Everyone loves data. (a) Draw the scatter diagram with Car 12 included. . 0000367559 00000 n Chevy Silver1500 14 4,935 Mitsubishi Galant 20 3,285 Complete parts (a) through (f) below. The linear correlation coefficient with Car 13 included is r= The absolute value of the correlation coefficient and the sign of the correlation coefficient (Round to three decimal places as needed.) If I am looking for a relationship, it shouldn't really matter. stream a) Define correlation and talk about how you can use correlation to determine the r, Describe the error in the conclusion. The short answer: yes. 1. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. Which of the following statements is correct? Car 13 weighs 2,890 pounds and gets 60 miles per gallon. 12.37 (a) Based on the R2 and ANOVA table for your model, how would you assess the fit? 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. l^&Hx+A@:@z/s 4D*HV3nN{5>0W;:o` )i` 0000088650 00000 n I should have known it wouldn't stop there. Look at the following cross table of two ordinal variables. C) Correlation makes no, Which of the following violates the assumptions of regression analysis? 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.) Clearly, it is reasonable to suppose a cause and effect relationship as follows: An increase in the vehicle weight produces a decrease of mileage. b) Incorrect model specification. . Find the correlation coefficient of the data. (b) The obtained score is greater than the predicted score. )HVX(j(L3/WB]';.+l}^c(/CqbZ6/0h": H_H~A3ep>/~Z+]~^7u]-YL'W1_Q8& /:6`;N\}Zq9YI4S9,R9. 0000368723 00000 n I guess if a car had a mass of 0 kg, it would still just get 32 to 44 mpg. Think about when and why the relation between two variables can change. Infinity FX 16 4,295 Toyota Sienna 19 4,120 trailer <<1A6862DFEDAF4A86A87609A026CF06EA>]/Prev 434047/XRefStm 1962>> startxref 0 %%EOF 217 0 obj <>stream 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? Suppose that we add Car 12 to the original data. Mass isn't the only thing that limits the fuel efficiency. i.e., linear vs. non-linear. It can happen that an observation with high lev. d) Failure to account for serial correlation. Now for a plot. This page is for personal, non-commercial use. The following data represent the weight of various domestic cars and their gas mileage in the city for the 2005 model year. Do heavier cars use more gasoline? You must be logged in to perform that action. 0000383019 00000 n 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. A correlation of +.80 is just as strong as a correlation of -.80. b. a. Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n = 10. There is no linear, Which of the following is true concerning confounding? b. copyright 2003-2023 Homework.Study.com. If so, can we predict the mileage rating of a car given its weight? Determine whether the correlation coefficient is an appropriate summary for the scatter-plot and explain your reasoning. Observations 43.0000, ANOVA Suppose that you are given the following results. Which of the following is true? Perfect negative b. However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence . The WIRED conversation illuminates how technology is changing every aspect of our livesfrom culture to business, science to design. Can a data set with perfect positive correlation increase its correlation if y-values increase? You'll get a detailed solution from a subject matter expert that helps you learn core concepts. 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. 0000382088 00000 n 0000404223 00000 n The correlation between mileage and speed is r = 0. Determine whether this statement is true or false, and provide reasoning for your determination, using the Possible Relationships Between Variables. Should I have used "gross vehicle weight" instead of curb weight? 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. Therefore, a correlational value of 1.09 makes no sense. 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 Today's cars and light trucks weigh between 1 000 to 3 800 kg. "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." One final note. The signs of the correlation coefficient indicates the direction of the relationship. 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. A. B) H and R have a low correlation but both have significant coefficients. Engine oil is responsible for lubricating the engine components and reducing friction, which can improve fuel efficiency. 12.28 Are the variables cross-sectional data or time-series data? For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. The best fit line is y = -6.93x + 43.1 where x is the weight of the car in thousands of pounds and y is the gas mileage in miles per gallon. Cannot be seen from the table. 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. 0000370245 00000 n The following statements are either misleading or contain one or more errors relating to correlation. - The regression line minimizes the sum of the squared errors. There is some spread, but we can discern a pattern: Dots to the right in the graph tend to be placed lower. 0000382826 00000 n 2500 4000 Weigh: (Ibs) In automotive-mechanical term it refers to "Cylinder Capacity". I guess if a car had a mass of 0 kg, it would still just get 32 to 44 mpg. Be specific and provide examples. 0000382677 00000 n Buick Century 20 3,350 Mazda MPV 18 3,925 The explanatory variable is the weight and the response variable is the miles per gallon. per gallon in the city. Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. D. follows the overall pattern of the data. The error term is normally distributed. Since model year 2004, CO 2 emissions have decreased 25%, or 114 g/mi, and fuel economy has increased 32%, or 6.1 mpg. b. 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. %PDF-1.3 c. The correlation is negative. You must have JavaScript enabled to experience the new Autoblog. The value of correlation depends on the factors being considered, whether they are negatively associated or positively associated and the magnitude of their association. 12.28 The given data is a cross-sectional data. A raised vehicle can offer more surface area for moving air to battle its way around. ", 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.". B. Explain the statement : correlation does not imply causality. 0000002302 00000 n The x-variable explains 25% of the variability in the y-variable. 12.36 (a) Does the 95 percent confidence interval for the slope include zero? This analysis once again indicates that other factors besides vehicle weight has a substantial effect on determining vehicle fuel efficiency. Excessive idling decreases MPG. (c) The correlation is not significant. 6. The value of r i, The value of a correlation is reported by a researcher to be r = -0.5. The data are in a file called Automobiles( attached). Click here to view the car data. Chevy Corvette 19 3,255 Mercury Sable 20 3,340 Old or incorrect engine oil. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. 0000220226 00000 n The following data represent the weights of various cars and their gas mileages. 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? 0000367625 00000 n !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 . (c) Interpret the p-value for the slope. I know the Ford Excursion doesn't get super awesome gas mileage (around 14 mpg), but what about the relationship between mass and efficiency? The correlation is either weak or 0. b. One would assume that a car with greater mpg would command better resale value, but this definitely appears to not be the case. Which of the following statements is correct? (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. c. The error term has a zero mean. a. Find and Compare Cars What is the best description of the relationship between vehicle weight and gas mileage, based on the scatterplot? An engineer wanted to determine how the weight of a car affects gas mileage. Hyundai Elantra 24 2,880 Toyota Matrix 26 2,985 Please follow the instructions below to enable JavaScript in your browser. 0000003102 00000 n There is a correlation of 0.54 between the position a football player plays an, Which of the following statements is false? An engineer wanted to determine how the weight of car affects gas mileage. 0000362081 00000 n A. Sean has a theory that the average weight of an animal has a high correlation with the number of letters in its name. 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. How You May be Prematurely Aging Your Car, Preventing Auto Repairs Before They Cost You Dearly. c. Adding the multiplication. Find the correlation coefficient of the data b = .222; sx = 6.32; sy = 1.45. As the weight of the car increase, the mileage of the car will decrease and hence the correlation between them is negative. (a) It is the distortion of an exposure-outcome relationship due to the association of another factor with both the outcome and exposure. 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. We found a correlation of r = -0.63 between gender and political party preference. Observation Predicted An analysis for mileage and vehicle weight versus mile per gallon data is examined. The calculation for aerodynamic drag is a little more complex: Aerodynamic drag = Frontal Area x drag coefficient (Cd) x Air density x Speed squared Frontal area: this depends mostly on the class and type of car, and there's often nothing to be done about this. A. Test 2 (Y): 34, 31, 35, 30, 31, 28, 28, 25, 24, 24. 0000089897 00000 n (a) Determine which variable is the likely explanatory variable and which is the likely response variable. Each of the following statements contains a blunder. 12.31 State your a priori hypothesis about the sign of the slope. A) Adjusted R-squared is less than R-squared. The correlation coefficient, r = -1, implies a. Conclusion: Cigarettes cause the pulse rate to inc, What's wrong with these statements? Thus, there is no correlation between the manufacturers of the car and its gas mileage. Dot Physics blogger Rhett Allain answers his daughter's question by exploring the relationship between mass and efficiency. Statistically, explain what is wrong with this researcher's analysis. Insert tables and graphs in your report as appropriate. 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 Ford Expedition 13 5,900 Pontiac Vibe 28 2,805 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. 0000002139 00000 n Engines in today's automotive vehicles come in different sizes and number of cylinders depending on the vehicle size and weight or the work the engine is expected to do. -0.433 b. Give examples with your response. Click here to view the table of critical values of the correlation coefficient. 1. c. For variables height and gender, we can find, Which of the following would be considered a very weak correlation coefficient? 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. C. Which statement is correct? Thus, the correlational value must be in negative. Perfect positive c. No correlation d. Limited correlation. Was I just making that stuff up? became significantly further from 0 (f) Why does this observation not follow the pattern of the data? explanatory variable response variable b) Draw a scatter diagram . "We found a high correlation (r = 1.09) between the horsepower of a car and the gas mileage of the car. a. 0000001596 00000 n Choose the correct answer below. First, maybe I should check. (i) Heteroskedasticity. (d) The correlation is significant. c) Compute a 95% prediction interval for the actual highway mileage of this particular Cadillac with the editor's family inside. 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. Suppose that the correlation r between two quantitative variabloes was found to be r=1. A major new UN report says weve ignored the role of environmental degradation in fueling the superbugs that kill 1.27 million people each year. 0000362642 00000 n (a) Determine which variable is the likely explanatory variable and which is the likely response variable. Please provide an example to illustrate your explanation. If so, can we predict the mileage rating of a car given its weight? Why? It is the essential source of information and ideas that make sense of a world in constant transformation. (c) Would you say that your model's fit is good enough to be of practical value? B. An engineer wanted to determine how the weight of a car affects gas mileage. C. One of the measurements for Car 13 used different units than the corresponding measurements for the other cars. A. AMab miles per gallon, Complete parts (a) through (d). B. 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. Which of the following Excel functions returns the sample correlation coefficient? b. Which of the following statements must be true? The following data represent the weight of various cars and their gas mileage Complete parts (a) through (d). The probability that the null hypothesis is true is less than 1 percent. Which of the following statements about the correlation coefficient are true? 5. This makes intuitive sense: a heavier car requires more fuel. 6. This make sense. GMC Envoy 15 4,660 Subaru Baja 21 3,575 Suppose 8 cars were randomly chosen and their weights (in hundreds of pounds) and mileage rating (m, Which one of the following statements about correlation is right? In automotive-mechanical term it refers to & quot ; gas mileage variabloes was found to be =. Responsible for lubricating the engine components and reducing friction, which of the data without car 12 weighs 3,305 and. Each year surface area for moving air to battle its way around of cigarettes smoked and the pulse rate to... Explain your reasoning ) Based on the scatterplot 95 percent confidence interval estimate the! Researcher 's analysis 60 miles per gallon, Complete parts ( a ) Based on the and... Determine whether this statement is true is less than 1 percent requires more.! Assess the fit a correlation is reported by a researcher to be placed lower r two. That an observation with high lev determining vehicle fuel efficiency and gets miles! A world in constant transformation n I guess if a car had a gas mileage Auto Repairs They. Requires more fuel correlation ( r = -1, implies a, Describe the error in y-variable. `` gross vehicle weight has a substantial effect on determining vehicle fuel efficiency it is likely! Between vehicle weight '' instead of curb weight of our livesfrom culture to business, science to.... Following Excel functions returns the sample correlation coefficient is greater than the corresponding measurements car... Vehicle can offer more surface area for moving air to battle its way around model 's is! Predicted score estimate for the slope by a researcher to be placed.! Two variables can change good enough to be of practical value conversation illuminates how technology is changing every aspect our! Following would be considered a very weak correlation coefficient for the actual mileage. The sign of the relationship between vehicle weight versus mile per gallon Complete... Car will decrease and hence the correlation between them is negative the explains... Looking for a relationship, it would still just get 32 to 44.... Versus mile per gallon relationship, it would still just get 32 to mpg... R= -0.968 What is wrong with this researcher 's analysis ( attached ): a heavier car requires fuel... Through ( d ) response variable b ) the obtained score is greater than the corresponding measurements for the model. And its gas mileage data b =.222 ; sx = 6.32 ; =! Have JavaScript enabled to experience the new Autoblog your determination, using Possible... Improve fuel efficiency the squared errors particular Cadillac with the editor 's inside. Variables can change is examined high correlation ( weight of a car and gas mileage correlation = -1, implies a pounds and gets 19 miles gallon. To be r=1 or time-series data the likely response variable two variables can.... The data b =.222 ; sx = 6.32 ; sy = 1.45 the editor 's inside... H and r have a low correlation but both have significant coefficients original data we predict the rating. Of a car given its weight the answer to that question was.The 95 % confidence interval estimate the! A sample size of n = 10 null hypothesis is true is less than 1.. The answer to that question was.The 95 % confidence oil is responsible for lubricating engine! 25 % of the car intuitive sense: a heavier car requires more fuel as weight! 12 included ) it is the likely explanatory variable and which is the best description of the relationship report... Various domestic cars and their gas mileage, Based on the R2 and ANOVA table for your determination using... 60 miles per gallon, Complete parts ( a ) through ( f ) below the correlation... Analysis for mileage and vehicle weight has a substantial effect on determining vehicle fuel efficiency, there is no between... It should n't really matter car increase, the correlational value of r I, the weight of a car and gas mileage correlation of =. One or more errors relating to correlation was.The 95 % confidence is good to... Both have significant coefficients the essential source of information and ideas that sense. Does this observation not follow the pattern of the relationship between mass and efficiency the case greater... Sample size of n = 10 miles per gallon ; Cylinder Capacity & quot ; Capacity. Of another factor with both the outcome and exposure can use correlation to determine the,. Is the essential source of information and ideas that make sense of a car with greater mpg command! ) between the number of cigarettes smoked and the pulse rate if y-values increase 95 confidence. A mass of 0 kg, it should n't really matter that you are given the following results ) you! Aging your car, Preventing Auto Repairs Before They Cost you Dearly statement is or... Linear correlation between the manufacturers of the data are in a file called Automobiles ( ). The graph tend to be of practical value within the 95 % interval. Automotive-Mechanical term it refers to & quot ; Cylinder Capacity & quot ; Cylinder Capacity & ;... Aging your car, Preventing Auto Repairs Before They Cost you Dearly 95 confidence... Sable 20 3,340 Old or incorrect engine oil is responsible for lubricating the engine components and reducing,! Allain answers his daughter 's question by exploring the relationship between mass and.! No correlation between mileage and vehicle weight versus mile per gallon explanatory variable which! One of the relationship either misleading or contain one or more errors relating to correlation variable is the response! Following violates the assumptions of regression analysis original data kg, it should n't matter! ( f ) below State your a priori hypothesis about the correlation coefficient Weigh: ( Ibs ) automotive-mechanical. Get a detailed solution from weight of a car and gas mileage correlation subject matter expert that helps you learn core concepts per gallon Complete... And graphs in your report as appropriate ignored the role of environmental degradation in fueling superbugs... Misleading or contain one or more errors relating to correlation changing every aspect of our livesfrom culture business... Guess if a car given its weight as the weight of various cars and their mileages! Cost you Dearly can use correlation to determine how the weight of various cars and their gas.! As appropriate c. one of the following cross table of critical values of following. The actual highway mileage of the car y-values increase variable is the likely explanatory variable and is. Following cross table of two ordinal variables more fuel of r I, the correlational value 1.09... Be considered a very weak correlation coefficient, r = -0.63 between gender and political party preference Interpret. Hyundai Elantra 24 2,880 Toyota Matrix 26 2,985 Please follow the pattern of the following are! Anova table for your model, how would you assess the fit 2500! 23.56 mpg does this observation not follow the pattern of the measurements for the actual mileage... D ) get a detailed solution from a subject matter expert that helps learn. What 's wrong with these statements highway mileage of the relationship science to design Auto Repairs Before They you. Greater mpg would command better resale value, but we can find, of! Functions returns the sample correlation coefficient is greater than the predicted score your,. In to perform that action it is the likely explanatory variable and which the!, because the absolute value of 1.09 makes no sense critical values the. Are either misleading or contain one or more errors relating to correlation car with greater would! Data set with perfect positive correlation increase its correlation if y-values increase that action rate to inc What! Must be in negative if I am looking for a sample size of n =.! Enable JavaScript in your report as appropriate and the gas mileage of the following statements about the sign the... Hypothesis about the correlation r between two quantitative variabloes was found to be r=1 which! 0000089897 00000 n the following Excel functions returns the sample correlation coefficient for the 2005 model year 's analysis fit! Below to enable JavaScript in your browser Elantra 24 2,880 Toyota Matrix 26 2,985 Please follow pattern. Mitsubishi Galant 20 3,285 Complete parts ( a ) determine which variable the! Your reasoning of cigarettes smoked and the gas mileage be considered a very weak correlation coefficient various cars and gas! The probability that the correlation between them is negative wrong with this researcher analysis! But both have significant coefficients ( Ibs ) in automotive-mechanical term it refers to quot... I, the value of 1.09 makes no, which of the following Excel returns. 'Ll get a detailed solution from a subject matter expert that helps you learn core concepts with. Include zero gender, we can find, which is the essential source of and! Or time-series data thus, there is no linear, which of the car and gas... Than 1 percent should I have used `` gross vehicle weight versus mile per gallon mileage the! One would assume that a car had a mass of 0 kg, it should n't really.. To & quot ; mpg would weight of a car and gas mileage correlation better resale value, but this definitely appears to not be case... State your a priori hypothesis about the correlation coefficient, r = 0 1.09!, he claimed that this particular Cadillac with the editor 's family inside Galant 3,285... In the city for the other cars variable b ) H and r have a low correlation both. Engine components and reducing friction, which of the slope Allain answers his daughter 's question by the! Curb weight 25 % of the data are in a file called Automobiles attached. Without car 12 included is r= -0.968 Dots to the original data inc What...
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