weight of a car and gas mileage correlationweight of a car and gas mileage correlation

b. this giant list of 2009 cars with their listed fuel economy ratings. 12.36 (a) Does the 95 percent confidence interval for the slope include zero? 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. No, there is no correlation. The error term is uncorrelated with an explanatory variable. c. Yes, there is a positive correlation. If which of the following statements is correct if (Do not calculate a t-value: Hint - use the Critical Values of the PPMC - table, The following statements are about a standard deviation of residuals. 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? a. ", 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.". Kia Rio 25 2,295. Everyone loves data. These include your car model, the year of production, the engine size, and your driving efficiency. (A) CORREL (B) COVARIANCE.S (C) CORREL.S (D) CORRELATION, Explain the following terms in your own words: - Positive correlation - Negative correlation - No correlation. Honda Odyssey 18 4,315 Toyota Celica 23 2,570 -0.433 b. Since model year 2004, CO 2 emissions have decreased 25%, or 114 g/mi, and fuel economy has increased 32%, or 6.1 mpg. Hence the priori hypothesis about the sign of slope is "The slope is negative". I should have known it wouldn't stop there. 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. Mondays massive earthquake has triggered a swarm of aftershocks, which will make a humanitarian disaster even more devastating. Japanese cars tend to get worse gas mileage than other cars. So, I cut this huge (and redundant) list down some and started googling to find mass data. Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distributions under H_0)? 0000362642 00000 n However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence . Based on a gallon of gasoline costing. 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 became significantly closer to O A. (b) The intercept is 4.62 mpg. B) H and R have a low correlation but both have significant coefficients. Redraw the scatter diagram with Car 13 included. has a weight within the range of the other cars' weights. II. Use of this site constitutes acceptance of our User Agreement and Privacy Policy and Cookie Statement and Your California Privacy Rights. The value of correlation depends on the factors being considered, whether they are negatively associated or positively associated and the magnitude of their association. 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? ", 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. A. Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n = 10. a. How You May be Prematurely Aging Your Car, Preventing Auto Repairs Before They Cost You Dearly. )HVX(j(L3/WB]';.+l}^c(/CqbZ6/0h": H_H~A3ep>/~Z+]~^7u]-YL'W1_Q8& /:6`;N\}Zq9YI4S9,R9. 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. than 121 inches. A) Adjusted R-squared is less than R-squared. 2023 Cond Nast. Check your in-box to get started. What is interesting to note here, is the strong negative correlation between city_mpg and highway_mpg. Question 9 30 seconds Q. Complete parts (a) through (f) below. Residual 41.000 256.027 6.245 b. 12.35 Use Excel, MegaStat, or MINITAB to fit the regression model, including residuals and standardized residuals. became significantly further from 0 O A. C. D. became significantly closer to 0 Can a data set with perfect positive correlation increase its correlation if y-values increase? 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. l^&Hx+A@:@z/s 4D*HV3nN{5>0W;:o` )i` c. The error terms decrease as x values increase. Which of the following statements is correct? 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.) Dividing the sum of the Z score multiplications by the standard error. Each of the following statements contains a blunder. Engine oil is responsible for lubricating the engine components and reducing friction, which can improve fuel efficiency. 2500 4000 Weigh: (Ibs) 0000382826 00000 n A. Gas Mileage A lift kit can negatively affect fuel economy in a couple of ways. CAN'T COPY THE TABLE Suppose that you are given the following results. 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. d. b. If I am looking for a relationship, it shouldn't really matter. As the number of cigarettes increases the pulse rate increases. c. The range of values for a correlation is from 0 to 1. d. All of, Which statement best describes this regression (Y = highway miles per gallon in 91 cars)? 0000369380 00000 n 12.28 Are the variables cross-sectional data or time-series data? 0000368723 00000 n 1. 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. Mass isn't the only thing that limits the fuel efficiency. O A. 6 0 obj Which of the following statements regarding the coefficient of correlation is true? But they also hold genetic benefits for species. Was I just making that stuff up? What does the y-intercept mean? Beginning in 2007, data are for passenger cars, light trucks, vans, and sport utility vehicles with a wheelbase equal to or less. Which one could be true? 0000362552 00000 n The EPA says that for every 100 pounds taken out of the vehicle, the fuel economy is increased by 1-2 percent. For cases like this, I just took the first reasonable number I found. The model is linear. Choose the correct graph below. 0000085638 00000 n Explain the statement : correlation does not imply causality. endstream endobj startxref 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. In this case, I went for the "curb weight" and converted to kilograms. 157 2500 3300 4100 Weight (lbs) 15711 2500 3300 4100 Weight (lbs) 157 2500 3300 4100 Weight (lbs) 15+ 2500 3300 4100 Weight (lbs) (b) Compute the linear correlation coefficient with Car 12 included. 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? d. The error term has a constant variance. Thus, the correlational value must be in negative. There is a linear correlation between the number of cigarettes smoked and the pulse rate as the number of cigarettes increases the pulse rate increases. copyright 2003-2023 Homework.Study.com. i.e., linear vs. non-linear. Here are the fitting functions. (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. (d) Comment on the type of relation that appears to exist between the weight of a car and its miles per gallon in the city based on the scatter diagram and the linear correlation coefficient. It is natural to expect a negative relation between mileage and weight of the vehicle. I guess if a car had a mass of 0 kg, it would still just get 32 to 44 mpg. Find the correlation coefficient of the data b = .222; sx = 6.32; sy = 1.45. (b) Draw a scatter diagram of the data. A positive error e value indicates: (a) The predicted score is greater than the obtained score. Buick Rendezvous 18 4,230 Mazda 6 19 3,355 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. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. The probability that the null hypothesis is true is less than 1 percent. Select all that apply. df SS MS F Significance F It can happen that an observation with high lev. So the question boils down to which engine has more friction per cycle, and which car has more weight to carry around. If correlation does not imply causation, what does it imply? Clearly, it is reasonable to suppose a cause and effect relationship as follows: An increase in the vehicle weight produces a decrease of mileage. B. OC. B. c) Compute a 95% prediction interval for the actual highway mileage of this particular Cadillac with the editor's family inside. Ultimately, you can't trace fuel economy simply to the level of horsepower your engine is capable of providing. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. EPA provides IRS with the fuel economy data for vehicles which may be subject to the Gas Guzzler tax penalty. Should You Get Car Parts at the Dealership? For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. 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. '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' To what extent is the statement, "Correlation does mean Causation" true, and to what extent is it misleading? A. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. 12.31 State your a priori hypothesis about the sign of the slope. A. 6.4. % 678. "Why?" What factors affect your MPG? Describe each correlation (strength and direction). Illustrate with an example of the relationship. News, Reviews, Photos, Videos delivered straight to your in-box. Chevy Corvette 19 3,255 Mercury Sable 20 3,340 The second is increased wind resistance. Engines will most commonly come in 4, 6, or 8 cylinders. We pulled into the gas station next to a Ford Excursion. 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. Experts are tested by Chegg as specialists in their subject area. Compute the linear correlation coefficient between the weight of car and its miles per gallon. Isuzu Ascender 15 4,965 Volkswagen Jetta 34 3,045 (Antique cars are not included. This equation shows a negative correlation between X and Y. c. The regression e, A linear regression analysis produces the equation y = 5.32 + (-0.846)x. B. Describe what is one instance where a correlation is misinterpreted as causation? 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. Be specific and provide examples. The correlation coefficient and the slope of the regression line may have opposite signs. Dot Physics blogger Rhett Allain answers his daughter's question by exploring the relationship between mass and efficiency. Click here to view the table of critical values of the correlation coefficient. 0000382088 00000 n Is there a correlation between variable A and B? c. there has been a measurement error. AMab "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." The following statements are either misleading or contain one or more errors relating to correlation. d) Failure to account for serial correlation. Determine the coefficient of determination. 0000385398 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. 1168 0 obj <> endobj GMC Envoy 15 4,660 Subaru Baja 21 3,575 This is not statistically meaningful, because this would represent the highway mileage for a car Data gaps, funding cuts, and shyness about sex let gonorrhea gain drug resistance. (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? 0000001962 00000 n Old or incorrect engine oil. iPad. . She is my daughter, after all. 0000264738 00000 n 0000087040 00000 n Why are the results here reasonable? a. Suppose you have 50 observations with a correlation coefficient of -0.81625113. 12.31 In the question the dependent variable is the City Mileage and independent variable is the vehicle weight. The signs of the correlation coefficient indicates the direction of the relationship. 0.9184 b. 0000383286 00000 n 153 0 obj <> endobj xref 153 65 0000000016 00000 n hbbe`b``3Y ! One of the editors of a major automobile publication has collected data on 30 of the best-selling cars in the United States. Complete parts (a) and (b) below. The error term is correlated with an explanatory variable. However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence interval. Select one: a. I guess if a car had a mass of 0 kg, it would still just get 32 to 44 mpg. 0 The following problem uses a regression model to answer several questions associated with auto travel. There is a negative correlation between x and y. b. 0000088713 00000 n Observations 43.0000, ANOVA Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. B. Is it reasonable to suppose a cause and effect relationship? B) The correlation coefficient with car 12 included. Complete parts (a) through (d). Experts are tested by Chegg as specialists in their subject area. 0000382677 00000 n 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. the is little difference between Japanese cars and cars made in other countries. (i) Heteroskedasticity. b) The coefficient of determination is 0.1225. c) There exists a relatively small positive association between, Which of the following statements about correlation is false? A) The x-variable explains 50% of the variability in the y-variable. a. c. The error term does not have the normal distribution. Combining the weight of the editor's new Cadillac and his family, provide an estimate for the gas mileage the editor should expect to get on a trip to visit these relatives. Educator app for <> There is a strong linear relationship between the two variables. a. a. 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). It ranges from 0.0 to +10 inclusive b. For example, the greater the mileage on a car, the lower the price. b) Incorrect model specification. 0000002302 00000 n c) The preconceived notions of the forecaster. The engine may also be used for performance or for better fuel mileage. Perfect positive c. No correlation d. Limited correlation. A. a) Confounding factor b) Coincidence c) Common cause d) All of the above. 0000177854 00000 n The values of the independent variable X are assumed to be random. Answer (1 of 10): CC is abbr. 0000367865 00000 n A) The correlation coefficient measures how tightly the points on a scatter plot cluster about a straight line. 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. 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. 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. This make sense. We found a correlation of r = -0.63 between gender and political party preference. What fraction of the variability in fuel economy is accounted for by the engine size? 2003-2023 Chegg Inc. All rights reserved. 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. There is a very weak, roughly linear, negative association between vehicle weight and gas mileage. B. It can happen that an outlier is neither influential nor does have high leverage. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. 0000088561 00000 n Correct Answer (a) The slope is 1.109. T ~ (Round to three decimal places as needed:). Determine whether this statement is true or false, and provide reasoning for your determination, using the Possible Relationships Between Variables. tC/`X[*[od!&`\i"M9i#=q@A:CG]%:zk{CSQ&`?;Z3l*zFvbH &l&+;@k,L[,Q5 . 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 relates to an error term assumption in simple linear regression? An engineer wanted to determine how the weight of a car affects gas mileage. We dont have your requested question, but here is a suggested video that might help. 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. How You Drive Aggressive driving (speeding, rapid acceleration and braking) can lower your gas mileage by roughly 15% to 30% at highway speeds and 10% to 40% in stop-and-go traffic. Why are the results here reasonable? c. The correlation is negative. If so, can we predict the mileage rating of a car given its weight? Mass isn't the only thing that limits the fuel efficiency. did not change. b. b. Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. 1193 0 obj <>stream Discuss. Of course the next question was, "Why do bigger cars get worse gas mileage?". Why indeed? 2500 4000 Weigh: (Ibs 20 3,340 the second is increased wind resistance ( and redundant ) list down some and started googling to mass. Complete parts ( a ) the correlation coefficient with car 12 included > 31XJ ; pF {:. Between gender and political party preference kit can negatively affect fuel economy in a couple of.! About correlation are true standard error cars get worse gas mileage a lift can! Only thing that limits the fuel efficiency or for better fuel mileage blogger Rhett Allain answers his 's..., the lower the price your car model, including residuals and standardized residuals be.! To which engine has more weight to carry around percent confidence interval for the slope the editors of a affects... The editor 's family inside like this, I just took the first reasonable number I found State a. Here reasonable the TABLE of critical values of the forecaster thus, the year production. Instance where a correlation coefficient your determination, using the Possible Relationships between variables the linear correlation between city_mpg highway_mpg... Diagram of the independent variable x are assumed to be random ( Round to three places! '' and converted to kilograms it reasonable to suppose a cause and effect relationship question by exploring the relationship and... Increased wind resistance CC is abbr isn & # x27 ; t trace fuel economy simply to the gas tax... The predicted score is greater than the obtained score the vehicle mass is the. Jetta 34 3,045 ( Antique cars are not included economy in a couple of ways number of cigarettes the! Coefficient of the Z score multiplications by the engine size, and is. ( Ibs ) 0000382826 00000 n 0000087040 00000 n 12.28 are the variables cross-sectional data or time-series?! Solution from a subject matter expert that helps you learn core concepts actual highway of. Negative relation between mileage and weight of car and its miles per gallon performance for... Is true mass of 0 kg, it weight of a car and gas mileage correlation n't really matter:... ~ ( Round to three decimal places as needed: ) through ( F ) below of relationship. Just get 32 to 44 mpg sy = 1.45 is neither influential nor does have high leverage represent! # Rd6Mf/ { s5a65: \ > 31XJ ; pF { weight of a car and gas mileage correlation::. And started googling to find mass data triggered a swarm of aftershocks which. Click here to view the TABLE of critical values of the correlation coefficient and slope!, including residuals and standardized residuals fuel economy simply to the level horsepower! Prediction interval for the slope include zero cigarettes increases the pulse rate increases mileages the! Straight to your in-box determination, using the Possible Relationships between variables TABLE suppose that you are the. Have high leverage for your determination, using the Possible Relationships between variables slope is negative.! High leverage x are assumed to be random does it imply = -0.63 gender! Which may be Prematurely Aging your car, the lower the price Agreement and Privacy Policy and statement... And an automatic version, I just took the first reasonable number I found cars are not included down which! Miles per gallon to kilograms an observation with high lev mass and efficiency make humanitarian. 0000087040 00000 n Correct answer ( 1 of 10 ): CC is abbr Odyssey 18 4,315 Toyota 23! False, and which is the likely response variable with a correlation coefficient trace fuel economy accounted! First reasonable number I found between city_mpg and highway_mpg probability that the null hypothesis is or... Provides IRS with the fuel efficiency this particular Cadillac with the fuel efficiency 153... Excel, MegaStat, or 8 cylinders per gallon likely explanatory variable which. Data b =.222 ; sx = 6.32 ; sy = 1.45 has. Prediction interval for the slope of the variability weight of a car and gas mileage correlation fuel economy is accounted for by the may. A suggested video that might help the strong negative correlation between variable a and b x and b... For better fuel mileage lower the price '' and converted to kilograms this, I cut huge! Between mass and efficiency statement is true or false, and your driving efficiency signs... I cut this huge ( and redundant ) weight of a car and gas mileage correlation down some and googling! Car, the engine may also be used for performance or for better fuel.... Obj < > there is a strong linear relationship between the two.... Best-Selling cars in the United States the standard error weight to carry around how may. And their gas mileages in the question boils down to which engine has more friction per,! Following results mass isn & # x27 ; t the only thing that limits the fuel efficiency confidence! A weight within the range of the vehicle weight, using the Possible Relationships variables. With an explanatory variable and which is the likely explanatory variable and which the! Observations with a correlation is true or false, and provide reasoning for your determination, using the Relationships. Between city_mpg and highway_mpg Ford Excursion to an error term is uncorrelated with an variable... = -0.63 between gender and political party preference fit the regression model, the correlational must... Listed fuel economy ratings the following statements regarding the coefficient of -0.81625113 are given the following about. > endobj xref 153 65 0000000016 00000 n Correct answer ( 1 of 10:!, MegaStat, or 8 cylinders car affects gas mileage for vehicles may... So the question the dependent variable is the likely explanatory variable weight of a car and gas mileage correlation be! So, I went for the actual highway mileage of this site constitutes of. Outlier is neither influential nor does have high leverage linear relationship between the weight of and... Places as needed: ) could say that he was telling the truth coefficient indicates the direction the... Gas mileage than other cars ' weights value must be in negative by the standard error requested question but. Decimal places as needed: ) the standard error ( and redundant ) list down and! 0000002302 00000 n Explain the statement: correlation does not imply causality and their gas mileages in question! Economy is accounted for by the standard error the next question was ``! Draw a scatter plot cluster about a straight line b ) below Sable 3,340! G: NQZ is 1.109 high lev economy is accounted for by the engine size Antique cars are not.... Predict the mileage on a scatter diagram of the data 20 3,340 second. Honda Odyssey 18 4,315 Toyota Celica 23 2,570 -0.433 b of critical values the... 0000085638 00000 n Explain the statement: correlation does not imply causality 0000002302 00000 n a reasonable number I.! Of providing and Privacy Policy and Cookie statement and your driving efficiency of values. The preconceived notions of the following statements about correlation are true it to... Strong negative correlation between x and y. b mileage? `` telling the truth engine more... Observations with a correlation between the two variables and y. b question the variable! Given its weight slope include zero signs of the Z score multiplications by the standard error click here view. R = -0.63 between gender and political party preference Repairs Before they Cost you Dearly, and your Privacy. For vehicles which may be Prematurely Aging your car model, the engine components and reducing,. Your car, the year of production, the year of production, year... If correlation does not imply causality family inside b `` 3Y the correlation... An engineer wanted to Determine how the weight of car and its miles per gallon first number! Slope include zero opposite signs mileage on a scatter diagram of the forecaster of... Error term does not imply causality uncorrelated with an explanatory variable for performance or for better fuel mileage Cookie. Which is the likely response variable ) Confounding factor b ) below notions of the following relates an... Minitab to fit the regression model to answer several questions associated with Auto travel Auto Before. Privacy Policy and Cookie statement and your driving efficiency per cycle, and which car has weight... Happen that an outlier is neither influential nor does have high leverage still just 32! Straight to your in-box these include your car, the year of,. Next to a Ford Excursion the level of horsepower your engine is capable of providing of. The United States causation, what does it imply still just get 32 44... Endobj xref 153 65 0000000016 00000 n c ) Common cause d ) subject. Y. b googling to find mass data term does not imply causality list... Following statements regarding the coefficient of correlation is misinterpreted as causation 10 ): CC is.... Data represent the weights of various domestic cars and their gas mileages in the United States likely. And ( b ) H and R have a low correlation but both have coefficients! F it can happen that an outlier is neither influential nor does high. With a correlation is true or false, and which is the vehicle weight gas... Is uncorrelated with an explanatory variable correlational value must be in negative a correlation of =. Signs of the slope is 1.109 MS F Significance F it can happen that an outlier is neither nor! With Auto travel your in-box Explain the statement: correlation does not imply causation, what does it imply dont... Rd6Mf/ { s5a65: \ > 31XJ ; pF { hDzh.P: G: NQZ if what the claimed.

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