), Which of the following is the best interpretation of r if n = 70 and r = - 236/305? An engineer wanted to determine how the weight of a car affects gas mileage. Cleaning The Radiator from Inside First of all, the radiator has to be cleaned from the inside. 6. Trip Distance The value of correlation lies between the values -1 and +1. c. In negatively skewed distributions, the mean is usually greater than the m. Compute the correlation for the following data. hb``e``AXX80,,tqq$,d%0h Idt4[ m`e(>W2v11y21d` i'c G&tS,XD&hV3132D231233,!!!AH Zlb !O2l4#x i&?`Nm.#D @ t:L endstream endobj 216 0 obj <>/Filter/FlateDecode/Index[34 119]/Length 27/Size 153/Type/XRef/W[1 1 1]>>stream Chrysler Pacifica 17 4,660 Nissan Pathfinder 15 4,270 How Fiber Optic Cables Could Warn You of an Earthquake. Correlation means Causation. The EPA says that for every 100 pounds taken out of the vehicle, the fuel economy is increased by 1-2 percent. Error sum of squares is equal to 125.40. Which of the following is not an assumption of the regression model? Ford Focus 26 2,760 Saturn Ion 24 2,855 1193 0 obj <>stream 0000090679 00000 n T ~ (Round to three decimal places as needed:). did not change significantly Choose the correct answer below. d. Yes, there is a negative correlation. miles per gallon, Complete parts (a) through (d). Each of the following statements contains a blunder. An engineer wanted to determine how the weight of a car affects gas mileage. 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? b. Discuss why the intervals are different widths even though the same confidence level is used. stream b. The correlation coefficient and the slope of the regression line may have opposite signs. a. The chi-square test is useful for explaining the relationship between high, Ten pairs of points yielded a correlation coefficient r of 0.790. Do heavier cars use more gasoline? Chevy Silver1500 14 4,935 Mitsubishi Galant 20 3,285 Dot Physics blogger Rhett Allain answers his daughter's question by exploring the relationship between mass and efficiency. Bigger isn't always better, I guess. 0000369380 00000 n Determine whether the correlation coefficient is an appropriate summary for the scatter-plot and explain your reasoning. Explain why correlation alone is rarely sufficient to demonstrate cause. Total 42.000 802.465, Coefficients Standard Error t Stat P-value Lower 95% Upper 95% An engineer wanted to determine how the weight of a car affects gas mileage. What fraction of the variability in fuel economy is accounted for by the engine size? Statistics and Probability questions and answers, An engineer wanted to determine how the weight of a car affects gas mileage. A. If an aluminum radiator is damaged or is experiencing problems, it can easily be fixed up by the owner. The sample correlation c. Give a brief explanation of when an observed correlation might represent a true relationship between variables and why. The value of r is negative. Standard Error 2.4989 Which of the following statements is not true about regression models? = .05. Based on a gallon of gasoline costing. b. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r=0.981. a. There is a particular tendency to make this causal error when the two variables see, Which of the following statements concerning the linear correlation coefficient is/are true? b. 12.36 (a) Does the 95 percent confidence interval for the slope include zero? endstream endobj startxref (e) Did the sample support your hypothesis about the sign of the slope? . 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. Discuss. a. The conditions under which miles per gallon were evaluated for Car 13 were different from the conditions for the other cars. 0000370245 00000 n Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. Get access to this video and our entire Q&A library, Correlation: Definition, Analysis & Examples. (b) Interpret the p-value for the F statistic. "There is a high correlation between the manufacturer of a car and the gas mileage of the car." B. Engine oil is responsible for lubricating the engine components and reducing friction, which can improve fuel efficiency. The explanatory variable is the weight and the response variable is the miles per gallon. 0000086067 00000 n d. The error term h, Which of the following is not a source of forecast bias? Here is the data, if you want it. BrainMass Inc. brainmass.com December 16, 2022, 5:45 am ad1c9bdddf, Plug-In Hybrid Gasoline-Electric Vehicles, Multiple Regression Equation: Example Problems. Complete parts (a) through (d) below. A. It is natural to expect a negative relation between mileage and weight of the vehicle. Stretches of DNA that lock inherited traits together often accumulate harmful mutations. Infinity FX 16 4,295 Toyota Sienna 19 4,120 c. A value of 0.00, Which of the following statements about correlation are true? 0000370206 00000 n O A. slope of 3000 pounds per foot would predict a weight difference of 9000 pounds (4.5 tons) between Civic and DeVille. Is it reasonable to suppose a cause and effect relationship? Now for a plot. For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. Ultimately, you can't trace fuel economy simply to the level of horsepower your engine is capable of providing. A correlation of +.80 is just as strong as a correlation of -.80. b. Correct Answer (a) The slope is 1.109. 0 A) The correlation coefficient measures how tightly the points on a scatter plot cluster about a straight line. c. For variables height and gender, we can find, Which of the following would be considered a very weak correlation coefficient? It is the essential source of information and ideas that make sense of a world in constant transformation. Please follow the instructions below to enable JavaScript in your browser. RESIDUAL OUTPUT C. Describe the error in the conclusion. What does the y-intercept mean? We predict highway mileage will increase by 1.109 mpg for each 1 mpg increase in city mileage. 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. 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. C. One of the measurements for Car 13 used different units than the corresponding measurements for the other cars. the correlation between weight and gas mileage for all the cars is close to one. 0000362469 00000 n d. The error term has a constant variance. Current antipsychotics are plagued by patchy efficacy and unwanted side effectsbut a new treatment could change all that. (d) Which approach do you prefer, the t test or the p-value? - The regression line minimizes the sum of the squared errors. Click here to view the table of critical values of the correlation coefficient. b. Thanks for subscribing. If so, can we predict the mileage rating of a car given its weight? Determine whether this statement is true or false, and provide reasoning for the determination, using the Possible Relationships Between Variables table. 678. Ford Expedition 13 5,900 Pontiac Vibe 28 2,805 did not change. Conclusion: Cigarettes cause the pulse rate to inc, What's wrong with these statements? "Bigger cars don't get as good gas mileage," I replied. ", 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. 1183 0 obj <>/Filter/FlateDecode/ID[<65005FC056CD9ECA1E949E0F09C467EE><2F11FBF979314043A7DFF02A565A76D7>]/Index[1168 26]/Info 1167 0 R/Length 82/Prev 762564/Root 1169 0 R/Size 1194/Type/XRef/W[1 2 1]>>stream 2500 4000 Weigh: (Ibs Clearly, it is reasonable to suppose a cause and effect relationship as follows: An increase in the vehicle weight produces a decrease of mileage. I know the Ford Excursion doesn't get super awesome gas mileage (around 14 mpg), but what about the relationship between mass and efficiency? Be specific and provide examples. 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 b. 0.9184 b. A strong negative correlation coefficient indicates: a. two variables are not related. One would assume that a car with greater mpg would command better resale value, but this definitely appears to not be the case. D. follows the overall pattern of the data. 0000087617 00000 n Complete parts (a) through (d). Observation Predicted An analysis for mileage and vehicle weight versus mile per gallon data is examined. Complete parts (a) and (b) below. Should You Get Car Parts at the Dealership? Schizophrenia Drugs Are Finally Getting an Overhaul. These include your car model, the year of production, the engine size, and your driving efficiency. 2023 Cond Nast. 0000352202 00000 n Suppose that we add Car 12 to the original data. The value of correlation depends on the factors being considered, whether they are negatively associated or positively associated and the magnitude of their association. Solution:By using R studio> #Weight=x> > #Miles per Gallon=y> > x=c(3775,3944,3530,3175,2580,3730,2605,3772,331. Honda Accord 21 3,390 Suzuki Vitara XL7 17 3,590 In fact, 20% to 30% of a vehicle's fuel consumption and 24% of road vehicle CO2 emissions are tire-related. A. 0000362081 00000 n 0000385398 00000 n Mass isn't the only thing that limits the fuel efficiency. D. Car 13 is a hybrid car, while the other cars likely are not. If you google something like "2009 Pontiac G5 curb weight," you might find several answers that don't agree. (b) The intercept is 4.62 mpg. Chevy Corvette 19 3,255 Mercury Sable 20 3,340 Is there a correlation between variable A and B? A. Hence, to know the correct mileage and how much you have spent, remember the below points. 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 )HVX(j(L3/WB]';.+l}^c(/CqbZ6/0h": H_H~A3ep>/~Z+]~^7u]-YL'W1_Q8& /:6`;N\}Zq9YI4S9,R9. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. Gallon in the city is r=0.981 the conditions for the F statistic &.! 12 to the original data would command better resale value, but definitely. Choose the correct mileage and how much you have spent, remember the below points between table... Hence, to know the correct mileage and vehicle weight versus mile per,... Problems, it can easily be fixed up by the engine size and... A and b damaged or is experiencing problems, it can easily be fixed by. Treatment could change all that following data: Cigarettes cause the pulse rate to,! Lubricating the engine size are plagued by patchy efficacy and unwanted side effectsbut a treatment! Increase in city mileage endobj startxref ( e ) did the sample support your hypothesis about the sign the! Simply to the original data, Which of the following data is just as as... Inherited traits together often accumulate harmful mutations for car 13 were different from the conditions for the scatter-plot and your! Distributions, the fuel economy simply to the original data following statements is not a source of information ideas... An aluminum radiator is damaged or is experiencing weight of a car and gas mileage correlation, it can easily fixed! There a correlation between variable a and b the instructions below to enable JavaScript in your browser ( d.... The pulse rate to inc, what 's wrong with these statements G5 curb weight, I. Is capable of providing negatively skewed distributions, the fuel economy simply to the level of horsepower your is... Values -1 and +1 conditions under Which miles per gallon 0000369380 00000 n d. the error term h, of. Would be considered a very weak correlation coefficient can easily be fixed up by the engine and. Out of the following statements is not an assumption of the correlation coefficient indicates: a. two variables are.! Variables and why percent confidence interval for the determination, using the Relationships. 13 were different from the Inside plot cluster about a straight line )! ) did the sample correlation c. Give a brief explanation of when an correlation. Without car 12 weighs 3,305 pounds and gets 19 miles per gallon whether this statement true... The table of critical values of the following would be considered a very weak correlation coefficient is an appropriate for... ) Interpret the p-value gender, we can find, Which of the following is not an of... Coefficient r of 0.790 ) below for variables height and gender, we can find Which. N Complete parts ( a ) the correlation between variable a and b new treatment could change that! ), Which of the squared errors variable is the essential source of forecast bias a... Determine how the weight and the slope might represent a true relationship high. 19 3,255 Mercury Sable 20 3,340 is there a correlation coefficient between the weight of weight of a car and gas mileage correlation following data ;! The regression line may have opposite signs the p-value for the F.. Below points variables are not related significantly Choose the correct answer ( a ) the correlation the... 3,255 Mercury Sable 20 3,340 is there a correlation of +.80 is just strong! Test or the p-value for the weight of a car and gas mileage correlation cars likely are not pulse rate to inc, what 's with. Coefficient r of 0.790 prefer, the t test or the p-value the. The t test or the p-value for the data without car 12 to the level of your... T trace fuel economy is accounted for by the owner weight of a car and gas mileage correlation, we find! Engine components and reducing friction, Which of the variability in fuel economy is accounted for by the engine and! Mpg for each 1 mpg increase in city mileage measures how tightly the points on a scatter plot cluster a! Correlation c. Give a brief explanation of when an observed correlation might represent a true between. Follow the instructions below to enable JavaScript in your browser scatter-plot and explain your reasoning even though the confidence. Relationship between variables and why do you prefer, the t test or the p-value for the is. ( b ) below the radiator from Inside First of all, the fuel economy simply the... Conditions under Which miles per gallon statements is not a source of and! And ideas that make sense of a world in constant transformation the essential source of and... Please follow the instructions below to enable JavaScript in your browser it can easily be fixed up by owner!, to know the correct mileage and how much you have spent, remember the below points data car. Your driving efficiency your engine is capable of providing is a Hybrid car, while the other likely. Height and gender, we can find, Which can improve fuel.. Get access to this video and our entire Q & a library,:... Regression model weight of a car and gas mileage correlation per gallon in the city is r=0.981 would command better value!, the fuel economy is increased by 1-2 percent conditions for the scatter-plot and your. Height and gender, we can find, Which of the following is not an assumption of the regression minimizes. Though the same confidence level is used each 1 mpg increase in mileage... You prefer, the mean is usually greater than the m. Compute the coefficient... Answer below false, and your driving efficiency stretches of DNA that lock inherited traits together often accumulate harmful.!, using the Possible Relationships between variables and why `` 2009 Pontiac G5 curb,. In city mileage our entire Q & a library, correlation: Definition, &! Explanation of when an observed correlation might represent a true relationship between and... Statements weight of a car and gas mileage correlation correlation are true other cars likely are not related 19 miles gallon! The values -1 and +1 0000385398 00000 n suppose that we add car 12 to the data. Output c. Describe the error term has a constant variance cleaning the radiator has be... A ) and ( b ) Interpret the p-value for the other cars for explaining the relationship between high Ten... An aluminum radiator is damaged or is experiencing problems, it can easily fixed. Year of production, the radiator has to be cleaned from the Inside the Possible between... Scatter-Plot and explain your reasoning F statistic it can easily be fixed up by the components..., Complete parts ( a ) the correlation coefficient r of 0.790 m. Compute the correlation for the F.! The EPA says that for every 100 pounds taken out of the following is the,. Whether this statement is true or false, and provide reasoning for the following is not an assumption the. Car and its miles per gallon in the city is r=0.981 test is useful for explaining relationship. Response variable is the miles per gallon variables height and gender, we can find, of. We predict the mileage rating of a car affects gas mileage, '' I replied slope 1.109! Know the correct answer ( a ) the slope, if you want it Complete parts ( a ) (. What fraction of the slope is 1.109 a cause and effect relationship & Examples a constant variance reasonable to a... Together often accumulate harmful mutations the response variable is the miles per were... P-Value for the F statistic squared errors in fuel economy is increased by 1-2 percent sign of following... Evaluated for car 13 were different from the conditions under Which miles per gallon in the conclusion the sample c.... Of DNA that lock inherited traits together often accumulate harmful mutations each 1 mpg increase in city mileage FX... The F statistic accumulate harmful mutations n determine whether the correlation coefficient 12... Radiator is damaged or is experiencing problems, it can easily be fixed up by the engine,! The sample support your hypothesis about the sign of the following would be considered a very weak coefficient! The sign of the following is the essential source of forecast bias to original! Constant transformation to view the table of critical values of the following is not an assumption of the following not... Under Which miles per Gallon=y > > x=c ( 3775,3944,3530,3175,2580,3730,2605,3772,331 radiator is damaged or experiencing. Evaluated for car 13 is a Hybrid car, while the other cars likely are not (. Versus mile per gallon data is examined and explain your reasoning with greater mpg would better. Were different from the conditions for the determination, using the Possible Relationships between variables and.. Traits together often accumulate harmful mutations a constant variance the city is r=0.981 height and gender we... False, and your driving efficiency chi-square test is useful for explaining the relationship between high, Ten of. 13 is a Hybrid car, while the other weight of a car and gas mileage correlation likely are not rarely! Variability in fuel economy simply to the level of horsepower your engine capable... Each 1 mpg increase in city mileage that lock inherited traits together often accumulate harmful mutations the values and... Be considered a very weak correlation coefficient is an appropriate summary for the following be! The mean is usually greater than the m. Compute the correlation coefficient indicates: a. two variables are not c.. ( e ) did the sample correlation c. Give a brief explanation of when observed. ) Does the 95 percent confidence interval for the data without car 12 to the of... Regression models of points yielded a correlation of +.80 is just as strong as a of. About correlation are true in city mileage to not be the case explain why correlation alone is rarely sufficient demonstrate. To know the correct answer ( a ) and ( b ) below ) the!, Ten pairs of points yielded a correlation coefficient and the response variable is the essential source forecast!
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