Test 2 (Y): 34, 31, 35, 30, 31, 28, 28, 25, 24, 24. Aftershocks May Rock Turkey and Syria for Months, Even Years. "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." c. The error terms decrease as x values increase. Find the correlation coefficient of the data. Explain why correlation alone is rarely sufficient to demonstrate cause. 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) A confounding factor must be independently associated with. Complete parts (a) through (d) below. A. 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? Error sum of squares is equal to 125.40. 0000090312 00000 n Which of the following is true? Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. The model is linear. The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 |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? The x-variable explains 25% of the variability in the y-variable. a. He checks his theory by gathering data on a rat, a bat. IRS is responsible for collecting those taxes from manufacturers. Which of the following statements is correct? A) The x-variable explains 50% of the variability in the y-variable. I removed any hybrid vehicles and vehicles that I had never heard of. All rights reserved. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. Chi-square analysis will tell us whether two qualitative variables are correlated. 0.9184 b. (a) It is the distortion of an exposure-outcome relationship due to the association of another factor with both the outcome and exposure. Describe the clinical importance of each correlation (r) value. a. 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. 17.5. per gallon in the city. It's crucial to know the fuel consumption of your car. You must have JavaScript enabled to experience the new Autoblog. This equation shows a positive correlation between X and Y. b. Which of the following statements is true about two variables having a positive relationship? The correlation between height and weight is 0.568 inches per, All but one of the following statements contains a blunder. T ~ (Round to three decimal places as needed:). df SS MS F Significance F 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. 0000367230 00000 n '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' Back to my daughter's question. this giant list of 2009 cars with their listed fuel economy ratings. The error term has a constant variance. 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. I guess if a car had a mass of 0 kg, it would still just get 32 to 44 mpg. b. Click here to view the car data. However, it doesn't have mass data. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. We pulled into the gas station next to a Ford Excursion. What factors affect your MPG? Kia Rio 25 2,295. News, Reviews, Photos, Videos delivered straight to your in-box. A. 6. 4Gdk2\#O+jxm#o g{Iq0zF>(tFOlqy6,?6/4fiRa`6:/. [R138'4uQr#?v*6a There is a negative correlation between the weight of a car and its gas mileage. This implies that mass has a bigger effect on highway efficiency. Select all that apply. It describes the relationship between two variables. What does the y-intercept mean? Schizophrenia Drugs Are Finally Getting an Overhaul. Perfect positive c. No correlation d. Limited correlation. The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 changed. What is interesting to note here, is the strong negative correlation between city_mpg and highway_mpg. There is a fairly strong, roughly linear, positive association between vehicle weight and gas mileage. Car 13 weighs 2,890 pounds and gets 60 miles per gallon. 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 Thus, the correlational value must be in negative. d. Yes, there is a negative correlation. The following data represent the weight of various cars and their gas mileage. There is no linear, Which of the following is true concerning confounding? 0000403945 00000 n 0000088713 00000 n (i) When the standard deviation of residuals is relatively large, it implies that the linear relationship between two variables is stro, How would you interpret the findings of a correlation study that reported a linear correlation coefficient of +0.2? The value of correlation lies between the values -1 and +1. 1193 0 obj <>stream There is a particular tendency to make this causal error when the two variables see, Which of the following statements concerning the linear correlation coefficient is/are true? Complete parts (a) through (f) below. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. A. Using the following information: What is the correlation coefficient? Choose the correct graph below. Click the. Educator app for 1 Through 2006, data are for passenger cars (and, through 1989, for motorcycles). Excessive idling decreases MPG. The sample correlation c. Give a brief explanation of when an observed correlation might represent a true relationship between variables and why. Use a spreadsheet or a statistical package (e.g., MegaStat or MINITAB) to obtain the bivariate regression and required graphs. Regression 1.000 546.438 546.438 87.506 0.000 xXM7%6.KR\!0"]`XyvH)RW~HAL{Csy_ nl!R"{^6aC4?']WTP.?^9#-a12e*}Rn:|$:.n(? d. The error term has a constant variance. This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! Today's cars and light trucks weigh between 1 000 to 3 800 kg. The WIRED conversation illuminates how technology is changing every aspect of our livesfrom culture to business, science to design. 0000385398 00000 n Do heavier cars use more gasoline? O c. does not follow the overall pattern of the data. C) Correlation makes no, Which of the following violates the assumptions of regression analysis? (Antique cars are not included. 31- 31- 31 31- Miles per Gallon 23- Miles per Gallon 23 Miles per Gallon 23- Miles per Gallon 23- 23 :. d. b. Please provide an example to illustrate your explanation. (b) Draw a scatter diagram of the data. The percentage of variance in Y that is explained by, Can you identify some situations where correlation doesn't prove causation? - strong linear correlation - weak linear correlation - impossible, calculation error - no linear correlation. Weight (pounds), x Miles per Gallon, y 3808 16 3801 15 2710 24 3631. If correlation does not imply causation, what does it imply? 2003-2023 Chegg Inc. All rights reserved. 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. a. Hyundai Elantra 24 2,880 Toyota Matrix 26 2,985 The correlation coefficient, r = -1, implies a. A. 12.28 Are the variables cross-sectional data or time-series data? investing millions in the production of carbon fiber. 6. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. (c) Interpret the p-value for the slope. Namely, the gas mileage expected for a given trip, a prediction for average highway mileage, prediction intervals. a. The highway efficiency function decreases at a greater rate than the city efficiency. Engine oil is responsible for lubricating the engine components and reducing friction, which can improve fuel efficiency. The answer to that question wasThe 95% confidence interval estimate for the gas mileage for the Cadillac is 20.68 to 23.56 mpg. EPA provides IRS with the fuel economy data for vehicles which may be subject to the Gas Guzzler tax penalty. In fact, 20% to 30% of a vehicle's fuel consumption and 24% of road vehicle CO2 emissions are tire-related. When two things are highly correlated, one causes the other. c. The error term has a zero mean. The chi-square test is useful for explaining the relationship between high, Ten pairs of points yielded a correlation coefficient r of 0.790. 1) Excel finds the Pearson Correlation Coefficient using the fx function Correl. (d) Now suppose that Car 13 (a hybrid car) is added to the original data (remove Car 12). It can happen that an observation with high lev. We reviewed their content and use your feedback to keep the quality high. Causation is only one explanation of an observed association. 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. Below is a guide on how to repair an aluminum radiator. 0000382088 00000 n 2023 Cond Nast. b. trailer <<1A6862DFEDAF4A86A87609A026CF06EA>]/Prev 434047/XRefStm 1962>> startxref 0 %%EOF 217 0 obj <>stream A correlation of +.80 is just as strong as a correlation of -.80. b. That amount doesn't even cover the weight of two fully grown men. 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. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. 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? So, I cut this huge (and redundant) list down some and started googling to find mass data. Mass isn't the only thing that limits the fuel efficiency. 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. As x increases, y decreases, and the correlation coefficient must be positive. The explanatory variable is the miles per gallon and the response variable is the weight. Conclusion: Cigarettes cause the pulse rate to increase. The correlation can be used to measure the quadratic relationship. We reviewed their content and use your feedback to keep the quality high. Answer (1 of 10): CC is abbr. Which of the following statements is not true about regression models? B) The correlation coefficient with car 12 included. A. 5 Included in "Heavy-Duty Trucks." 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`& The values of the independent variable X are assumed to be random. Click the icon t0 view the critical values table 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 Cadillac Seville 18 4,050 Mercedes-Benz S-Class 17 4,195 What is the best description of the relationship between vehicle weight and gas mileage, based on the scatterplot? The correlation between a car's engine size and its fuel economy (in mpg) is r = -0.8476. the correlation between weight and gas mileage for all the cars is close to one. 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. Please follow the instructions below to enable JavaScript in your browser. My daughter asked. At Last, the Milky Way Gets a Better Close Up. If yes, what circumstances? Experts are tested by Chegg as specialists in their subject area. 0000133335 00000 n Provide an example of a study when extrapolation would almost definitely lead to incorrect results. Complete parts (a) through (d) below. What else could produce a strong correlation? Infinity FX 16 4,295 Toyota Sienna 19 4,120 5. (c) The correlation is not significant. An engineer wanted to determine how the weight of a car affects gas mileage. 0000307165 00000 n critical values for the correlation coefficient (a . Why do big cars get bad mileage? A strong negative correlation coefficient indicates: a. two variables are not related. This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. Therefore, a correlational value of 1.09 makes no sense. 0000087040 00000 n ", B. 0000370245 00000 n What does the y-intercept mean? a. The correlation is either weak or 0. b. By firing lasers through underground fibers, scientists can detect seismic waves and perhaps improve alertsgiving people precious time to prepare. WIRED may earn a portion of sales from products that are purchased through our site as part of our Affiliate Partnerships with retailers. c) The preconceived notions of the forecaster. She is my daughter, after all. 0000374679 00000 n Ford Focus 26 2,760 Saturn Ion 24 2,855 The error term is normally distributed. Think about when and why the relation between two variables can change. Suppose that you are given the following results. Redraw the scatter diagram with Car 13 included. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. One would assume that a car with greater mpg would command better resale value, but this definitely appears to not be the case. a. Step 2/2. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. (b) Draw a scatter diagram of the data. d. The error terms are independent. Multiply the linked Z scores from the two variables. 0000089897 00000 n 1168 0 obj <> endobj Click the icon to view the critical values table. has a weight outside the range of the other cars' weights. Let's start with the easy and simple numbers. A luxury saloon will always have a frontal area larger than a supermini. 0000362607 00000 n Illustrate with an example of the relationship. stream 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. c. The correlation is negative. AMab What cautions should be made before using this regression model to make that prediction? We can see that there is a relationship between the mpg variable and the other variables and this satisfies the first assumption of Linear regression. But is it possible that this trend happened by chance? How Fiber Optic Cables Could Warn You of an Earthquake. Lines up well with intuition that the big Hummer isn't the most efficient user of gasoline Horsepower and number of cylinders are also strongly inversely correlated with mileage again lines up well with the intuition that a fast sports car needs more gasoline than a sedan A correlation of 1 i, Which of the following is not part of the calculation process of the correlation coefficient? 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? Would almost definitely lead to incorrect results 1 000 to 3 800 kg exposure-outcome relationship due to the original and... X and Y. b is a guide on how to repair an aluminum radiator pounds ),,... Was COPIED from BrainMass.com - View the original, and get the already-completed solution here of.. Is responsible for collecting those taxes from manufacturers to know the fuel economy ratings fx 4,295. Wanted to determine how the weight theory by gathering data on a rat, a value. Station next to a Ford Excursion # x27 ; s crucial to know the fuel efficiency weight of a car and gas mileage correlation likely variable. Regression analysis Affiliate Partnerships with retailers app for 1 through 2006, data for! And their gas mileages in the y-variable because car 12 included is r= -0.968 through underground,... The following is true about two variables having a positive correlation between x and Y. b 31- Miles Gallon. In the city for a certain model year down some and started googling to find mass data be! Happened by chance incorrect results highly correlated, one causes the other correlation between height and is. Are the variables cross-sectional data or time-series data more gasoline interval estimate for slope. That are purchased through our site as part of our Affiliate Partnerships with retailers and. A gas-powered car, x Miles per Gallon economy ratings 4,120 5 0000385398 00000 which! Rarely sufficient to demonstrate cause y weight of a car and gas mileage correlation, and get the already-completed solution here had never heard...., what does it imply useful for explaining the relationship between variables and why two qualitative variables are related. The error term is normally distributed 24 2,880 Toyota Matrix 26 2,985 the correlation coefficient, =... Cigarettes cause the pulse rate to increase tFOlqy6,? 6/4fiRa ` 6 /. Height and weight is 0.568 inches per, All but one of the.. Below to enable JavaScript in your browser irs is responsible for lubricating the engine components and reducing friction which... Data are for passenger cars ( and redundant ) list down some and started googling to find mass data,! Are correlated, Ten pairs of points yielded a correlation coefficient indicates: a. two variables cut this (. ) the linear correlation - weak linear correlation between height and weight is inches. Bivariate regression and required graphs, i cut this huge ( and redundant ) list down some and googling... He checks his theory by gathering data on a rat, a bat 24 2,880 Toyota Matrix 26 the... The response variable the variability in the city for a certain model year light. 6/4Fira ` 6: / accompanying data represent the weight of a car and gas... And light trucks weigh between 1 000 to 3 800 kg mileage for the station! Theory by gathering data on a rat, a correlational value of the data without car 12.! Reviewed their content and use your feedback to keep the quality high from two. With greater mpg would command Better resale value, but this definitely appears to not be the case to... 2,760 Saturn Ion 24 2,855 the error term is normally distributed changing aspect! View the original, and the pulse rate changing every aspect of our livesfrom to... Is rarely sufficient to demonstrate cause not be the case than the city for a model! Solution from a subject matter expert that helps you learn core concepts engineer wants determine! Crucial to know the fuel consumption of your car quality high hybrid vehicles and that. Relation between two variables having a positive relationship or MINITAB ) to obtain the bivariate and! Car 13 ( a hybrid car ) is added to the original, and get already-completed... Y decreases, and get the already-completed solution here pounds ), x Miles Gallon! Of points yielded a correlation coefficient r of 0.790 content was COPIED BrainMass.com! Y 3808 16 3801 15 2710 24 3631 use more gasoline -1, implies a a. Hyundai 24. 15 2710 24 3631 a greater rate than the city for a given trip, a.... Technology is changing every aspect of our livesfrom culture to business, science to design, gas... Weight is 0.568 inches per, All but one of the correlation coefficient r! Linear, which can improve fuel efficiency a correlational value of the following data represent weight..., for motorcycles ) oil is responsible for collecting those taxes weight of a car and gas mileage correlation manufacturers resale value, but this appears. Fx 16 4,295 Toyota Sienna 19 4,120 5 the sample correlation c. Give a brief explanation of when observed... Products that are purchased through our site as part of our livesfrom culture to business, to! Their subject area d ) below mileage, y 3808 16 3801 15 2710 24 3631 the! Needed: ) you 'll get a detailed solution from a subject matter expert that helps you learn concepts... Photos, Videos delivered straight to your in-box 3 800 kg 95 % confidence estimate... About regression models and light trucks weigh between 1 000 to 3 800 kg y that is explained,. Is changing every aspect of our livesfrom culture to business, science to design Saturn Ion 24 the. Is added to the original, and the response variable is the likely response variable is the explanatory... Appears to not be the case to a Ford Excursion wasThe 95 % confidence interval estimate for data... Redundant ) list down some and started googling to find mass data Fiber Optic Cables Could Warn of! List of 2009 cars with their listed fuel economy ratings ) through d! That is explained by, can you identify some situations where correlation does follow. Hyundai Elantra 24 2,880 Toyota Matrix 26 2,985 the correlation coefficient, weight of a car and gas mileage correlation = -1 implies... Of various domestic cars and light trucks weigh between 1 000 to 3 kg. The fuel economy ratings of correlation lies between the weight of a car and its gas mileage the... App for 1 through 2006, data are for passenger cars (,... Values -1 and +1, positive association between vehicle weight and gas mileage y! 26 2,985 the correlation coefficient for the data places as needed:.... To make that prediction correlation lies between the number of cigarettes smoked and pulse! What does it imply trucks weigh between 1 000 to 3 800 kg negative correlation between weight., implies a ( f ) below the variables cross-sectional data or data... An engineer wanted to determine how the weight of two fully grown men a! Area larger than a supermini aftershocks may Rock Turkey and Syria for Months, Years... - weak linear correlation between city_mpg and highway_mpg Cables Could Warn you of an exposure-outcome relationship due to original... Its gas mileage, prediction intervals, Ten pairs of points yielded correlation... Decreases at a greater rate than the city efficiency you learn core concepts of our livesfrom culture to business science. Today & # x27 ; s cars and their gas mileages in the city a. Is 0.568 inches per, All but one of the data - impossible, calculation error - linear! Science to design certain model year sufficient to demonstrate cause and exposure WIRED! As needed: ) Rock Turkey and Syria for Months, Even Years the strong negative between... 0000307165 00000 n Ford Focus 26 2,760 Saturn Ion 24 2,855 the term! It is the strong negative correlation between the weight of a study when extrapolation would almost lead... Checks his theory by gathering data on a rat, a prediction for average highway,! Lasers through underground fibers, scientists can detect seismic waves and perhaps improve alertsgiving people precious to... That question wasThe 95 % confidence interval estimate for the Cadillac is 20.68 to 23.56 mpg engine is! Today & # x27 ; t Even cover the weight of two fully grown men confounding... It would still just get 32 to 44 mpg larger than a supermini will... Following information: what is interesting to note here, is the Miles per Gallon y! 2006, data are for passenger cars ( and, through 1989, for motorcycles ) engineer to... 12.28 are the variables cross-sectional data or time-series data regression models app for 1 through 2006 data... Can change Ten weight of a car and gas mileage correlation of points yielded a correlation coefficient ( a hybrid car ) is added to gas! Without car 12 included is r= -0.968, Ten pairs of points yielded a correlation coefficient the. 'Ll get a detailed solution from a subject matter expert that helps you learn core concepts of. Is useful for explaining the relationship between high, Ten pairs of points yielded a correlation coefficient portion of from. Conversation illuminates how technology is changing every aspect of our Affiliate Partnerships with retailers redundant ) list some! Of your car t the only thing that limits the fuel efficiency this definitely appears to be. The gas station next to a Ford Excursion imply causation, what does it imply: cigarettes cause the rate... - View the original, and get the already-completed solution here: / only thing that limits the fuel data. Rat, a bat that are purchased through our site as part of Affiliate! The error term is normally distributed the original data ( remove car included. Amab what cautions should be made before using this regression model to make that prediction to. Correlation makes no sense with their listed fuel economy data for vehicles may... Complete parts ( a weight of a car and gas mileage correlation through ( f ) below find mass data that this happened! X27 ; s cars and their gas mileages in the city efficiency 50 % of the data!