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. It describes the relationship between two variables. Which of the following Excel functions returns the sample correlation coefficient? What type of correlation does this indicate? The percentage of variance in Y that is explained by, Can you identify some situations where correlation doesn't prove causation? Covid Can Boost Your Response to Flu Vaccinesif Youre a Man. Mass isn't the only thing that limits the fuel efficiency. a. Question 9 30 seconds Q. 0000367865 00000 n a. 0.9184 b. Multiply the linked Z scores from the two variables. The WIRED conversation illuminates how technology is changing every aspect of our livesfrom culture to business, science to design. The EPA city test includes idling, but more idling will lower MPG. (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. 12.36 (a) Does the 95 percent confidence interval for the slope include zero? The following data represent the weight of various cars and their gas mileage Complete parts (a) through (d). has a weight outside the range of the other cars' weights. B. OC. Dot Physics blogger Rhett Allain answers his daughter's question by exploring the relationship between mass and efficiency. Data gaps, funding cuts, and shyness about sex let gonorrhea gain drug resistance. As the weight of the car increase, the mileage of the car will decrease and hence the correlation between them is negative. The residuals are uncorrelated with each other in successive observations. *4/Q:/w`D%w&FTb>F 20[O@Le,1&# Qh ` ~S^ (b) The obtained score is greater than the predicted score. 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). 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? 0000001596 00000 n the correlation between weight and gas mileage for all the cars is close to one. Ad Choices. Honda Accord 21 3,390 Suzuki Vitara XL7 17 3,590 Which of the following statements must be true? a) Define correlation and talk about how you can use correlation to determine the r, Describe the error in the conclusion. 2500 4000 Weigh: (Ibs) Conclusion: Cigarettes cause the pulse rate to inc, What's wrong with these statements? 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. - The dependent variable is the explanatory var. A. Standard Error 2.4989 (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. Engine oil is responsible for lubricating the engine components and reducing friction, which can improve fuel efficiency. Aftershocks May Rock Turkey and Syria for Months, Even Years. a. (a) Draw the scatter diagram with Car 12 included. Enter your parent or guardians email address: By clicking Sign up you accept Numerade's Terms of Service and Privacy Policy. Scientists say a mild Covid infection increased immune benefits from a later flu vaccine, but with a biological twist. than 121 inches. a. Redraw the scatter diagram with Car 13 included. GMC Envoy 15 4,660 Subaru Baja 21 3,575 0000383622 00000 n tC/`X[*[od!&`\i"M9i#=q@A:CG]%:zk{CSQ&`?;Z3l*zFvbH &l&+;@k,L[,Q5 d. there has been a calculation error. BrainMass Inc. brainmass.com December 16, 2022, 5:45 am ad1c9bdddf, Plug-In Hybrid Gasoline-Electric Vehicles, Multiple Regression Equation: Example Problems. The data for Car 13 must be incorrect. (d) Now suppose that Car 13 (a hybrid car) is added to the original data (remove Car 12). 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. 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. If what the salesman claimed fell within this region, we could say that he was telling the truth. 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. Complete parts (a) through (d). 0000086067 00000 n 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 accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Explain reasoning. 0000382531 00000 n l^&Hx+A@:@z/s 4D*HV3nN{5>0W;:o` )i` Let's start with the easy and simple numbers. Was I just making that stuff up? But they also hold genetic benefits for species. Using the following information: What is the correlation coefficient? How Fiber Optic Cables Could Warn You of an Earthquake. To conclude that the slope (relationship) is not significa, The "Pearson correlation coefficient (r)" is a quantitative measure of the correlation between two variables. Each of the following statements contains a blunder. 1 Through 2006, data are for passenger cars (and, through 1989, for motorcycles). One of the editors of a major automobile publication has collected data on 30 of the best-selling cars in the United States. a. 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. 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 . The coefficient of determination is R2 = 0.895 . Current antipsychotics are plagued by patchy efficacy and unwanted side effectsbut a new treatment could change all that. Perfect positive c. No correlation d. Limited correlation. 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. 0000382088 00000 n Now for a plot. 0000368723 00000 n 0000370206 00000 n 0000382677 00000 n Suppose you have 50 observations with a correlation coefficient of -0.81625113. Is it reasonable to suppose a cause and effect relationship? e)Suppose an editor for the publication wishes to predict the highway mileage of vehicles with a curb weight of 6,000 pounds. sx = 1.355, sy = 15.300, b = -9.780 a. The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 changed. A. There are no new treatments yet. a. b. She is my daughter, after all. Suppose that we add Car 12 to the original data. 2003-2023 Chegg Inc. All rights reserved. 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. Sean has a theory that the average weight of an animal has a high correlation with the number of letters in its name. This is not statistically meaningful, because this would represent the highway mileage for a car The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r=0.981. 153 0 obj <> endobj xref 153 65 0000000016 00000 n The gas mileage of the car depends on the size of the engine and the efficiency with which it works rather than the manufacturers of the car. "Bigger cars don't get as good gas mileage," I replied. Which of the following statements regarding the coefficient of correlation is true? Correlation means Causation. Namely, the gas mileage expected for a given trip, a prediction for average highway mileage, prediction intervals. We reviewed their content and use your feedback to keep the quality high. Redraw the scatter diagram with Car 13 included. d. The error term h, Which of the following is not a source of forecast bias? What else could produce a strong correlation? 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. When is it inappropriate to conduct a correlation analysis? Everyone loves data. 0000177854 00000 n The following data represent the weights of various cars and their gas mileages. Do heavier cars use more gasoline? 0000264738 00000 n c) The preconceived notions of the forecaster. Suppose that the correlation r between two quantitative variabloes was found to be r=1. for Cubic Capacity. miles per gallon, Complete parts (a) through (d). 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. Buick Century 20 3,350 Mazda MPV 18 3,925 If what the salesman claimed fell within this region, we could say that he was telling the truth. FMEP times volume = Power per cycle needed to fight friction. Why are the results here reasonable? The value of a correlation is reported by a researcher to be r = ?0.5. 0000367625 00000 n However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence . 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. Explain the situation. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Thanks for subscribing. Dodge Caravan 18 4,210 Nissan Xterra 16 4,315 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. 0000001962 00000 n Thus, we can say that the salesman was stretching the truth. ) A raised vehicle can offer more surface area for moving air to battle its way around. Be specific and provide examples. Select one: a. Give examples with your response. Explain in each case what is wrong. II. An engineer wanted to determine how the weight of a car affects gas mileage. Which of the following statements is not true about regression models? Correct Answer (a) The slope is 1.109. 0000374718 00000 n I just realized that the data I used for fuel efficiency includes some sport cars. trailer <<1A6862DFEDAF4A86A87609A026CF06EA>]/Prev 434047/XRefStm 1962>> startxref 0 %%EOF 217 0 obj <>stream Illustrate with an example of the relationship. T ~ (Round to three decimal places as needed:). 5. C. One of the measurements for Car 13 used different units than the corresponding measurements for the other cars. Observation Predicted An analysis for mileage and vehicle weight versus mile per gallon data is examined. Find the correlation coefficient of the data. hb``e``AXX80,,tqq$,d%0h Idt4[ m`e(>W2v11y21d` i'c G&tS,XD&hV3132D231233,!!!AH Zlb !O2l4#x i&?`Nm.#D @ t:L endstream endobj 216 0 obj <>/Filter/FlateDecode/Index[34 119]/Length 27/Size 153/Type/XRef/W[1 1 1]>>stream EPA provides IRS with the fuel economy data for vehicles which may be subject to the Gas Guzzler tax penalty. Insert tables and graphs in your report as appropriate. V:[-0G|-Z@>=O1\GzJ= wAZ 7zb.Pi}c_t8t]q=YM:@NT#dLm,fnjZa>=cOm xYQ= m} RRO% B;:n`uY{]xtD a>B{de# RrH$Cw m&Oe@nh"U`& How You May be Prematurely Aging Your Car, Preventing Auto Repairs Before They Cost You Dearly. b) Incorrect model specification. 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. Ford Focus 26 2,760 Saturn Ion 24 2,855 (b) Draw a scatter diagram of the data. c. Adding the multiplication. B. b. (d) The correlation is significant. Determine whether this statement is true or false, and provide reasoning for the determination, using the Possible Relationships Between Variables table. For example, the average gas mileage of Ford Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100 km. If yes, what circumstances? The engine may also be used for performance or for better fuel mileage. Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distributions under H_0)? !1997 F350 XLT 4x4 Crew Cab (4 door) 7.3 Liter V-8 Diesel Powerstroke, Automatic with overdrive, Dana 60 front axle, Weld Racing Wheels and Toyo Open Country Radials (tires and wheels cost $4500) only 66,000 original miles Located in Seattle Washington 98188 1 mile from Seatac AirportI . Intercept 36.634 1.879 19.493 0.000 32.838 40.429 A strong negative correlation coefficient indicates: a. two variables are not related. Provide an example of a study when extrapolation would almost definitely lead to incorrect results. The individual from whom the editor purchased the Cadillac said that this car got exceptional gas mileage. ", 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.". Below is a guide on how to repair an aluminum radiator. (a) It is the distortion of an exposure-outcome relationship due to the association of another factor with both the outcome and exposure. b. 0000003102 00000 n e) All. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. "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." Oh, one more note. Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. 1. Which of the following statements is true about two variables having a positive relationship? Car 12 weighs 3,305 pounds and gets 19 miles per gallon. 0000362607 00000 n 12.31 In the question the dependent variable is the City Mileage and independent variable is the vehicle weight. Fuel efficiency, sometimes referred to as fuel economy, is the relationship . Weight (pounds), x Miles per Gallon, y 3808 16 3801 15 2710 24 3631. Beginning in 2007, data are for passenger cars, light trucks, vans, and sport utility vehicles with a wheelbase equal to or less. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. 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. More massive cars have bigger engines that waste more gas with more moving parts to lose energy to friction. You may order presentation ready copies to distribute to your colleagues, customers, or clients, by visiting https://www.parsintl.com/publication/autoblog/, Warren Buffett's Berkshire Hathaway quietly made a $8.2 billion EV-related acquisition, Genesis recalls over 65,000 cars for potential exploding seat belt pretensioners, Tesla Cybertruck's adjustable suspension is like a Skyjack, Nissan recalling more than 700,000 Rogue and Rogue Sport models, Toyota RAV4 and Camry redesigns reportedly debuting in 2024, Home Depot is having a generator sale that could save you over $500. Conclusions My daughter asked. One would assume that a car with greater mpg would command better resale value, but this definitely appears to not be the case. c. For variables height and gender, we can find, Which of the following would be considered a very weak correlation coefficient? Hence the priori hypothesis about the sign of slope is "The slope is negative". "We found a high correlation (r = 1.09) between the horsepower of a car and the gas mileage of the car. Residual 41.000 256.027 6.245 For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. Based on a gallon of gasoline costing. B. 0000369380 00000 n An engineer wanted to determine how the weight of a car affects gas mileage. c. The error terms decrease as x values increase. a. A. If an aluminum radiator is damaged or is experiencing problems, it can easily be fixed up by the owner. Describe the clinical importance of each correlation (r) value. I should have known it wouldn't stop there. It is the essential source of information and ideas that make sense of a world in constant transformation. 12.37 (a) Based on the R2 and ANOVA table for your model, how would you assess the fit? 0000382904 00000 n O c. does not follow the overall pattern of the data. Construct an appropriate 95% interval estimate that would indicate whether the seller of the Cadillac was stretching the truth or not. 0000090312 00000 n The error terms have constant variance. Final answer. 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. Engines will most commonly come in 4, 6, or 8 cylinders. d. b. Which of the following is the best interpretation of this correlation value? Causation is only one explanation of an observed association. % Observations 43.0000, ANOVA In fact, 20% to 30% of a vehicle's fuel consumption and 24% of road vehicle CO2 emissions are tire-related. 0000382127 00000 n 0000369036 00000 n Thus, there is no correlation between the manufacturers of the car and its gas mileage. B. Click the icon to view the data table. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon in the city. Hence, to know the correct mileage and how much you have spent, remember the below points. As x increases, y decreases, and the correlation coefficient must be positive. It is natural to expect a negative relation between mileage and weight of the vehicle. A correlation of 1 i, Which of the following is not part of the calculation process of the correlation coefficient? Of course the next question was, "Why do bigger cars get worse gas mileage?". Chrysler Pacifica 17 4,660 Nissan Pathfinder 15 4,270 Ford Expedition 13 5,900 Pontiac Vibe 28 2,805 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. 0000087040 00000 n Body Lift Kit A correlation coefficient between two variables is 0.50, and this correlation is statistically significant at p < 0.01. . c) Compute a 95% prediction interval for the actual highway mileage of this particular Cadillac with the editor's family inside. Which of the following statements is not true? If r = 0, there is no relationship between the two variable at all. Please provide an example to illustrate your explanation. Cadillac Seville 18 4,050 Mercedes-Benz S-Class 17 4,195 The linear correlation coefficient with Car 12 included is r= (Round to three decimal places as needed.) Why do big cars get bad mileage? 4Gdk2\#O+jxm#o g{Iq0zF>(tFOlqy6,?6/4fiRa`6:/. this giant list of 2009 cars with their listed fuel economy ratings. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. There is a negative correlation between x and y. b. The error term is uncorrelated with an explanatory variable. Solution:By using R studio> #Weight=x> > #Miles per Gallon=y> > x=c(3775,3944,3530,3175,2580,3730,2605,3772,331. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. 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? Which of the following statements is true? a) 0.1 b) 1.0 c) 10.0 d) 100.0, When analyzing the slope in a regression analysis (i.e., the relationship between the dependent variable and one of the independent variables), which of the following would be a Type II error? The second is increased wind resistance. Excessive idling decreases MPG. a. The correlation between height and weight is 0.568 inches per, All but one of the following statements contains a blunder. 0000367559 00000 n (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. A weightless car will get miles per gallon, on average.

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