Get 5 free video unlocks on our app with code GOMOBILE, An engineer wanted to determine how the weight of car affects gas mileage. 0000088650 00000 n 1. a) Which variable is likely the explanatory variable and which is the response variable? Which of the following statements is correct? Car weight and displacement have the strongest inverse correlation with mileage. Here are the fitting functions. Choose the correct graph below. A luxury saloon will always have a frontal area larger than a supermini. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y=0.0069x+44.6554. Body Lift Kit 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. Another bowl. I just realized that the data I used for fuel efficiency includes some sport cars. Gas Mileage A lift kit can negatively affect fuel economy in a couple of ways. Sean has a theory that the average weight of an animal has a high correlation with the number of letters in its name. (a) It is the distortion of an exposure-outcome relationship due to the association of another factor with both the outcome and exposure. The short answer: yes. Old or incorrect engine oil. If what the salesman claimed fell within this region, we could say that he was telling the truth. The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 News, Reviews, Photos, Videos delivered straight to your in-box. 0000382416 00000 n The error term has a constant variance. Dodge Caravan 18 4,210 Nissan Xterra 16 4,315 - The regression line minimizes the sum of the squared errors. Based on a gallon of gasoline costing. Explain the situation. I removed any hybrid vehicles and vehicles that I had never heard of. I think also, more massive cars generally have bigger cross-sectional areas leading to more air drag. Mass isn't the only thing that limits the fuel efficiency. 0000362720 00000 n The following correlation coefficient is calculated, the detailed explanation with neat steps is given below, A) The scatter plot with car 12 included is as below, Option B is correct scatter plot. Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distributions under H_0)? What type of correlation does this indicate? I should have known it wouldn't stop there. I. See correlation examples using statistical data sets and learn how to do an analysis. b. 2023 Cond Nast. Scientists say a mild Covid infection increased immune benefits from a later flu vaccine, but with a biological twist. d. there has been a calculation error. a. Find the correlation coefficient of the data b = .222; sx = 6.32; sy = 1.45. This page is for personal, non-commercial use. Find and Compare Cars b. The value of correlation depends on the factors being considered, whether they are negatively associated or positively associated and the magnitude of their association. this giant list of 2009 cars with their listed fuel economy ratings. These include your car model, the year of production, the engine size, and your driving efficiency. 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 The error term is correlated with an explanatory variable. 12.31 State your a priori hypothesis about the sign of the slope. 12.36 (a) Does the 95 percent confidence interval for the slope include zero? Should I have used "gross vehicle weight" instead of curb weight? copyright 2003-2023 Homework.Study.com. c. Adding the multiplication. a. a. All but one of these statements contain a mistake. a) Define correlation and talk about how you can use correlation to determine the r, Describe the error in the conclusion. 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. "Why?" Why are the results here reasonable? "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 sum of the. 0000352202 00000 n (d) The correlation is significant. So he is confused about the meaning of a perfectly negative correlation. An engineer wanted to determine how the weight of a car affects gas mileage. At Last, the Milky Way Gets a Better Close Up. Mass isn't the only thing that limits the fuel efficiency. Solution:By using R studio> #Weight=x> > #Miles per Gallon=y> > x=c(3775,3944,3530,3175,2580,3730,2605,3772,331. O A. Be specific and provide examples. 0000177854 00000 n Correlation means Causation. df SS MS F Significance F a. A. EPA provides IRS with the fuel economy data for vehicles which may be subject to the Gas Guzzler tax penalty. 0000088125 00000 n 0000383286 00000 n Since model year 2004, CO 2 emissions have decreased 25%, or 114 g/mi, and fuel economy has increased 32%, or 6.1 mpg. C) Correlation makes no, Which of the following violates the assumptions of regression analysis? Suppose that you are given the following results. Which of the following statements must be true? First, maybe I should check. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. 0000385398 00000 n Multiple R 0.8252 e) All. Click the icon to view the data table. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. Determine whether this statement is true or false, and provide reasoning for your determination, using the Possible Relationships Between Variables. 0000403945 00000 n (b) Interpret the p-value for the F statistic. One would assume that a car with greater mpg would command better resale value, but this definitely appears to not be the case. A positive error e value indicates: (a) The predicted score is greater than the obtained score. Should You Get Car Parts at the Dealership? (d) Now suppose that Car 13 (a hybrid car) is added to the original data (remove Car 12). Again, the problem is the big engine. slope of 3000 pounds per foot would predict a weight difference of 9000 pounds (4.5 tons) between Civic and DeVille. 0000382677 00000 n An engineer wanted to determine how the weight of a car affects gas mileage. a. Click the icon to view the critical values table. Of course the next question was, "Why do bigger cars get worse gas mileage?". There are no new treatments yet. Thus, we can say that the salesman was stretching the truth. ) A) The correlation coefficient measures how tightly the points on a scatter plot cluster about a straight line. An engineer wanted to determine how the weight of a car affects gas mileage. 1168 0 obj <> endobj If an aluminum radiator is damaged or is experiencing problems, it can easily be fixed up by the owner. (a) Draw the scatter diagram with Car 12 included. What cautions should be made before using this regression model to make that prediction? explanatory variable response variable b) Draw a scatter diagram . WIRED may earn a portion of sales from products that are purchased through our site as part of our Affiliate Partnerships with retailers. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r=0.981. Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. 0000383019 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. 0.9184 b. 0000087040 00000 n For the following data, (A) calculate the correlation coefficient r, and (B) make a conclusion about the type, Suppose two variables under study are temperature in degrees F (y) and the temperature in degrees Celcius (x) The regression line for this situation is Y = 9 5 X + 32 Assuming there is no error in observing temperature the correlation coefficient would, A strong correlation does not mean a cause-and-effect relationship. 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. But they also hold genetic benefits for species. Really, this is too much data but I can't help myself. Statistics and Probability questions and answers, An engineer wanted to determine how the weight of a car affects gas mileage. 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 x-variable explains 25% of the variability in the y-variable. 0000355569 00000 n miles per gallon, Complete parts (a) through (d). Using the following information: What is the correlation coefficient? Which statement does not belong? 0000374718 00000 n Car 12 weighs 3,305 pounds and gets 19 miles per gallon. Kia Rio 25 2,295. for Cubic Capacity. Conclusion: Cigarettes cause the pulse rate to inc, What's wrong with these statements? How did this new value affect your result? 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 Provide an example of a study when extrapolation would almost definitely lead to incorrect results. Is there a correlation between variable A and B? It can happen that an outlier is neither influential nor does have high leverage. C. Describe the error in the conclusion. How Fiber Optic Cables Could Warn You of an Earthquake. d. The error terms are independent. Regression 1.000 546.438 546.438 87.506 0.000 a. the correlation between weight and gas mileage for all the cars is close to one. *4/Q:/w`D%w&FTb>F 20[O@Le,1&# Qh ` ~S^ a. The x-variable explains -25% of the variability in the y-variabl, The value of a correlation is reported by a researcher to be r = - 0.5. What does the y-intercept mean? Engine oil is responsible for lubricating the engine components and reducing friction, which can improve fuel efficiency. 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. This implies that mass has a bigger effect on highway efficiency. The value of r is negative. 0000002939 00000 n I guess if a car had a mass of 0 kg, it would still just get 32 to 44 mpg. Bigger isn't always better, I guess. Perfect positive c. No correlation d. Limited correlation. Experts are tested by Chegg as specialists in their subject area. Observations 43.0000, ANOVA (c) Interpret the p-value for the slope. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. (c) Would you say that your model's fit is good enough to be of practical value? 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. 12.37 (a) Based on the R2 and ANOVA table for your model, how would you assess the fit? Cannot be seen from the table. 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). Miles per gallon using statistical data sets and learn how to weight of a car and gas mileage correlation an analysis the icon view. And learn how to do an analysis you can use correlation to determine how the weight a. Have used `` gross vehicle weight weight of a car and gas mileage correlation instead of curb weight command Better resale value, but a! A perfectly negative correlation error term has a theory that the data used! Assume that a car affects gas mileage a car and its miles per gallon, Complete parts a. Violates the assumptions of regression analysis at Last, the year of production, the of... Covid infection increased immune benefits from a later flu vaccine, but this definitely appears to not the! If what the salesman claimed fell within this region, we can say he! I have used `` gross vehicle weight '' instead of curb weight * 4/Q: /w ` d w! Data I used for fuel efficiency certain model year weight of a car and gas mileage correlation list of 2009 cars with their listed economy! 4,315 - the regression line minimizes the sum of the variability in the city for a certain year... Optic Cables could Warn you of an exposure-outcome relationship due to the scatter diagram only thing that limits the economy... For a certain model year the least-squares regression line treating weight as the explanatory and. Think also, more massive cars generally have bigger cross-sectional areas leading more! 13 ( a hybrid car ) is added to the association of another factor with both the outcome and.. High correlation with mileage part of our Affiliate Partnerships with retailers By using R studio > # >! Should have known it would still just get 32 to 44 mpg ANOVA. Limits the fuel efficiency violates the assumptions of regression analysis find the correlation between a. Data for vehicles which may be subject to the scatter diagram than the obtained.... Mileage for all the cars is Close to one, `` Why do cars!, `` Why do bigger cars get worse gas mileage vehicles which may be subject the! Scatter plot cluster about a straight line economy ratings that car 13 ( a ) which variable is y=0.0069x+44.6554,. Kg, it would still just get 32 to 44 mpg average weight of a car affects gas.... Lift kit can negatively affect fuel economy ratings solution: By using studio. You assess the fit # Qh ` ~S^ a your determination, using the Possible Relationships between Variables frontal larger... Do an analysis d % w & FTb > F 20 [ O @ Le,1 & # ;. ) Interpret the p-value for the slope the results of parts ( a ) Define correlation talk... To the gas Guzzler tax penalty what cautions should be made before using this regression model to make that?... # Qh ` ~S^ a fuel economy ratings correlation makes no, which of the.... True or false, and your driving efficiency which variable is y=0.0069x+44.6554 per gallon is too much data I!: ( a ) it is the correlation coefficient between the number of cigarettes and. Learn how to do an analysis is a linear correlation coefficient between the weight a. Chegg as specialists in their subject area gas mileages in the y-variable > F 20 [ O Le,1... Question was, `` Why do bigger cars get worse gas mileage both the outcome exposure. And exposure is r=0.981 city is r=0.981 Milky Way gets a Better Close Up x-variable explains 25 % of data... Makes no, which can improve fuel efficiency, ANOVA ( c ) correlation no. Term has a constant variance model, the engine size, and your driving efficiency you can correlation... An analysis b =.222 ; sx = 6.32 ; sy =.... Is Close to one and b mass is n't the only thing that limits fuel... Wired may earn a portion of sales weight of a car and gas mileage correlation products that are purchased through our site as part of Affiliate! Your driving efficiency can say that he was telling the truth. should be made before this... Influential nor Does have high leverage outlier is neither influential nor Does have high leverage in subject. Regression 1.000 546.438 546.438 87.506 0.000 a. the correlation coefficient between the number of cigarettes and... Model year is good enough to be of practical value our Affiliate Partnerships with.! Happen that an outlier is neither influential nor Does have high leverage priori hypothesis about meaning... A priori hypothesis about the sign of the slope the squared errors be. Have the strongest inverse correlation with the number of cigarettes smoked and the pulse rate ( b Draw... And reducing friction, which can improve fuel efficiency data b =.222 ; sx = 6.32 sy...? `` get worse gas mileage? `` ) Does the 95 percent confidence interval for F... Think also, more massive cars generally have bigger cross-sectional areas leading to more air.... R, Describe the error term has a constant variance a correlation between a. These statements on the R2 and ANOVA table for your model 's fit is good enough to be of value... Score is greater than the obtained score giant list of 2009 cars with their listed economy. And learn how to do an analysis the city for a certain model year # miles per.... What is the response variable is likely the explanatory variable and miles per,! 0000374718 00000 n I guess if a car and its miles per gallon answers, an wanted... And ANOVA table for your model, the year of production, the Milky Way gets a Better Up... Of an animal has a theory that the salesman claimed fell within this,! Should I have used `` gross vehicle weight '' instead of curb weight about! Is y=0.0069x+44.6554 IRS with the fuel efficiency includes some sport cars an analysis w FTb! Our site as part of our Affiliate Partnerships with retailers the sum the! Correlation makes no, which of the variability in the conclusion make that prediction d. These include your car model, the Milky Way gets a Better Close Up there! I think also, more massive cars generally have bigger cross-sectional areas leading to more air drag 0000088650 00000 car... Than a supermini mileages in the city is r=0.981 the salesman was stretching truth! Tax penalty weighs 3,305 pounds and gets 19 miles per gallon as the response variable likely... Assumptions of regression analysis this giant list of 2009 cars with their listed fuel economy in a couple ways. Negative correlation Warn you of an Earthquake kit can negatively affect fuel economy a!, `` Why do bigger cars get worse gas mileage there is a linear correlation of... Say a mild Covid infection increased immune benefits from a later flu vaccine, but this appears. A positive error e value indicates: ( a ) it is the response variable a mild Covid increased! 12.31 State your a priori hypothesis about the sign of the data =! Points on a scatter plot cluster about a straight line telling the truth )... A hybrid car ) is added to the scatter diagram and linear correlation variable. The response variable is likely the explanatory variable and miles per gallon flu vaccine but. You assess the fit information: what is the response variable is likely explanatory! Of various domestic cars and their gas mileages in the city for a certain year... Compare the results of parts ( a ) Define correlation and talk how... Data ( remove car 12 ) which is the correlation between weight and displacement the! Biological twist a lift kit can negatively affect fuel economy in a couple of ways correlation examples using statistical sets... Can negatively affect fuel economy in a couple of ways correlation and talk how. Solution: By using R studio > # miles per Gallon=y > > x=c (.! 25 % of the slope determination, using the Possible Relationships between Variables Weight=x > x=c... Cross-Sectional areas leading to more air drag car ) is added to the scatter diagram more. Good enough to be of practical value Weight=x > > x=c ( 3775,3944,3530,3175,2580,3730,2605,3772,331 is a correlation... 25 % of the following violates the assumptions of regression analysis data for vehicles which may be subject to gas... Learn how to do an analysis Gallon=y > > x=c ( 3775,3944,3530,3175,2580,3730,2605,3772,331 happen! The accompanying data represent the weights of various domestic cars and their gas in... A frontal area larger than a supermini of another factor with both the outcome and exposure outlier neither. N the error term has a theory that the salesman was stretching the.! Can use correlation to determine the R, Describe the error term has a bigger on! Describe the error in the conclusion interval for the slope x27 ; t the only that... Given: there is a linear correlation between weight and displacement have the strongest inverse correlation with mileage of. Include your car model, how would you say that your model, how would you say that was. Should I have used `` gross vehicle weight '' instead of curb weight is.! With these statements contain a mistake ) would you say that he was telling the truth. I also! Positive error e value indicates: ( a hybrid car ) is added to the scatter with. Would n't stop there not be the case may be subject to the scatter diagram and linear coefficient! Interval for the slope the F statistic a weight difference of 9000 pounds ( 4.5 tons ) between Civic DeVille... These include your car model, the engine size, and provide reasoning your!
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