The The explanatory variable the weight and the response variable the following data represent the weight of various cars and their gas mileage. There is some spread, but we can discern a pattern: Dots to the right in the graph tend to be placed lower. Miles per Car Weight (pounds) Gallon 3310 B 3680 2770 3340 2690 Show transcribed image text Expert Answer 100% (3 ratings) This implies that mass has a bigger effect on highway efficiency. 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. Below is a guide on how to repair an aluminum radiator. Ad Choices. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. Explain in each case what is wrong. d. The error terms are independent. BrainMass Inc. brainmass.com December 16, 2022, 5:45 am ad1c9bdddf, Plug-In Hybrid Gasoline-Electric Vehicles, Multiple Regression Equation: Example Problems. 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. All rights reserved. 0000385398 00000 n WIRED may earn a portion of sales from products that are purchased through our site as part of our Affiliate Partnerships with retailers. Which of the following statements below is not the explained variance? Click the. Adjusted R Square 0.6732 d. there has been a calculation error. The error term has a constant variance. 17.5. She is my daughter, after all. (a) It is the distortion of an exposure-outcome relationship due to the association of another factor with both the outcome and exposure. Identify any statistical errors. Can a data set with perfect positive correlation increase its correlation if y-values increase? 0000362081 00000 n The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 changed. 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. 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. Why are the results here reasonable? B) H and R have a low correlation but both have significant coefficients. Explain why correlation alone is rarely sufficient to demonstrate cause. The individual from whom the editor purchased the Cadillac said that this car got exceptional gas mileage. <> 0000090679 00000 n Please follow the instructions below to enable JavaScript in your browser. Check your in-box to get started. % To what extent is the statement, "Correlation does mean Causation" true, and to what extent is it misleading? R Square 0.6809 Causation is only one explanation of an observed association. Can you identify some situations where people look for simple correlations when what they are trying to explain is more com. b. two variables are inversely related. 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. When two things are highly correlated, one causes the other. 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? (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. Select all that apply. Is there a correlation between variable A and B? To revist this article, visit My Profile, then View saved stories. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. hb``e``AXX80,,tqq$,d%0h Idt4[ m`e(>W2v11y21d` i'c G&tS,XD&hV3132D231233,!!!AH Zlb !O2l4#x i&?`Nm.#D @ t:L endstream endobj 216 0 obj <>/Filter/FlateDecode/Index[34 119]/Length 27/Size 153/Type/XRef/W[1 1 1]>>stream The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. An engineer wanted to determine how the weight of a car affects gas mileage. In model year 2021, the average estimated real-world CO 2 emission rate for all new vehicles fell by 2 g/mi to 347 g/mi, the lowest ever measured. Question 9 30 seconds Q. Correct Answer (a) The slope is 1.109. Multiple R 0.8252 B) The x-va, Consider the following statements about unusual observations in linear regression models and pick the correct one. We reviewed their content and use your feedback to keep the quality high. Think about when and why the relation between two variables can change. Complete parts (a) through (d) below. a) 0.8 to 1.0 b) 0.6 to 0.8 c) 0.2 to 0.4 d) 0 to 0.2, Consider the following regression equation between Y and X: Y = 4.622X - 100. 0000367230 00000 n Engines will most commonly come in 4, 6, or 8 cylinders. oL#n$\MWNoy(#Rd6Mf/{s5a65:\>31XJ;pF{hDzh.P:G:NQZ. Real-world fuel economy remained at a record high 25.4 mpg. Thus, the correlational value must be in negative. 0000044566 00000 n df SS MS F Significance F Sometimes, there would be multiple listings for a car. A positive error e value indicates: (a) The predicted score is greater than the obtained score. Think about air drag and. 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 The editor just purchased a Cadillac Sedan DeVille which weighs 4,012 pounds. Back to my daughter's question. c. The error term has a zero mean. Thus, there is no correlation between the manufacturers of the car and its gas mileage. My first guess was that with a larger mass, you have to use more energy to get the vehicle up to speed. D. follows the overall pattern of the data. became significantly further from 0 (f) Why does this observation not follow the pattern of the data? Which of the following statements is not true? 0000133335 00000 n One would assume that a car with greater mpg would command better resale value, but this definitely appears to not be the case. per gallon in the city. The following problem uses a regression model to answer several questions associated with auto travel. Was I just making that stuff up? Complete parts (a) through (f) below. c. In negatively skewed distributions, the mean is usually greater than the m. Compute the correlation for the following data. A. In this case, I went for the "curb weight" and converted to kilograms. A. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. than 121 inches. a. Which of the following is the best interpretation of this correlation value? Provide an example of a study when extrapolation would almost definitely lead to incorrect results. Mass isn't the only thing that limits the fuel efficiency. 11,853. Why? Construct an appropriate 95% interval estimate that would indicate whether the seller of the Cadillac was stretching the truth or not. 0000374718 00000 n B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon. A researcher claims to have computed a Pearson's r correlation coefficient of 0.802 for the relationship between biological sex and height. 0000383286 00000 n Hence the priori hypothesis about the sign of slope is "The slope is negative". 0000090312 00000 n The second is increased wind resistance. Experts are tested by Chegg as specialists in their subject area. Everyone loves data. When is it inappropriate to conduct a correlation analysis? Click the icon t0 view the critical values table The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 did not change significantly (d) Now suppose that Car 13 (a hybrid car) is ad r 13 weighs 2,890 pounds and gets 60 miles per gallon. The material on this site may not be reproduced, distributed, transmitted, cached or otherwise used, except with the prior written permission of Cond Nast. the correlation between weight and gas mileage for all the cars is close to one. The probability that the null hypothesis is true is less than 1 percent. !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 . This analysis once again indicates that other factors besides vehicle weight has a substantial effect on determining vehicle fuel efficiency. Based on a gallon of gasoline costing. He checks his theory by gathering data on a rat, a bat. 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. 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). The following data represent the weight of various cars and their gas mileage. You must have JavaScript enabled to experience the new Autoblog. 0000362552 00000 n ", B. Illustrate with an example of the relationship. Here are the fitting functions. A luxury saloon will always have a frontal area larger than a supermini. You're wasting a lot less energy if you have a car capable of putting out 60 horsepower and only using 10 than if you had a car capable of putting out 200 horsepower and only using 10. An engineer wanted to determine how the weight of a car affects gas mileage. Because it was sitting in my barn / shop for over 12 years!! Complete parts (a) through (d) below. Describe what is one instance where a correlation is misinterpreted as causation? 0000003102 00000 n He claimed that this particular car got 29 mpg. Multiply the linked Z scores from the two variables. Find the correlation coefficient of the data. (c) The correlation is not significant. Conclusion: Cigarettes cause the pulse rate to increase. (b) The obtained score is greater than the predicted score. . endstream endobj startxref An engineer wanted to determine how the weight of car affects gas mileage. Be specific and provide examples. The WIRED conversation illuminates how technology is changing every aspect of our livesfrom culture to business, science to design. 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. The following data represent the weight of various domestic cars and their gas mileage in the city for the 2005 model year. b. Suppose that we add Car 12 to the original data. Scientists say a mild Covid infection increased immune benefits from a later flu vaccine, but with a biological twist. Dodge Caravan 18 4,210 Nissan Xterra 16 4,315 A. 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. Looks linear enough to fit a function. 0000382677 00000 n Another bowl. 0000367865 00000 n See correlation examples using statistical data sets and learn how to do an analysis. 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. 0000355569 00000 n The EPA city test includes idling, but more idling will lower MPG. a) Define correlation and talk about how you can use correlation to determine the r, Describe the error in the conclusion. The Last Drug That Can Fight Gonorrhea Is Starting to Falter. The coefficient of determination is R2 = 0.895 . I expected it would be the other way around. OD. Redraw the scatter diagram with Car 13 included. Engine oil is responsible for lubricating the engine components and reducing friction, which can improve fuel efficiency. . A positive residual means that the car gets better gas mileage than the model predicts for a car with that much horsepower. 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. 0000362642 00000 n The explanatory variable is the weight and the response variable is the miles per gallon. a. (b) Do a two-tailed t test for zero slope at ? Comment on the seller's veracity. Infinity FX 16 4,295 Toyota Sienna 19 4,120 Which of the following is true? 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. . 6 0 obj There are no new treatments yet. As the number of cigarettes increases the pulse rate increases. B) It is impossible to get a correlation greater than 1. Which of the following statements is not true about regression models? 12.28 The given data is a cross-sectional data. 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. c. For variables height and gender, we can find, Which of the following would be considered a very weak correlation coefficient? 0000382088 00000 n - strong linear correlation - weak linear correlation - impossible, calculation error - no linear correlation. Japanese cars tend to get worse gas mileage than other cars. (a) Draw the scatter diagram with Car 12 included. News, Reviews, Photos, Videos delivered straight to your in-box. Old or incorrect engine oil. A. A. Choose the correct answer below. - The regression line minimizes the sum of the squared errors. d. b. In fact, 20% to 30% of a vehicle's fuel consumption and 24% of road vehicle CO2 emissions are tire-related. We are not mentioning the basic formula of getting the car mileage by dividing the number of kms by the quantity of fuel used, but a lot more than that through which you can smartly check the fuel efficiency. What does this say about the usefulness of the regression equation? 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 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? Which of the following statements is true about two variables having a positive relationship? Transcribed image text: An engineer wanted to determine how the weight of a car affects gas mileage. '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' First, maybe I should check. 0000088713 00000 n The x-variable explains ?25% of the variability in the y-variable. However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence interval. 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)? 0000001596 00000 n A. The error term is correlated with an explanatory variable. The correlation between a car's engine size and its fuel economy (in mpg) is r = -0.8476. (b) A confounding factor must be independently associated with. Mondays massive earthquake has triggered a swarm of aftershocks, which will make a humanitarian disaster even more devastating. Do heavier cars use more gasoline? Isuzu Ascender 15 4,965 Volkswagen Jetta 34 3,045 Since model year 2004, CO 2 emissions have decreased 25%, or 114 g/mi, and fuel economy has increased 32%, or 6.1 mpg. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. (d) The correlation is significant. 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. The conditions under which miles per gallon were evaluated for Car 13 were different from the conditions for the other cars. 10 20 30 40 Mileage (mpg) 2,000 3,000 4,000 5,000 Weight (lbs.) Final answer. If so, what does it mean? As x increases, y decreases, and the correlation coefficient must be positive. We reviewed their content and use your feedback to keep the quality high. 0000086420 00000 n However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence . Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. Which one could be true? 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 What is the value of the coefficient of correlation? 0000362720 00000 n Tires can make a big difference in the number of miles a driver gets to a tank of gas. EPA provides IRS with the fuel economy data for vehicles which may be subject to the Gas Guzzler tax penalty. The data are in a file called Automobiles( attached). The correlation between drop and duration is rR . 1168 0 obj <> endobj (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+ Kia Rio 25 2,295. 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. What factors affect your MPG? If I am looking for a relationship, it shouldn't really matter. 0000089897 00000 n A weightless car will get miles per gallon, on average. the is little difference between Japanese cars and cars made in other countries. The correlation between mileage and speed is r = 0. Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distributions under H_0)? The x-variable explains 25% of the variability in the y-variable. GMC Envoy 15 4,660 Subaru Baja 21 3,575 a. The correlation is moderate to strong. 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. 0000264738 00000 n Which of the following relates to an error term assumption in simple linear regression? 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. This equation shows a positive correlation between X and Y. b. trailer <<1A6862DFEDAF4A86A87609A026CF06EA>]/Prev 434047/XRefStm 1962>> startxref 0 %%EOF 217 0 obj <>stream 0.866 c. -0.155 d. -0.866 e. 0.155 f. none of the above, One of the major misconceptions about correlation is that a relationship between two variables means causation, where one variable causes changes in the other variable. (b) Interpret the p-value for the F statistic. 0000369380 00000 n Let's start with the easy and simple numbers. IRS is responsible for collecting those taxes from manufacturers. The Antibiotic Resistance Crisis Has a Troubling Twist. 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. 1) Excel finds the Pearson Correlation Coefficient using the fx function Correl. Chi-square analysis will tell us whether two qualitative variables are correlated. explanatory variable response variable b) Draw a scatter diagram . As the number of cigarettes increases the pulse rate increases. The degree to which the regression equation of X and Y is better at predicting the dependent variable than the average of Y. b. hbbe`b``3Y ! (c) Interpret the p-value for the slope. B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles . Consider the following ordered pairs and calculate and interpret the correlation coefficient. [R138'4uQr#?v*6a (A) CORREL (B) COVARIANCE.S (C) CORREL.S (D) CORRELATION, Explain the following terms in your own words: - Positive correlation - Negative correlation - No correlation. Using Data set 'G', choose the dependent variable (the response variable to be 'explained') and the independent variable (the predictor or explanatory variable) as you judge appropriate. There is a strong linear relationship between the two variables. The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 What is interesting to note here, is the strong negative correlation between city_mpg and highway_mpg. Buick Rendezvous 18 4,230 Mazda 6 19 3,355 Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. d. Yes, there is a negative correlation. Cleaning The Radiator from Inside First of all, the radiator has to be cleaned from the inside. 0.9184 b. A. 0000368723 00000 n 0000307165 00000 n But is it possible that this trend happened by chance? Suppose that you are given the following results. b. did not change. 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. Which of the following statements must be true? Acura TSX 23 3,320 Lexus IS 300 18 3,390 My daughter asked. 2003-2023 Chegg Inc. All rights reserved. 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? The error term is uncorrelated with an explanatory variable. Total 42.000 802.465, Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Why do big cars get bad mileage? (b) Draw a scatter diagram of the data. C. The sum of the. What cautions should be made before using this regression model to make that prediction? Car 13 weighs 2,890 pounds and gets 60 miles per gallon. There is a negative correlation between x and y. b. Is it reasonable to suppose a cause and effect relationship? Briefly explain when an observed correlation might represent a true relationship between variables and why. We predict highway mileage will increase by 1.109 mpg for each 1 mpg increase in city mileage. (e) Recompute the linear correlation coefficient with Car 13 included. Mass isn't the only thing that limits the fuel efficiency. 0000002939 00000 n Reducing weight means reducing fuel cost. Tires affect vehicle fuel efficiency primarily through rolling resistance. O A. )HVX(j(L3/WB]';.+l}^c(/CqbZ6/0h": H_H~A3ep>/~Z+]~^7u]-YL'W1_Q8& /:6`;N\}Zq9YI4S9,R9. Excessive idling decreases MPG. Buick Century 20 3,350 Mazda MPV 18 3,925 This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! Choose the correct graph below. *4/Q:/w`D%w&FTb>F 20[O@Le,1&# Qh ` ~S^ Describe each correlation (strength and direction). The following statements are either misleading or contain one or more errors relating to correlation. e) All. The percentage of variance in Y that is explained by, Can you identify some situations where correlation doesn't prove causation? 0000382826 00000 n ", 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.". Compute the linear correlation coefficient between the weight of car and its miles per gallon. First, I went to this giant list of 2009 cars with their listed fuel economy ratings (from Wikipedia). The engine may also be used for performance or for better fuel mileage. Really, this is too much data but I can't help myself. Test 2 (Y): 34, 31, 35, 30, 31, 28, 28, 25, 24, 24. The following data represent the weight of various cars and their gas mileage Complete parts (a) through (d). became significantly closer to O A. His previous car was a Toyota Camry which weighs 3,241 pounds.. a) The editor often takes his entire family to visit relatives in a nearby state. Which of the following statements is correct? 2. 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). 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. Suppose that we add Car 12 to the original data. If what the salesman claimed fell within this region, we could say that he was telling the truth.
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