A. Click the icon to view the critical values table. A. a) Confounding factor b) Coincidence c) Common cause d) All of the above. 0000370206 00000 n a. Thus, there is no correlation between the manufacturers of the car and its gas mileage. (i) Heteroskedasticity. 0000368723 00000 n 0000001596 00000 n (c) The correlation is not significant. 2023 Cond Nast. 5. 6. To conclude that the slope (relationship) is not significa, The "Pearson correlation coefficient (r)" is a quantitative measure of the correlation between two variables. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. 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 became significantly further from 0 (f) Why does this observation not follow the pattern of the data? (b) Draw a scatter diagram of the data. A recent study found that for every 100-kg reduction, the combined city/highway fuel consumption could decrease by about 0.4 L/100 km for cars and about 0.5 L/100 km for light trucks (MIT 2008). 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 c) Compute a 95% prediction interval for the actual highway mileage of this particular Cadillac with the editor's family inside. Mass isn't the only thing that limits the fuel efficiency. This is not statistically meaningful, because this would represent the highway mileage for a car DATA SET G Mileage and Vehicle weight MPG, Vehicle City MPG Weight Vehicle City MPG Weight, Acura CL 20 3,450 Land Rover 17 3,640 Ford Focus 26 2,760 Saturn Ion 24 2,855 The following data represent the weight of various domestic cars and their gas mileage in the city for the 2005 model year. 6. What does the y-intercept mean? b. two variables are inversely related. (e) Did the sample support your hypothesis about the sign of the slope? In fact, 20% to 30% of a vehicle's fuel consumption and 24% of road vehicle CO2 emissions are tire-related. For example, the greater the mileage on a car, the lower the price. 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. B. If an aluminum radiator is damaged or is experiencing problems, it can easily be fixed up by the owner. Ad Choices. An engineer wanted to determine how the weight of a car affects gas mileage. Suppose that we add Car 12 to the original data. The first is added weight. An engineer wanted to determine how the weight of a car affects gas mileage. (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+ Which of the following is true? Why are the results here reasonable? Determine the coefficient of determination. Here is some data. 1. 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? All rights reserved. Aftershocks May Rock Turkey and Syria for Months, Even Years. ", 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. 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. Experts are tested by Chegg as specialists in their subject area. i.e., linear vs. non-linear. What is the best description of the relationship between vehicle weight and gas mileage, based on the scatterplot? Complete parts (a) through (d) below. 12.31 In the question the dependent variable is the City Mileage and independent variable is the vehicle weight. Why indeed? Thus, we can say that the salesman was stretching the truth. ) Redraw the scatter diagram with Car 13 included. 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. 0000087617 00000 n Consider the following ordered pairs and calculate and interpret the correlation coefficient. There is some spread, but we can discern a pattern: Dots to the right in the graph tend to be placed lower. What does the y-intercept mean? Think about air drag and. R Square 0.6809 b. Chevy Corvette 19 3,255 Mercury Sable 20 3,340 a. Was I just making that stuff up? Construct an appropriate 95% interval estimate that would indicate whether the seller of the Cadillac was stretching the truth or not. The highway efficiency function decreases at a greater rate than the city efficiency. Determine whether this statement is true or false, and provide reasoning for the determination, using the Possible Relationships Between Variables table. Correct Answer (a) The slope is 1.109. This make sense. Find and Compare Cars a) Define correlation and talk about how you can use correlation to determine the r, Describe the error in the conclusion. Comment on the seller's veracity. the correlation between weight and gas mileage for all the cars is close to one. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Why are the results here reasonable? Car Weight (pounds) Miles per Gallon A 2690 26 B 3100 21 C 3985 18 D 3590 18 E 3475 20 (a) Compute the linear correlation coefficient between the weight of a car and its miles per gallon. Illustrate with an example of the relationship. Which statement is correct? 0.9184 b. a. The explanatory variable is the weight and the response variable is the miles per gallon. Chi-square analysis will tell us whether two qualitative variables are correlated. (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. V:[-0G|-Z@>=O1\GzJ= wAZ 7zb.Pi}c_t8t]q=YM:@NT#dLm,fnjZa>=cOm xYQ= m} RRO% B;:n`uY{]xtD a>B{de# RrH$Cw m&Oe@nh"U`& 0000399948 00000 n 0000177854 00000 n 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. 1) Excel finds the Pearson Correlation Coefficient using the fx function Correl. The percentage of variance in Y that is explained by, Can you identify some situations where correlation doesn't prove causation? The error term is uncorrelated with an explanatory variable. Do the same for a car with city mileage 28 mpg. The correlation coefficient and the slope of the regression line may have opposite signs. The data are in a file called Automobiles( attached). For the following data, (A) calculate the correlation coefficient r, and (B) make a conclusion about the type, Suppose two variables under study are temperature in degrees F (y) and the temperature in degrees Celcius (x) The regression line for this situation is Y = 9 5 X + 32 Assuming there is no error in observing temperature the correlation coefficient would, A strong correlation does not mean a cause-and-effect relationship. Select one: a. a. Standard Error 2.4989 Use of this site constitutes acceptance of our User Agreement and Privacy Policy and Cookie Statement and Your California Privacy Rights. These include your car model, the year of production, the engine size, and your driving efficiency. Really, this is too much data but I can't help myself. In the scatter plot, the data points are plotted on a graph in a plane. Let's start with the easy and simple numbers. 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? B. a. strong linear correlation b. weak linear correlation c. no linear correlation d. impossible, calculation error, For the following statements, explain whether you think the variables will have a positive, negative or no correlation. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. My first guess was that with a larger mass, you have to use more energy to get the vehicle up to speed. 0000264738 00000 n a. Ford Expedition 13 5,900 Pontiac Vibe 28 2,805 More massive cars have bigger engines that waste more gas with more moving parts to lose energy to friction. Which of the following violates the assumptions of regression analysis? (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. 2500 4000 Weigh: (Ibs A. AMab It is natural to expect a negative relation between mileage and weight of the vehicle. 12.31 State your a priori hypothesis about the sign of the slope. A weightless car will get miles per gallon, on average. 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. (b) The obtained score is greater than the predicted score. b. - The dependent variable is the explanatory var. Using the following information: What is the correlation coefficient? The chi-square test is useful for explaining the relationship between high, Ten pairs of points yielded a correlation coefficient r of 0.790. Thanks for subscribing. (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. Body Lift Kit 0000362642 00000 n 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. 2003-2023 Chegg Inc. All rights reserved. But is it possible that this trend happened by chance? 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. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. B. Thus, the correlational value must be in negative. There is a strong linear relationship between the two variables. Explain reasoning. 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 positive error e value indicates: (a) The predicted score is greater than the obtained score. Our experts can answer your tough homework and study questions. Intercept 36.634 1.879 19.493 0.000 32.838 40.429 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.) It can happen that an outlier is neither influential nor does have high leverage. 0000383286 00000 n If not, what does it mean? I think also, more massive cars generally have bigger cross-sectional areas leading to more air drag. What cautions should be made before using this regression model to make that prediction? There is a fairly strong, roughly linear, positive association between vehicle weight and gas mileage. Which of the following is not an assumption of the regression model? Multiply the linked Z scores from the two variables. 0000002139 00000 n What is the value of the coefficient of correlation? Car 12 weighs 3,305 pounds and gets 19 miles per gallon. One of the editors of a major automobile publication has collected data on 30 of the best-selling cars in the United States. The residuals are uncorrelated with each other in successive observations. Causation is only one explanation of an observed association. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. a) Omission of important variables. Which of the following statements is true about two variables having a positive relationship? 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. a. C. The sum of the. Again, the problem is the big engine. 0000367625 00000 n a. b. CAN'T COPY THE TABLE For instance, a diesel car emitting 95g CO2 per kilometre consumes around 3.7 litres of fuel per 100km, while a petrol car consumes around 4 litres/100km for the same CO2 emissions. 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. The Antibiotic Resistance Crisis Has a Troubling Twist. 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. 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 analysis once again indicates that other factors besides vehicle weight has a substantial effect on determining vehicle fuel efficiency. 0000382275 00000 n What does this say about the usefulness of the regression equation? 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 . Complete parts (a) and (b) below. Find EPA fuel economy estimates based on vehicle model or class. So the question boils down to which engine has more friction per cycle, and which car has more weight to carry around. b. B. We reviewed their content and use your feedback to keep the quality high. 1. If yes, what circumstances? The correlation between mileage and speed is r = 0. tC/`X[*[od!&`\i"M9i#=q@A:CG]%:zk{CSQ&`?;Z3l*zFvbH &l&+;@k,L[,Q5 Test 2 (Y): 34, 31, 35, 30, 31, 28, 28, 25, 24, 24. Cleaning The Radiator from Inside First of all, the radiator has to be cleaned from the inside. The explanatory variable is the miles per gallon and the response variable is the weight. oL#n$\MWNoy(#Rd6Mf/{s5a65:\>31XJ;pF{hDzh.P:G:NQZ. Which of the following statements is not true about regression models? II. did not change significantly Choose the correct answer below. Click here to view the table of critical values of the correlation coefficient. a. miles per gallon, Complete parts (a) through (d). d. The error terms are independent. ", B. 0000370245 00000 n c) The preconceived notions of the forecaster. Suppose that we add Car 12 to the original data. 0000382127 00000 n 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. (A) CORREL (B) COVARIANCE.S (C) CORREL.S (D) CORRELATION, Explain the following terms in your own words: - Positive correlation - Negative correlation - No correlation. The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 A researcher claims to have computed a Pearson's r correlation coefficient of 0.802 for the relationship between biological sex and height. Which of the following is the best interpretation of this correlation value? This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! C. Describe the error in the conclusion. Hence, to know the correct mileage and how much you have spent, remember the below points. 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. Explain how the two correlations differ. critical values for the correlation coefficient (a . b. BMW 3 Series 19 3,390 Lincoln Aviator 13 5,000 . (ii) A sample correlation coefficient of .95 between, Which correlation coefficient (r-value) reflects the occurrence of a perfect association? Fuel efficiency, sometimes referred to as fuel economy, is the relationship . Statistics and Probability questions and answers. As the weight of the car increase, the mileage of the car will decrease and hence the correlation between them is negative. a. Looks linear enough to fit a function. Complete parts (a) through (f) below. A. Here are the fitting functions. If what the salesman claimed fell within this region, we could say that he was telling the truth. 0000404223 00000 n An engineer wanted to determine how the weight of a car affects gas mileage. One final note. For cases like this, I just took the first reasonable number I found. Identify any statistical errors. Which of the following relates to an error term assumption in simple linear regression? c. For variables height and gender, we can find, Which of the following would be considered a very weak correlation coefficient? Honda Odyssey 18 4,315 Toyota Celica 23 2,570 Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distributions under H_0)? Ultimately, you can't trace fuel economy simply to the level of horsepower your engine is capable of providing.