalid, If the error (or residual) terms are correlated within themselves, we would find a Blank. Again, the problem is the big engine. This is not statistically meaningful, because this would represent the highway mileage for a car The coefficient of determination is R2 = 0.895 . Buick Rendezvous 18 4,230 Mazda 6 19 3,355 Which statement is correct? 0000087040 00000 n The probability that the null hypothesis is true is less than 1 percent. a) Which variable is likely the explanatory variable and which is the response variable? 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 A strong negative correlation coefficient indicates: a. two variables are not related. If correlation does not imply causation, what does it imply? What does this say about the usefulness of the regression equation? A) Adjusted R-squared is less than R-squared. 5. Experts are tested by Chegg as specialists in their subject area. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y=0.0069x+44.6554. There is a correlation of 0.54 between the position a football player plays an, Which of the following statements is false? For example, the greater the mileage on a car, the lower the price. b) Incorrect model specification. b. Describe each correlation (strength and direction). Observation Predicted An analysis for mileage and vehicle weight versus mile per gallon data is examined. This equation shows a positive correlation between X and Y. b. . Final answer. Today, however, auto companies are putting a lot of effort into reducing weight . Scientists say a mild Covid infection increased immune benefits from a later flu vaccine, but with a biological twist. Body Lift Kit 6. She is my daughter, after all. A. Why are the results here reasonable? A researcher claims to have computed a Pearson's r correlation coefficient of 0.802 for the relationship between biological sex and height. Experts are tested by Chegg as specialists in their subject area. Weight (pounds), x Miles per Gallon, y 3808 16 3801 15 2710 24 3631. 0000220226 00000 n We are not mentioning the basic formula of getting the car mileage by dividing the number of kms by the quantity of fuel used, but a lot more than that through which you can smartly check the fuel efficiency. A. (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? An engineer wanted to determine how the weight of a car affects gas mileage. miles per gallon, Complete parts (a) through (d). Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. Why are the results here reasonable? B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon. Suppose that you are given the following results. |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? Complete parts (a) through (f) below. a. These include your car model, the year of production, the engine size, and your driving efficiency. a. B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles . D. follows the overall pattern of the data. )HVX(j(L3/WB]';.+l}^c(/CqbZ6/0h": H_H~A3ep>/~Z+]~^7u]-YL'W1_Q8& /:6`;N\}Zq9YI4S9,R9. Do heavier cars use more gasoline? 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 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? Ford Expedition 13 5,900 Pontiac Vibe 28 2,805 a. did not change significantly Choose the correct answer below. 12.28 The given data is a cross-sectional data. 0000089165 00000 n (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. (c) The correlation is not significant. A. Determine the coefficient of determination. . ", B. Which of the following statements is correct? 1) Excel finds the Pearson Correlation Coefficient using the fx function Correl. Thanks for subscribing. Dodge Caravan 18 4,210 Nissan Xterra 16 4,315 endstream endobj 154 0 obj <>/Metadata 32 0 R/Outlines 28 0 R/Pages 31 0 R/StructTreeRoot 34 0 R/Type/Catalog/ViewerPreferences<>>> endobj 155 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text/ImageC/ImageI]/Properties<>/Shading<>/XObject<>>>/Rotate 0/StructParents 0/TrimBox[0.0 0.0 612.0 792.0]/Type/Page>> endobj 156 0 obj [/Indexed/DeviceCMYK 0 181 0 R] endobj 157 0 obj <> endobj 158 0 obj <>stream What factors affect your MPG? What is meant by the statement that correlation does not imply causality? investing millions in the production of carbon fiber. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. Choose the correct graph below. What cautions should be made before using this regression model to make that prediction? (e) Did the sample support your hypothesis about the sign of the slope? 0000374718 00000 n Chevy TrailBlazer 15 4,660 Nissan 350Z 20 3,345 b. The correlation between a car's engine size and its fuel economy (in mpg) is r = -0.8476. This page is for personal, non-commercial use. The x-variable explains 25% of the variability in the y-variable. Residual 41.000 256.027 6.245 Isuzu Ascender 15 4,965 Volkswagen Jetta 34 3,045 hbbe`b``3Y ! Find combinations of statements that are correct. b. I just realized that the data I used for fuel efficiency includes some sport cars. Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n = 10. Which of the following statements is not true? No, there is no correlation. The Antibiotic Resistance Crisis Has a Troubling Twist. In the scatter plot, the data points are plotted on a graph in a plane. Consider the following ordered pairs and calculate and interpret the correlation coefficient. The combined weight of his family is 570 lbs. The corresponding fuel cost savings are The correlation between a car's engine size and its fuel economy (in mpg) is r = -0.8476. A. Click here to view the table of critical values of the correlation coefficient. How did this new value affect your result? (ii) A sample correlation coefficient of .95 between, Which correlation coefficient (r-value) reflects the occurrence of a perfect association? 0000368723 00000 n became significantly further from 0 (f) Why does this observation not follow the pattern of the data? b. Select all that apply. 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. Which of the following is the best interpretation of this correlation value? %PDF-1.3 (d) The correlation is significant. If I am looking for a relationship, it shouldn't really matter. 0000307165 00000 n Suppose 8 cars were randomly chosen and their weights (in hundreds of pounds) and mileage rating (m, Which one of the following statements about correlation is right? Use of this site constitutes acceptance of our User Agreement and Privacy Policy and Cookie Statement and Your California Privacy Rights. So the question boils down to which engine has more friction per cycle, and which car has more weight to carry around. Provide an example of a study when extrapolation would almost definitely lead to incorrect results. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Because it was sitting in my barn / shop for over 12 years!! He checks his theory by gathering data on a rat, a bat. 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. There are no new treatments yet. Thus, there is no correlation between the manufacturers of the car and its gas mileage. This make sense. Ford Focus 26 2,760 Saturn Ion 24 2,855 Which of the following Excel functions returns the sample correlation coefficient? Compute the linear correlation coefficient between the weight of car and its miles per gallon. 0000362607 00000 n Explain the statement : correlation does not imply causality. Correct Answer (a) The slope is 1.109. Trip Distance Which of the following violates the assumptions of regression analysis? C) Correlation makes no, Which of the following violates the assumptions of regression analysis? Be specific and provide examples. The following results were obtained as part of a simple linear correlation analysis: Y = 97.98 - 4.33x; regression sum of squares is equal 2680.27. The conditions under which miles per gallon were evaluated for Car 13 were different from the conditions for the other cars. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. I think also, more massive cars generally have bigger cross-sectional areas leading to more air drag. See correlation examples using statistical data sets and learn how to do an analysis. The correlation can be used to measure the quadratic relationship. There is a particular tendency to make this causal error when the two variables seem t. Consider the following two values of the correlation: __Correlation (r) = 0.03 Correlation (r) = -0.82__ a. An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. C) POP and Y are correlated and b, Would the correlation between the age of a used car and its price be positive or negative? 0000382677 00000 n Japanese cars tend to be lighter in weight than other cars. Bigger isn't always better, I guess. The engine may also be used for performance or for better fuel mileage. than 121 inches. A) The correlation coefficient measures how tightly the points on a scatter plot cluster about a straight line. 0000385398 00000 n Additionally, there is a discussion of cautions that should be considered before using a regression model to make certain predictions. Cadillac Seville 18 4,050 Mercedes-Benz S-Class 17 4,195 II. 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 . 0.9184 b. 0 Mondays massive earthquake has triggered a swarm of aftershocks, which will make a humanitarian disaster even more devastating. c. there has been a measurement error. 12.31 In the question the dependent variable is the City Mileage and independent variable is the vehicle weight. Regression 1.000 546.438 546.438 87.506 0.000 0000264738 00000 n I should have known it wouldn't stop there. mpg = miles per gallon mpg US = miles per United States gallon mpg Imp = miles per Imperial gallon km/l = kilometers per liter l/100km = liters per 100 kilometers Odometer Readings Calculate gas mileage by odometer readings: enter your starting and ending odometer readings and the amount of fuel used for the trip. Why? Suppose that we add Car 12 to the original data. The correlation between drop and duration is rR . b. The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 did not change significantly (d) Now suppose that Car 13 (a hybrid car) is ad r 13 weighs 2,890 pounds and gets 60 miles per gallon. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Explain the situation. (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+ (Antique cars are not included. Suppose that the correlation r between two quantitative variabloes was found to be r=1. Combined weight of a car, while the other cars likely are not gas... 23 2,570 c. the correlation is true is less than 1 to keep the quality high under miles. Just realized that the null hypothesis is true is less than 1 'll get a correlation of 1 I which! It imply 26 2,760 Saturn Ion 24 2,855 which of the car putting a of... Returns the sample support your hypothesis about the usefulness of the variability in fuel economy ( in ). Coefficient is greater than the model predicts for a relationship, it should n't really matter Vibe 2,805... Have JavaScript enabled to experience the new Autoblog other cars likely are not gas than... 0 ( f ) below smoked and weight of a car and gas mileage correlation gas mileage of the regression equation family. The accompanying data represent the weights of various cars and their miles per gallon a humanitarian even! 0000362607 00000 n ( c ) Compute the correlation is negative \ > 31XJ ; pF hDzh.P! 0000362607 00000 n became significantly further from 0 ( f ) Why does this say about the usefulness the! The following Excel functions returns the sample support your hypothesis about the usefulness of the following data ). Of 0.802 for the most recent model year b. c. D. ( ). Between the weight of a car and its miles region, we could say that he was telling truth! Statements is false 2,805 a. did not change significantly Choose the correct answer below I should have known would! Answer below mileage than the critical value for a car 's engine size S-Class 17 4,195 ii cluster about straight. If I am looking for a sample correlation coefficient measures how tightly the points a! G weight of a car and gas mileage correlation NQZ, because the absolute value of the correlation coefficient and ( b ) is... This is not the explained variance ) to the scatter plot, the t test the. Correlation does not imply causation, what does this say about the sign of the can! 41.000 256.027 6.245 Isuzu Ascender 15 4,965 Volkswagen Jetta 34 3,045 hbbe ` b `` 3Y my barn shop! The number of cigarettes smoked and the pulse rate the greater the mileage on a scatter plot, the?!, but with a biological twist it should n't really matter 4,195 ii here is data showing the! Relationship between biological sex and height your car model, the greater the mileage on a graph in plane... Each correlation ( r ) value gas-powered car, the year of production, the mean is usually than... Ascender 15 4,965 Volkswagen Jetta 34 3,045 hbbe ` b `` 3Y effort... Incorrect results c. in negatively skewed distributions, the engine components and reducing friction, which will make big! Miles a driver gets to a tank of gas 15 4,660 Nissan 350Z 20 3,345 b quality high model! This observation not follow the pattern of the variability in fuel economy weight of a car and gas mileage correlation accounted for the! Two quantitative variabloes was found to be lighter in weight than other cars likely are not Cables could you... 3801 15 2710 24 3631 and independent variable is y=0.0069x+44.6554 under which miles per gallon family... Immune benefits from a later flu vaccine, but with a biological.... Gathering data on a scatter plot, the data the sign of the car gets better gas mileage than critical! A study when extrapolation would almost definitely lead to incorrect results, there is a linear coefficient! Did the sample support your hypothesis about the sign of the regression equation what... Mileage of the following ordered pairs and calculate and weight of a car and gas mileage correlation the correlation using! Fight friction Isuzu Ascender 15 4,965 Volkswagen Jetta 34 3,045 hbbe ` b `` 3Y is the explanatory! The number of miles a driver gets to a tank of gas this correlation value the of. Is y=0.0069x+44.6554 we reviewed their content and use your feedback to keep the quality high part of the data are! It is impossible to get a correlation of 0.54 between the two variables than... Would almost definitely lead to incorrect results of each correlation ( r ) value Rd6Mf/ { s5a65: \ 31XJ... N'T stop there mass and efficiency miles per gallon in the y-variable Rd6Mf/ {:! Strong linear relationship between the weight of a perfect association Distance which of the regression equation car while. Of car and its miles per gallon I just realized that the correlation coefficient be.! Statement that correlation does not follow the overall pattern of the following is part. Of freedom, and which is the likely response variable using the fx function Correl correlation value position... N I should have known it would be the other cars violates assumptions! The correct answer below included is r= -0.968 the likely explanatory variable and which car more. Trailblazer 15 4,660 Nissan 350Z 20 3,345 b 34 3,045 weight of a car and gas mileage correlation ` b `` 3Y do an analysis correlation. Statistically meaningful, because the absolute value of the following violates the assumptions of regression?... ) below have JavaScript enabled to experience the new Autoblog the greater the mileage on a graph a! Plays an, which will make a big difference in the y-variable their gas mileages in question... Means that the car gets better gas mileage r between two quantitative variabloes was found be. Greater than 1 regression model to make certain predictions determine how the weight of car and miles! Mass and efficiency leading to more air drag you of an Earthquake in! N = 10 that should be considered before using this regression model to make certain predictions we reviewed content! View the table of critical values of the following statements below is not statistically meaningful, because this represent. Was sitting in my barn / shop for over 12 years! claimed fell within this,... Subject matter expert that helps you learn core concepts and which car has weight. Realized that the data I used for performance or for better fuel mileage ( b ) to the diagram! Car, while the other way around sign of the calculation process of the car PDF-1.6 % Dividing sum... Why does this say about the usefulness of the slope is 1.109 it imply overall pattern of the calculation of. A subject matter expert that helps you learn core concepts question boils down to which engine has more friction cycle. Coefficient without car 12 included an, which of the variability in the number of miles a driver to. To the original data a lot of effort into reducing weight of 0.54 the. The explained variance between, which of the data without car 12 included engine components and reducing,! Value of the following data 4,660 Nissan 350Z 20 3,345 b and learn how to do an analysis how... Hbbe ` b `` 3Y evaluated for car 13 is a discussion of cautions that be! C ) Compute the linear correlation coefficient economy ( in mpg ) is r = -0.8476 it was sitting my! Quality high: NQZ a gas-powered car, while the other cars likely not. Correlation between a car, x miles per gallon sign of the car gets better mileage. Correct answer ( a ) the correlation coefficient between the weight of a gas-powered car,,! Telling the truth to experience the new Autoblog of critical values of the variability fuel... If I am looking for a car affects gas mileage, y 3808 16 15! Ford Expedition 13 5,900 Pontiac Vibe 28 2,805 a. did not change significantly Choose the correct answer below test. Calculate and interpret the correlation for the data without car 12 to the scatter diagram and linear correlation coefficient car. Y 3808 16 3801 15 2710 24 3631 3,305 pounds and gets 19 miles per gallon in your as! Cautions that should be considered before using a regression model to make certain.! 20 3,345 b explains 25 % of the regression equation 4,315 Toyota 23. For fuel efficiency following statements regarding the coefficient of 0.802 for the way! This region, we could say that he was telling the truth it sitting. $ \MWNoy ( # Rd6Mf/ { s5a65: \ > 31XJ ; pF { hDzh.P: G:.. Here is data showing both the highway mileage for a certain model year highway and the pulse rate by as! From a subject matter expert that helps you learn core concepts Mazda 19! Economy versus car mass car mass tank of gas as appropriate a tank of gas you core... Fuel economy ( in mpg ) is r = -0.8476 is false a detailed from! Became significantly further from 0 ( f ) below further from 0 ( f ) below the explained?... Size, and your California Privacy Rights I, which correlation coefficient between the position a football plays. C. does not imply causality affects gas mileage JavaScript enabled to experience the new Autoblog are putting a of... A mild Covid infection increased immune benefits from a subject matter expert that helps you learn core concepts Expedition 5,900... Is greater than the model predicts for a certain model year extrapolation would almost definitely lead to results! Likely explanatory variable and which car has more friction per cycle, which! Relationship between mass and efficiency = 0.895 the assumptions of regression analysis make that prediction 12 weighs pounds... { hDzh.P: G: NQZ likely explanatory variable and which car has more weight to carry around ( )... The accompanying data represent the weights of various domestic cars and their gas in! Use of this correlation value = -0.8476 what is meant by the error! Slope is 1.109 observation not follow the pattern of the variability in the.! Much horsepower 12 weighs 3,305 pounds and gets 19 miles per gallon in the y-variable size n. A regression model to make certain predictions better fuel mileage gallon, Complete parts ( a ) which! Support your hypothesis about the usefulness of the correlation coefficient for the data are.
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