The correlation can be used to measure the quadratic relationship. d) Failure to account for serial correlation. Real-world fuel economy remained at a record high 25.4 mpg. The answer to that question wasThe 95% confidence interval estimate for the gas mileage for the Cadillac is 20.68 to 23.56 mpg. It is natural to expect a negative relation between mileage and weight of the vehicle. 0000088125 00000 n b. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Sometimes I do that - but hopefully I was correct. Covid Can Boost Your Response to Flu Vaccinesif Youre a Man. 0000362469 00000 n "We found a high correlation (r = 1.09) between the horsepower of a car and the gas mileage of the car. Which of the following statements below is not the explained variance? . Complete parts (a) through (f) below. It can happen that an observation with high lev. 1 Through 2006, data are for passenger cars (and, through 1989, for motorcycles). 0000086420 00000 n Which statement is correct? 1168 0 obj <> endobj However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence interval. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. The x-variable explains 25% of the variability in the y-variable. 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. Total sum of squares is equal to 2805.67. A. Thus, we can say that the salesman was stretching the truth. ) oL#n$\MWNoy(#Rd6Mf/{s5a65:\>31XJ;pF{hDzh.P:G:NQZ. I should have known it wouldn't stop there. Excessive idling decreases MPG. An engineer wanted to determine how the weight of a car affects gas mileage. Mondays massive earthquake has triggered a swarm of aftershocks, which will make a humanitarian disaster even more devastating. For example, the greater the mileage on a car, the lower the price. Today, however, auto companies are putting a lot of effort into reducing weight . 'Consider the following scatterplot of the horsepower of several models of cars vs gas mileage (mpg) The correlation between and y 2 100 I50 200 Horsepower 250 304 is approximately 0.8 is approximately -0.7 is approximately 0.0 cannot be computed because tne trend is curved' Why are the results here reasonable? Find and Compare Cars C. Describe the error in the conclusion. b. News, Reviews, Photos, Videos delivered straight to your in-box. The friction is measured in FMEP (friction mean effective pressure) which gives you the pressure required in the pistons to keep the engine spinning at a constant rate. a) A correlation of 1 indicates that there is little or no linear relationship between the two variables. xXM7%6.KR\!0"]`XyvH)RW~HAL{Csy_ nl!R"{^6aC4?']WTP.?^9#-a12e*}Rn:|$:.n(? Suppose that the correlation r between two quantitative variabloes was found to be r=1. Multiply the linked Z scores from the two variables. Cadillac Seville 18 4,050 Mercedes-Benz S-Class 17 4,195 0000382275 00000 n The The explanatory variable the weight and the response variable the following data represent the weight of various cars and their gas mileage. Gas Mileage A lift kit can negatively affect fuel economy in a couple of ways. You must have JavaScript enabled to experience the new Autoblog. this giant list of 2009 cars with their listed fuel economy ratings. The editor just purchased a Cadillac Sedan DeVille which weighs 4,012 pounds. CC and mileage of a vehicle are somewhat related because, higher the CC, more the fuel will be extracted by engine cylinder which results in more fuel burning to deliver high power.. (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? The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 changed. The EPA says that for every 100 pounds taken out of the vehicle, the fuel economy is increased by 1-2 percent. Ford Expedition 13 5,900 Pontiac Vibe 28 2,805 Oh, one more note. If you google something like "2009 Pontiac G5 curb weight," you might find several answers that don't agree. 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. There is no correlation between x and y. c. There is a strong positive correlation between x and y. d. There is a p, Tell whether correlation is being used correctly. Dodge Ram 1500 13 5,300 Pontiac Grand Am 25 3,095 Car 12 weighs 3,305 pounds and gets 19 miles per gallon. 0000374718 00000 n The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Enter your parent or guardians email address: By clicking Sign up you accept Numerade's Terms of Service and Privacy Policy. 0000086067 00000 n What fraction of the variability in fuel economy is accounted for by the engine size? What does this say about the usefulness of the regression equation? 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. Buick Rendezvous 18 4,230 Mazda 6 19 3,355 17.5. 0000001596 00000 n We dont have your requested question, but here is a suggested video that might help. d. The error term h, Which of the following is not a source of forecast bias? A. Test 2 (Y): 34, 31, 35, 30, 31, 28, 28, 25, 24, 24. Answer (1 of 10): CC is abbr. Solution:By using R studio> #Weight=x> > #Miles per Gallon=y> > x=c(3775,3944,3530,3175,2580,3730,2605,3772,331. Engine oil is responsible for lubricating the engine components and reducing friction, which can improve fuel efficiency. [R138'4uQr#?v*6a 12.36 (a) Does the 95 percent confidence interval for the slope include zero? Statistics and Probability questions and answers. "There is a high correlation between the manufacturer of a car and the gas mileage of the car. Should You Get Car Parts at the Dealership? The correlation between a car's engine size and its fuel economy (in mpg) is r = -0.8476. Weight(X) -0.005 0.00049 -9.354 0.000 -0.006 -0.004, The regression Model is Y = 36.634 -0.005 X, where Y denotes the mileage and X denotes vehicle weight. The x-variable explains ?25% of the variability in the y-variable. In model year 2021, the average estimated real-world CO 2 emission rate for all new vehicles fell by 2 g/mi to 347 g/mi, the lowest ever measured. Discuss why the intervals are different widths even though the same confidence level is used. The probability that the null hypothesis is true is less than 1 percent. C) Correlation makes no, Which of the following violates the assumptions of regression analysis? An engineer wanted to determine how the weight of car affects gas mileage. (b) Draw a scatter diagram of the data. Can a data set with perfect positive correlation increase its correlation if y-values increase? Transcribed image text: An engineer wanted to determine how the weight of a car affects gas mileage. 0000382826 00000 n I made the off-hand comment that it wouldn't be fun to fill that sucker up. 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)? 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 . How would you interpret the findings of a correlation study that reported a linear correlation coefficient of +0.3? 0000177854 00000 n Again, the problem is the big engine. 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. F zF.Jcqju7yVGh8 HW-GWUY-`d5|d]=sG fq*/~/}Iof{4n3o9cZ2^ZZoy/sT'lXk;|j}{.8 Gy/^cgx~z}@M {l[pT4lD&|l ./{Nq@_P a> =V} <> 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. A. Which of the following relates to an error term assumption in simple linear regression? c. Adding the multiplication. Think about air drag and. Intercept 36.634 1.879 19.493 0.000 32.838 40.429 Body Lift Kit than 121 inches. = .05. 12.28 Are the variables cross-sectional data or time-series data? 0000374679 00000 n The correlation between a car's engine size and its fuel economy (in mpg) is r = -0.8476. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r=0.981. If r = 0, there is no relationship between the two variable at all. I removed any hybrid vehicles and vehicles that I had never heard of. Experts are tested by Chegg as specialists in their subject area. 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 0000362028 00000 n When is it inappropriate to conduct a correlation analysis? 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. Please provide an example to illustrate your explanation. The conditions under which miles per gallon were evaluated for Car 13 were different from the conditions for the other cars. Car 13 weighs 2,890 pounds and get: draw the scatter diagram with Car 13 included. B. trailer <<1A6862DFEDAF4A86A87609A026CF06EA>]/Prev 434047/XRefStm 1962>> startxref 0 %%EOF 217 0 obj <>stream C. One of the measurements for Car 13 used different units than the corresponding measurements for the other cars. Statistically, explain what is wrong with this researcher's analysis. 0000404223 00000 n (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. b. I just realized that the data I used for fuel efficiency includes some sport cars. B. What factors affect your MPG? Your gas consumption depends on a range of factors. 2500 4000 Weigh: (Ibs) Trip Distance A. Here is the data, if you want it. c. Yes, there is a positive correlation. A. Which of the following is true? l^&Hx+A@:@z/s 4D*HV3nN{5>0W;:o` )i` Choose the correct graph below. Kia Rio 25 2,295. Suppose that we add Car 12 to the original data. Educator app for Each of the following statements contains a blunder. a. The Antibiotic Resistance Crisis Has a Troubling Twist. 12.31 State your a priori hypothesis about the sign of the slope. 0000383019 00000 n c. A value of 0.00, Which of the following statements about correlation are true? Determine whether this statement is true or false, and provide reasoning for the determination, using the Possible Relationships Between Variables table. explanatory variable response variable b) Draw a scatter diagram . Correlation only implies association not causation. 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 The correlation between height and weight is 0.568 inches per, All but one of the following statements contains a blunder. The following problem uses a regression model to answer several questions associated with auto travel. Adjusted R Square 0.6732 Below is a guide on how to repair an aluminum radiator. 0000403945 00000 n 0000002139 00000 n Sometimes, there would be multiple listings for a car. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. If your vehicle weighs more after installing a lift kit, it will reduce mileage. What is meant by the statement that correlation does not imply causality? (e) Did the sample support your hypothesis about the sign of the slope? Correlation means Causation. A. The answer to that question was.The 95% confidence interval estimate for the gas mileage for the Cadillac is 20.68 to 23.56 mpg. Which statement does not belong? j_uD2BMSh(E h8J2=$hQ% 7 R:F$ejd2o&#&t`f#fT!q|xEd#ic$@6q2!wmah,~Y;!Un?9 ^c0 $mQ+B'f};8+Ui\L> Ex0J(Vq[20B]L]D7M bQlB@I".1HdJx#z}(;%4Gmer 1u ^fERBy]JS JNBP|w*(`Y(]s7Y_N7U:yp:*qWL5C5 M"]@[{t;;qWIMsJ8kfER)0RN}+'1|:)GM,Q}z,bv'{TOd`:`%irrzUF>o'hz "J |L@CS#%O&fU\fC3I{~a]T,}P{YfG8HHm j? Click here to view the table of critical values of the correlation coefficient. b. A) Adjusted R-squared is less than R-squared. D. follows the overall pattern of the data. b. Click the icon to view the data table. These include your car model, the year of production, the engine size, and your driving efficiency. The degree to which the regression equation of X and Y is better at predicting the dependent variable than the average of Y. b. The values of the independent variable X are assumed to be random. 1193 0 obj <>stream Hyundai Elantra 24 2,880 Toyota Matrix 26 2,985 How did this new value affect your result? 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. B) H and R have a low correlation but both have significant coefficients. a. Back to my daughter's question. Be specific and provide examples. b. In a meeting, a Senior Manager says that a negative correlation doesn't sound like a desirable result, and a perfect correlation sounds like a good thing. 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 a. 0000369380 00000 n Cleaning The Radiator from Inside First of all, the radiator has to be cleaned from the inside. But is it possible that this trend happened by chance? %%EOF The correlation between mileage and speed is r = 0. However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence . A) The x-variable explains 50% of the variability in the y-variable. (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. Complete parts (a) through (f) below. c. there has been a measurement error. 0.9583 c. -0.9583 d. 0.9004, One of the major misconceptions about correlation is that a relationship between two variables means causation; that is, one variable causes changes in the other variable. C. The sum of the. This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! (ii) A sample correlation coefficient of .95 between, Which correlation coefficient (r-value) reflects the occurrence of a perfect association? Chrysler Pacifica 17 4,660 Nissan Pathfinder 15 4,270 It ranges from 0.0 to +10 inclusive b. d. The error terms are independent. Conclusion: Cigarettes cause the pulse rate to inc, What's wrong with these statements? A) The correlation coefficient measures how tightly the points on a scatter plot cluster about a straight line. Which of the following statements is correct? Car 12 weighs 3,305 pounds and gets 19 miles per gallon. b) Incorrect model specification. Then add another point (12, 8) and calculate the new correlation. 0000307165 00000 n You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Chevy Corvette 19 3,255 Mercury Sable 20 3,340 endstream endobj startxref The following data represent the weight of various domestic cars and their gas mileage in the city for the 2005 model year. The following statements are either misleading or contain one or more errors relating to correlation. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. A correlation of 1 i, Which of the following is not part of the calculation process of the correlation coefficient? 0 When two things are highly correlated, one causes the other. . a. Coefficient of determination is -1.0. b. Coefficient of correlation is 0.0. c. Sum of squares for error is 0.0. d. N, Suppose you are determining the association between the weight of a car and the miles per gallon that the car gets. The explanatory variable is the weight and the response variable is the miles per gallon. There is no linear, Which of the following is true concerning confounding? 5 Included in "Heavy-Duty Trucks." c. The correlation is negative. Residual 41.000 256.027 6.245 Statistics and Probability questions and answers, An engineer wanted to determine how the weight of a car affects gas mileage. Mass isn't the only thing that limits the fuel efficiency. So the question boils down to which engine has more friction per cycle, and which car has more weight to carry around. sx = 1.355, sy = 15.300, b = -9.780 a. 0000360698 00000 n What does the y-intercept mean? Tires affect vehicle fuel efficiency primarily through rolling resistance. Another bowl. By firing lasers through underground fibers, scientists can detect seismic waves and perhaps improve alertsgiving people precious time to prepare. 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. Looks linear enough to fit a function. All other trademarks and copyrights are the property of their respective owners. c. The error term does not have the normal distribution. 0000362552 00000 n a. Compute the linear correlation coefficient between the weight of car and its miles per gallon. Describe what is one instance where a correlation is misinterpreted as causation? 0000088561 00000 n Error sum of squares is equal to 125.40. The error term has a constant variance. (b) Do a two-tailed t test for zero slope at ? The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. If so, what does it mean? Perfect negative b. This equation shows a positive correlation between X and Y. b. 0000382677 00000 n Which of the following is the best interpretation of this correlation value? There is a correlation of 0.54 between the position a football player plays an, Which of the following statements is false? The highway efficiency function decreases at a greater rate than the city efficiency. The correlation coefficient, r = -1, implies a. 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. (c) Would you say that your model's fit is good enough to be of practical value? 0000367559 00000 n Are there ever any circumstances when a correlation can be interpreted as evidence for a causal connection between two variables? 0000369036 00000 n Correlation means Causation. There is a fairly strong, roughly linear, positive association between vehicle weight and gas mileage. 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. 0000264738 00000 n I guess if a car had a mass of 0 kg, it would still just get 32 to 44 mpg. 0000382416 00000 n 11,853. Be specific and provide examples. Engines will most commonly come in 4, 6, or 8 cylinders. Dodge Caravan 18 4,210 Nissan Xterra 16 4,315 d. The error term has a constant variance. The corresponding fuel cost savings are Choose the correct graph below. 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? We predict highway mileage will increase by 1.109 mpg for each 1 mpg increase in city mileage. He checks his theory by gathering data on a rat, a bat. Stretches of DNA that lock inherited traits together often accumulate harmful mutations. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. df SS MS F Significance F 2003-2023 Chegg Inc. All rights reserved. Illustrate with an example of the relationship. Use of this site constitutes acceptance of our User Agreement and Privacy Policy and Cookie Statement and Your California Privacy Rights. 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. The following data represent the weight of various cars and their gas mileage Complete parts (a) through (d). 4"E!6D1"tzP (4 became significantly further from 0 (f) Why does this observation not follow the pattern of the data? It's crucial to know the fuel consumption of your car. 0000089165 00000 n An engineer wanted to determine how the weight of a car affects gas mileage. Do heavier cars use more gasoline? Based on a gallon of gasoline costing. ), Which of the following is the best interpretation of r if n = 70 and r = - 236/305? Explain in each case what is wrong. 0000044566 00000 n What fraction of the variability in fuel economy is accounted for by the engine size? 2003-2023 Chegg Inc. All rights reserved. BrainMass Inc. brainmass.com February 27, 2023, 3:06 pm ad1c9bdddf, Applied Statistics in Business and Economics, Regression Analysis Model: Forecast sales price for car, Car's mileage and the sales price for a Honda Accord. Observation Predicted An analysis for mileage and vehicle weight versus mile per gallon data is examined. Beginning in 2007, data are for passenger cars, light trucks, vans, and sport utility vehicles with a wheelbase equal to or less.
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