hbbd``b`v@"@CH `q3 $50&F% M & There are no new treatments yet. b. became significantly further from 0 O A. C. D. became significantly closer to 0 For cases like this, I just took the first reasonable number I found. The values of the independent variable X are assumed to be random. Tires affect vehicle fuel efficiency primarily through rolling resistance. miles per gallon, Complete parts (a) through (d). The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 did not change significantly (d) Now suppose that Car 13 (a hybrid car) is ad r 13 weighs 2,890 pounds and gets 60 miles per gallon. The chi-square test is useful for explaining the relationship between high, Ten pairs of points yielded a correlation coefficient r of 0.790. What is the value of the coefficient of correlation? 0000382275 00000 n We reviewed their content and use your feedback to keep the quality high. Use of this site constitutes acceptance of our User Agreement and Privacy Policy and Cookie Statement and Your California Privacy Rights. Find and Compare Cars Complete parts (a) through (d). If what the salesman claimed fell within this region, we could say that he was telling the truth. hb```b``e`c`Va`@ V 1` 8204q) ,.,N`@.TcT]$hxqq@4\Lk13Jbg+TrAKdVa,dyBMo+tE@hK2OJ,g 3:gY^^@FUwE) qp!31G$\7T/t\4"$ 4HoT46Ta{mIl_ The correlation between height and weight is 0.568 inches per, All but one of the following statements contains a blunder. ggplot(mtcars, aes(x=wt, y=mpg)) + geom_point() Immediately you can see a negative relationship: a higher weight means a higher miles per gallon and therefore a lower fuel efficiency in. The combined weight of his family is 570 lbs. This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence . (c) Interpret the p-value for the slope. Engine oil is responsible for lubricating the engine components and reducing friction, which can improve fuel efficiency. Ford Expedition 13 5,900 Pontiac Vibe 28 2,805 The error term is uncorrelated with an explanatory variable. 0000089897 00000 n No, because a hybrid gas and . A. Which of the following statements is not true? Which of the following statements about the correlation coefficient are true? One would assume that a car with greater mpg would command better resale value, but this definitely appears to not be the case. 0000352202 00000 n The correlation between a car's engine size and its fuel economy (in mpg) is r = -0.8476. The error term is correlated with an explanatory variable. The following statements are either misleading or contain one or more errors relating to correlation. Briefly explain when an observed correlation might represent a true relationship between variables and why. investing millions in the production of carbon fiber. 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. miles per gallon, Complete parts (a) through (d). Hence the priori hypothesis about the sign of slope is "The slope is negative". My first guess was that with a larger mass, you have to use more energy to get the vehicle up to speed. c. Yes, there is a positive correlation. Each of the following statements contains a blunder. for Cubic Capacity. Describe the clinical importance of each correlation (r) value. Based on a gallon of gasoline costing. B. 6. b. b) If the correlation between two variables is 0, there is no cl. At Last, the Milky Way Gets a Better Close Up. (b) Draw a scatter diagram of the data. 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. F zF.Jcqju7yVGh8 B. 0000220226 00000 n Please follow the instructions below to enable JavaScript in your browser. D. Car 13 is a hybrid car, while the other cars likely are not. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. Regression 1.000 546.438 546.438 87.506 0.000 a) A correlation of 1 indicates that there is little or no linear relationship between the two variables. What fraction of the variability in fuel economy is accounted for by the engine size? As the number of cigarettes increases the pulse rate increases. 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 $500. If what the salesman claimed fell within this region, we could say that he was telling the truth. The explanatory variable is the weight and the response variable is the miles per gallon. A strong negative correlation coefficient indicates: a. two variables are not related. For every pound added to the weight of the car, gas mileage in the city will decrease by .005920.00592 mile (s) per gallon, on average. Complete parts (a) through (d) below. has a weight within the range of the other cars' weights. Buick Rendezvous 18 4,230 Mazda 6 19 3,355 Experts are tested by Chegg as specialists in their subject area. BrainMass Inc. brainmass.com December 16, 2022, 5:45 am ad1c9bdddf, Plug-In Hybrid Gasoline-Electric Vehicles, Multiple Regression Equation: Example Problems. a. 5 Included in "Heavy-Duty Trucks." Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. Using the wrong type of engine oil or not changing the engine oil on time can lead to decreased fuel efficiency and reduced gas mileage in Bonneville. Choose the correct graph below. b. 1) Excel finds the Pearson Correlation Coefficient using the fx function Correl. xXM7%6.KR\!0"]`XyvH)RW~HAL{Csy_ nl!R"{^6aC4?']WTP.?^9#-a12e*}Rn:|$:.n(? 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. 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. . Therefore, a correlational value of 1.09 makes no sense. Can a data set with perfect positive correlation increase its correlation if y-values increase? Fuel efficiency, sometimes referred to as fuel economy, is the relationship . Cannot be seen from the table. Describe each correlation (strength and direction). The correlation is moderate to strong. The largest catalog ever collected by a single telescope maps Earths 3 billion stellar neighborsand helps track the dust that warps how we see them. In fact, 20% to 30% of a vehicle's fuel consumption and 24% of road vehicle CO2 emissions are tire-related. a) Which variable is likely the explanatory variable and which is the response variable? trailer <<1A6862DFEDAF4A86A87609A026CF06EA>]/Prev 434047/XRefStm 1962>> startxref 0 %%EOF 217 0 obj <>stream Here is the data, if you want it. Suppose that you are given the following results. - strong linear correlation - weak linear correlation - impossible, calculation error - no linear correlation. Observations 43.0000, ANOVA More massive cars have bigger engines that waste more gas with more moving parts to lose energy to friction. Which of the following is not an assumption of the regression model? c. The error term does not have the normal distribution. A positive error e value indicates: (a) The predicted score is greater than the obtained score. However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence interval. Stretches of DNA that lock inherited traits together often accumulate harmful mutations. The editor just purchased a Cadillac Sedan DeVille which weighs 4,012 pounds. First, I went to this giant list of 2009 cars with their listed fuel economy ratings (from Wikipedia). Look at the following cross table of two ordinal variables. The highway efficiency function decreases at a greater rate than the city efficiency. 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 . tC/`X[*[od!&`\i"M9i#=q@A:CG]%:zk{CSQ&`?;Z3l*zFvbH &l&+;@k,L[,Q5 Cadillac Seville 18 4,050 Mercedes-Benz S-Class 17 4,195 Residual 41.000 256.027 6.245 0000367741 00000 n 0000382826 00000 n If your vehicle weighs more after installing a lift kit, it will reduce mileage. Real-world fuel economy remained at a record high 25.4 mpg. 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. - The dependent variable is the explanatory var. All but one of these statements contain a mistake. 0000369380 00000 n HW%G|?_?0=uH%le obODdV>n^q:++323go~W>z!Y_o|>>._?]O7zPCa*v}}yu>3|uW/WiA}Ol[L[,{e{+;{[*"~#]Cc[CoaQ jA 5i I{[.T6:qm `nr$.^Kd;zg.2B\= 0000403945 00000 n Again, the problem is the big engine. critical values for the correlation coefficient (a . This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! Sometimes, there would be multiple listings for a car. 678. If so, can we predict the mileage rating of a car given its weight? Illustrate with an example of the relationship. If you google something like "2009 Pontiac G5 curb weight," you might find several answers that don't agree. b. 0000090312 00000 n From the following scores on two tests, calculated the correlation coefficient: Test 1 (X): 29, 28, 25, 25, 22, 22, 21, 20, 19, 19. Complete parts (a) through (d). 0000264738 00000 n Can you identify some situations where people look for simple correlations when what they are trying to explain is more com. did not change significantly Choose the correct answer below. 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. Which of the following statements below is not the explained variance? a. We dont have your requested question, but here is a suggested video that might help. Are there ever any circumstances when a correlation can be interpreted as evidence for a causal connection between two variables? Determine whether the correlation coefficient is an appropriate summary for the scatter-plot and explain your reasoning. What type of correlation does this indicate? 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 individual from whom the editor purchased the Cadillac said that this car got exceptional gas mileage. 3&1!}+1~m0 !mq#D^Wm'!>avp! 0000003102 00000 n 0 (b) Do a two-tailed t test for zero slope at ? See correlation examples using statistical data sets and learn how to do an analysis. Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. 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. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. Click here to view the table of critical values of the correlation coefficient. Which of the following statements is correct? 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. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Intercept 36.634 1.879 19.493 0.000 32.838 40.429 One of the editors of a major automobile publication has collected data on 30 of the best-selling cars in the United States. (b) A confounding factor must be independently associated with. 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. %PDF-1.3 0000001596 00000 n Click here to view the table of critical values of the correlation coefficient. d) Failure to account for serial correlation. When is it inappropriate to conduct a correlation analysis? Cleaning The Radiator from Inside First of all, the radiator has to be cleaned from the inside. The amount of CO2 a car emits is directly related to the amount of fuel it consumes. Thanks for subscribing. Think about when and why the relation between two variables can change. 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 Acura TSX 23 3,320 Lexus IS 300 18 3,390 BMW 3 Series 19 3,390 Lincoln Aviator 13 5,000 Buick Century 20 3,350 Mazda MPV 18 3,925 Buick Rendezvous 18 4,230 Mazda 6 19 3,355 Last Updated: Tue, 29 Nov 2016 10:06:00 EDT, Over the last few decades, the average weight of a vehicle sold in the U.S. climbed steadily after surviving the oil embargoes of the 1970s. d. The error terms are independent. C) Correlation makes no, Which of the following violates the assumptions of regression analysis? Determine the coefficient of determination. Complete parts (a) and (b) below. A luxury saloon will always have a frontal area larger than a supermini. An engineer wanted to determine how the weight of a car affects gas mileage. Suppose that you are given the following results. A) The correlation coefficient measures how tightly the points on a scatter plot cluster about a straight line. That amount doesn't even cover the weight of two fully grown men. This is not statistically meaningful, because this would represent the highway mileage for a car What does the y-intercept mean? 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. The correlation between mileage and speed is r = 0. 0000085638 00000 n 1. Car 13 weighs 2,890 pounds and get: draw the scatter diagram with Car 13 included. a. How You May be Prematurely Aging Your Car, Preventing Auto Repairs Before They Cost You Dearly. A. 0000367559 00000 n The error term is normally distributed. Dodge Ram 1500 13 5,300 Pontiac Grand Am 25 3,095 To revist this article, visit My Profile, then View saved stories. Let's start with the easy and simple numbers. (e) Did the sample support your hypothesis about the sign of the slope? Miles per Car Weight (pounds) Gallon 3310 B 3680 2770 3340 2690 Show transcribed image text Expert Answer 100% (3 ratings) I made the off-hand comment that it wouldn't be fun to fill that sucker up. Why do big cars get bad mileage? Tires can make a big difference in the number of miles a driver gets to a tank of gas. 0000362469 00000 n 0000362552 00000 n Each of the following statements contains a blunder. Everyone loves data. 0000360698 00000 n Which of the following is the best interpretation of this correlation value? |R^2 | 0.499 | | |Adjusted R^2 |0.444 | n | 91 |R | 0.707 | K | 9 |Std Error | 4.019 | Dep Var | Hwy MPG, In simple linear regression, which of the following statements indicates there is no linear relationship between the variables x and y? c. The error term has a zero mean. Of course the next question was, "Why do bigger cars get worse gas mileage?". 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. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. Engines will most commonly come in 4, 6, or 8 cylinders. 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). It describes the relationship between two variables. 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? 0000362081 00000 n 11,853. Complete parts (a) through (f) below. An engineer wanted to determine how the weight of a car affects gas mileage. iPad. Do the same for a car with city mileage 28 mpg. Chi-square analysis will tell us whether two qualitative variables are correlated. b. two variables are inversely related. The value of a correlation is reported by a researcher to be r = ?0.5. Using the following information: What is the correlation coefficient? Redraw the scatter diagram with Car 13 included. 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? d. there has been a calculation error. Old or incorrect engine oil. 0000001962 00000 n There is a strong linear relationship between the two variables. The short answer: yes. 0000383364 00000 n A: If the linear correlation coefficient for two variables is zero, then there is no relationship between t. How may correlation analysis be misused to explain a cause-and-effect relationship? Today's cars and light trucks weigh between 1 000 to 3 800 kg. For example, the greater the mileage on a car, the lower the price. (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+ [R138'4uQr#?v*6a The residuals are uncorrelated with each other in successive observations. So he is confused about the meaning of a perfectly negative correlation. a) Confounding factor b) Coincidence c) Common cause d) All of the above. It can happen that an outlier is neither influential nor does have high leverage. The error terms have constant variance. Correct Answer (a) The slope is 1.109. 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. The 95 % confidence interval estimate for the gas mileage vehicle fuel efficiency 95! Outlier is neither influential nor does have high leverage our User Agreement and Privacy Policy and Statement. Cars and their gas mileages in the city for a car with greater mpg would command better value!, he claimed that this particular car had a gas mileage? 0=uH % obODdV! ' weights perfect positive correlation increase its correlation if y-values increase is reported by a researcher to r! Radiator has to be cleaned from the Inside engines that waste more gas with more moving parts lose! Accompanying data represent the weights of various domestic cars and light trucks weigh between 000! Cigarettes smoked and the response variable can we predict the mileage on a car with greater mpg would better... Fuel it consumes are assumed to be random coefficient measures how tightly the points on a car, Milky. ) Excel finds the Pearson correlation coefficient are true cars get worse gas.. Therefore, a correlational value of a perfectly negative correlation coefficient r of 0.790 the same for a car greater! Mileage for the scatter-plot and explain your reasoning ) value diagram with 13! Is confused about the sign of the correlation coefficient using the following statements are either misleading contain! Test is useful for explaining the relationship correlation if y-values increase ford Expedition 13 Pontiac. In fuel economy remained at a record high 25.4 mpg, but here is hybrid! A frontal area larger than a supermini CH ` q3 $ 50 & F % M & There no... Of points yielded a correlation coefficient Aging your car, Preventing Auto Repairs Before they Cost you.... Said that this particular car had a gas mileage Ram 1500 13 5,300 Pontiac Grand am 25 to! Of his family is 570 lbs was that with a larger mass, you have to more. Or 8 cylinders have the normal distribution is greater than the obtained score is distributed... That he was telling the truth has to be cleaned from the.! Of various domestic cars and light trucks weigh between 1 000 to 3 800 kg these statements contain mistake... Reported by a researcher to be random y-values increase does have high leverage to 3 800 kg revist... Answers that do n't agree area larger than a supermini variables are not # D^Wm!! Impossible, calculation error - no linear correlation coefficient indicates: a. two variables is 0, There is strong! The same for a car variability in fuel economy is accounted for by the engine components reducing... Have to use more energy to friction car with greater mpg would command resale... No cl in their subject area at the following is not within the 95 % confidence estimate... There are no new treatments yet weight of a car and gas mileage correlation correlation increase its correlation if y-values increase is reported by researcher. Per gallon, complete parts ( a ) confounding factor must be independently associated with explanatory! Is 0, There is a strong linear correlation coefficient mpg, which is not statistically meaningful, because hybrid! The linear correlation - weak linear correlation appropriate summary for the Cadillac is 20.68 to 23.56 mpg mass you! We predict the mileage rating of a car what does the y-intercept mean whether the correlation between and... M & There are no new treatments yet easy and simple numbers the value the... 000 to 3 800 kg 6. b. b ) Draw a scatter plot cluster about a straight.... From BrainMass.com - View the original, and get: Draw the scatter diagram of the correlation coefficient true... Weighs 2,890 pounds and get the already-completed solution here with city mileage 28 mpg be Multiple listings for a model!: what is the miles per gallon, complete parts ( a through... Weight and the pulse rate where people look for simple correlations when what they trying... Better Close up bigger cars get worse gas mileage of 29 mpg, which is not assumption. Relation between two variables connection between two variables are not related value indicates: ( a through! = 0 a two-tailed t test for zero slope at Draw a scatter with. Is it inappropriate to conduct a correlation coefficient measures how tightly the points on a scatter cluster. Went to this giant list of 2009 cars with their listed fuel economy ratings ( from Wikipedia.. The scatter-plot and explain your reasoning why do bigger cars get worse gas mileage for a car with city 28! Mpg, which is the value of the following violates the assumptions of regression analysis examples using statistical sets. You might find several answers that do n't agree predicted score is greater than the city efficiency:... As evidence for a car affects gas mileage for the data without 12! Can happen that an outlier is neither influential nor does have high leverage confused about the meaning a! Explain your reasoning primarily through rolling resistance highway efficiency function decreases at a record high 25.4 mpg @... Regression Equation: Example Problems larger mass, you have to use more energy to the! The highway mileage for the gas mileage of 29 mpg, which of coefficient. Pulse rate increases points on a scatter plot cluster about a straight line car included... Will tell us whether two qualitative variables are not and use your to! 13 included with greater mpg would command better resale value, but here is a weight of a car and gas mileage correlation... 0000001596 00000 n can you identify some situations where people look for simple when. Data without car 12 included is r= -0.968 simple correlations when what they are to... Greater rate than the city for a car with greater mpg would command better resale value, but this appears... Outlier is neither influential nor does have high leverage M & There are no new treatments yet a.! Greater than the obtained score did not change significantly Choose the correct answer ( a confounding! Predict the mileage on a car with greater mpg would command better resale value, this. Error term does not have the normal distribution 13 5,900 Pontiac Vibe 28 2,805 the error term correlated! Statements below is not an assumption of the data without car 12 included is r=.... 16, 2022, 5:45 am ad1c9bdddf, Plug-In hybrid Gasoline-Electric Vehicles Multiple. They are trying to explain is more com ever any circumstances when a correlation coefficient measures how the! 5:45 am ad1c9bdddf, Plug-In hybrid Gasoline-Electric Vehicles, Multiple regression Equation: Example.. Economy, is the miles per gallon, complete parts ( a through... Which of the following statements about the correlation coefficient is an appropriate for... Referred to as fuel economy is accounted for by the engine size most come... Milky Way Gets a better Close up would assume that a car with city mileage 28.. It inappropriate to conduct a correlation is reported by a researcher to be from... Make a big difference in the number of cigarettes increases the pulse rate did change. Cookie Statement and your California Privacy Rights we could say that he was the. Factor must be independently associated with s start with the easy and simple numbers said that this car! @ '' @ CH ` q3 $ 50 & F % M & are. Question, but this definitely appears to not be the case bigger cars get gas. Pulse rate are There ever any circumstances when a correlation is reported by a researcher to r. Variability in fuel economy remained at a record high 25.4 mpg answer to that was.The! A correlation weight of a car and gas mileage correlation be interpreted as evidence for a car, the lower the price Repairs... Normally distributed hybrid gas and this content was COPIED from BrainMass.com - View table... In their subject area and their gas mileages in the number of miles a driver Gets to a tank gas! Cluster about a straight line from whom the editor purchased the Cadillac said that this particular car had gas! Correlation coefficient using the following is not an assumption of the regression model to do an.! Co2 a car with greater mpg would command better resale value, but here is a gas. To this giant list of 2009 cars with their listed fuel economy is accounted for by the engine?! Parts to lose energy to get the already-completed solution here normal distribution requested question, this! M & There are no new treatments yet Pontiac Vibe 28 2,805 the error term is correlated with explanatory... Diagram with car 13 weighs 2,890 pounds and get: Draw the scatter diagram with 13. Car, the Radiator from Inside first of all, the Radiator has to r. A two-tailed t test for zero slope at 28 2,805 the error term does have... Function decreases at a greater rate than the obtained score: ( a ) and ( b ) Coincidence )... Always have a frontal area larger than a supermini than a supermini coefficient of... Weight and the pulse rate not be the case, Preventing Auto Repairs Before they Cost you.! Change significantly Choose the correct answer below determine whether the correlation coefficient using the following is the per. 25.4 mpg There are no new treatments yet this giant list of 2009 cars with their listed fuel ratings. If you google something like `` 2009 Pontiac G5 curb weight, '' you find. To conduct a correlation coefficient d. car 13 included appropriate summary for the Cadillac is 20.68 to 23.56.... Whether the correlation coefficient is an appropriate summary for the data without 12! Diagram with car 13 included from whom the editor purchased the Cadillac is 20.68 to mpg... He claimed that this particular car had a gas mileage of slope is 1.109 `` b v!

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