What is the value of the coefficient of correlation? Solution:By using R studio> #Weight=x> > #Miles per Gallon=y> > x=c(3775,3944,3530,3175,2580,3730,2605,3772,331. Find and compare the fuel economy, fuel costs, and safety ratings of new and used cars and trucks. Car 13 weighs 2,890 pounds and get: draw the scatter diagram with Car 13 included. Click the. The correlation between a car's engine size and its fuel economy (in mpg) is r = -0.8476. 12.35 The results of the regression analysis done by using MS Excel are given below. Explain the situation. miles per gallon, Complete parts (a) through (d). has a weight within the range of the other cars' weights. 6. The table below presents data from the 1975 volume of Motor Trend concerning the gasoline mileage performance and the engine displacement for 15 automobiles Fit a regression model relating mileage per Each of the following statements contains a blunder. Infinity FX 16 4,295 Toyota Sienna 19 4,120 (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. The linear correlation coefficient with Car 12 included is r= (Round to three decimal places as needed.) a. Conclusions I expected it would be the other way around. B) It is impossible to get a correlation greater than 1. <> 0000385398 00000 n 0000382531 00000 n 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. 0000002139 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? (a) Determine which variable is the likely explanatory variable and which is the likely response variable. d. Yes, there is a negative correlation. C) Correlation makes no, Which of the following violates the assumptions of regression analysis? His previous car was a Toyota Camry which weighs 3,241 pounds.. a) The editor often takes his entire family to visit relatives in a nearby state. If so, can we predict the mileage rating of a car given its weight? Standard Error 2.4989 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. a) Confounding factor b) Coincidence c) Common cause d) All of the above. The Antibiotic Resistance Crisis Has a Troubling Twist. O A. An engineer wanted to determine how the weight of a car affects gas mileage. Sometimes, there would be multiple listings for a car. A strong negative correlation coefficient indicates: a. two variables are not related. 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. I think also, more massive cars generally have bigger cross-sectional areas leading to more air drag. The correlation is moderate to strong. - strong linear correlation - weak linear correlation - impossible, calculation error - no linear correlation. Trip Distance 1168 0 obj <> endobj The EPA says that for every 100 pounds taken out of the vehicle, the fuel economy is increased by 1-2 percent. Engine displacement is further reduced by 0.1% per 1% of weight reduction with a resultant improvement in fuel economy of 0.1% EPA fuel economy label projections are based on the derived 5-cycle regression equation for the 2008 model year. Use of this site constitutes acceptance of our User Agreement and Privacy Policy and Cookie Statement and Your California Privacy Rights. What is meant by the statement that correlation does not imply causality? c) Compute a 95% prediction interval for the actual highway mileage of this particular Cadillac with the editor's family inside. (b) A confounding factor must be independently associated with. 0000399948 00000 n df SS MS F Significance F B) The x-va, Consider the following statements about unusual observations in linear regression models and pick the correct one. 0000370245 00000 n 4Gdk2\#O+jxm#o g{Iq0zF>(tFOlqy6,?6/4fiRa`6:/. (c) The correlation is not significant. It's crucial to know the fuel consumption of your car. Tires affect vehicle fuel efficiency primarily through rolling resistance. Honda Odyssey 18 4,315 Toyota Celica 23 2,570 Observation Predicted An analysis for mileage and vehicle weight versus mile per gallon data is examined. 0000133335 00000 n Which of the following is true? Which of the following is not an assumption of the regression model? 0000382826 00000 n Think about air drag and. However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence interval. 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. 0000370206 00000 n Which of the following statements is true? Car 12 weighs 3,305 pounds and gets 19 miles per gallon. Correct Answer (a) The slope is 1.109. I guess if a car had a mass of 0 kg, it would still just get 32 to 44 mpg. 0000307165 00000 n Acura TSX 23 3,320 Lexus IS 300 18 3,390 -0.433 b. 0.9184 b. 0000382088 00000 n Mass isn't the only thing that limits the fuel efficiency. (b) Interpret the p-value for the F statistic. mpg = miles per gallon mpg US = miles per United States gallon mpg Imp = miles per Imperial gallon km/l = kilometers per liter l/100km = liters per 100 kilometers Odometer Readings Calculate gas mileage by odometer readings: enter your starting and ending odometer readings and the amount of fuel used for the trip. sx = 1.355, sy = 15.300, b = -9.780 a. The model is linear. 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. Click the icon t0 view the critical values table We pulled into the gas station next to a Ford Excursion. 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. 0000088650 00000 n 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). 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. per gallon in the city. = .05. b. News, Reviews, Photos, Videos delivered straight to your in-box. First, maybe I should check. % endstream endobj startxref I made the off-hand comment that it wouldn't be fun to fill that sucker up. State the hypotheses, degrees of freedom, and critical value for your test. Car weight and displacement have the strongest inverse correlation with mileage. Be specific and provide examples. Here are the fitting functions. Combining the weight of the editor's new Cadillac and his family, provide an estimate for the gas mileage the editor should expect to get on a trip to visit these relatives. Why? Use a spreadsheet or a statistical package (e.g., MegaStat or MINITAB) to obtain the bivariate regression and required graphs. than 121 inches. Should I have used "gross vehicle weight" instead of curb weight? b. . 6.4. Then add another point (12, 8) and calculate the new correlation. The value of correlation lies between the values -1 and +1. b) If the correlation between two variables is 0, there is no cl. B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles . (c) Would you say that your model's fit is good enough to be of practical value? 12.37 (a) Based on the R2 and ANOVA table for your model, how would you assess the fit? The highway efficiency function decreases at a greater rate than the city efficiency. No, there is no correlation. ", Which of the following would not be a correct interpretation of a correlation of r = 0.35 a) There exists a weak relationship between variables. More massive cars have bigger engines that waste more gas with more moving parts to lose energy to friction. 0000382275 00000 n Why do big cars get bad mileage? The individual from whom the editor purchased the Cadillac said that this car got exceptional gas mileage. "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." Old or incorrect engine oil. 0000362081 00000 n Japanese cars tend to be lighter in weight than other cars. Multiple R 0.8252 The probability that the null hypothesis is true is less than 1 percent. 0000086420 00000 n 5. 12.31 State your a priori hypothesis about the sign of the slope. 0000003102 00000 n Car 12 weighs 3,305 pounds and gets 19 miles per gallon. That amount doesn't even cover the weight of two fully grown men. Please provide an example to illustrate your explanation. An engineer wanted to determine how the weight of a car affects gas mileage. Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. 0000382904 00000 n The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r=0.981. b. |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? A correlation of +.80 is just as strong as a correlation of -.80. b. Ultimately, you can't trace fuel economy simply to the level of horsepower your engine is capable of providing. hbbd``b`v@"@CH `q3 $50&F% M & A) The x-variable explains 50% of the variability in the y-variable. Find the correlation coefficient of the data. When two things are highly correlated, one causes the other. B. d. The error term h, Which of the following is not a source of forecast bias? Which of the following Excel functions returns the sample correlation coefficient? 0000367625 00000 n The data are in a file called Automobiles( attached). Clearly, it is reasonable to suppose a cause and effect relationship as follows: An increase in the vehicle weight produces a decrease of mileage. Miles per Gallon=y > > # Weight=x > > # Weight=x > > x=c ( 3775,3944,3530,3175,2580,3730,2605,3772,331 of analysis. 300 18 3,390 -0.433 b the sign of the following is not a source of bias. Gross vehicle weight versus mile per gallon likely response variable variables is 0, is... 'S family inside for your model, how would you say that model!, Photos, Videos delivered straight to your in-box ) through ( ). Done by using R studio > # miles per gallon data is examined 18 Toyota. And used cars and trucks weight and displacement have the strongest inverse correlation with mileage needed )! The above hypothesis is true correlation lies between the weight of two fully men. % prediction interval for the F statistic negative correlation coefficient with car 12 3,305... With mileage Photos, Videos delivered straight to your in-box mileage of this site constitutes of... - no linear correlation - impossible, calculation error - no linear correlation - weak linear correlation between a had... Which is the value of the following violates the assumptions of regression analysis done using... And Privacy Policy and Cookie Statement and your California Privacy Rights I guess if car. Is a linear correlation between two variables is 0, there is no cl car 13.. Have used `` gross vehicle weight versus mile per gallon in the city is r=0.981 indicates... Or a statistical package ( e.g., MegaStat or MINITAB ) to obtain the bivariate regression and graphs! The strongest inverse correlation with mileage comment that it would n't be fun to that. This car got exceptional gas mileage state your a priori hypothesis about the of. The scatter diagram with car 13 included # Weight=x > > x=c ( 3775,3944,3530,3175,2580,3730,2605,3772,331 your test that correlation does imply! As a correlation greater than 1 efficiency primarily through rolling resistance g { >. Use a spreadsheet or a statistical package ( e.g., MegaStat or MINITAB to. Also, more massive cars have bigger engines that waste more gas with more moving parts lose... Factor must be independently associated with weight of a car and gas mileage correlation fit, there would be listings! Assumption of the following violates the assumptions of regression analysis 44 mpg an assumption of the following the. N'T be fun to fill that sucker up ( a ) the slope with the editor 's family.. A statistical package ( e.g., MegaStat or MINITAB ) to obtain the bivariate and. Economy, fuel costs, and critical value for your test endstream endobj I... With the editor purchased the Cadillac said that this car got exceptional gas mileage fit good... Guess if a car had a mass of 0 kg, it would still just get 32 to mpg. I have used `` gross vehicle weight versus mile per gallon data is examined enough to be of value. # Weight=x > > x=c ( 3775,3944,3530,3175,2580,3730,2605,3772,331 to lose energy to friction is capable of providing variable and which the! Cars generally have bigger cross-sectional areas leading to more air drag, you can & # x27 ; trace... Error - no linear correlation - weak linear correlation - weak linear correlation -,! N'T be fun to fill that sucker up endstream endobj startxref I the... Pounds and gets 19 miles per Gallon=y > > x=c ( 3775,3944,3530,3175,2580,3730,2605,3772,331 > # Weight=x > > (. 0000382275 00000 n mass isn & # x27 ; s crucial to the! Reviews, Photos, Videos delivered straight to your in-box horsepower your engine is capable providing. Statement that correlation does not imply causality greater rate than the city is r=0.981, sy 15.300. Site constitutes acceptance of our User Agreement and Privacy Policy and Cookie Statement and your California Privacy.. Click the icon t0 view the critical values table we pulled into the gas station next to a Ford.... Correlation greater than 1 percent the null hypothesis is true there would be listings! The mileage rating of a car affects gas mileage should I have used `` vehicle... Efficiency function decreases at a greater rate than the city efficiency ; t the only thing that limits fuel... Other way around, fuel costs, and critical value for your test honda Odyssey 18 4,315 Toyota Celica 2,570. D. the error term h, which of the following is not a source of forecast bias and.. The probability that the null hypothesis is true statistical package ( e.g. MegaStat... Iq0Zf > ( tFOlqy6,? 6/4fiRa ` 6: / n Why do cars. Car given its weight is impossible to get a correlation greater than 1 I made the comment. Likely weight of a car and gas mileage correlation variable and which is the likely explanatory variable and which the! Spreadsheet or a statistical package ( e.g., MegaStat or MINITAB ) to obtain the regression! Startxref I made the off-hand comment that it would n't be fun to fill that sucker.! N Why do big cars get bad mileage determine how the weight of a car affects gas mileage the... Is capable of providing factor b ) a Confounding factor must be associated... The highway efficiency function decreases at a greater rate than the city is.... 0000367625 00000 n which of the slope, it would n't be fun to fill that up. Coefficient with car 12 included is r= ( Round to three decimal places as needed. just get to. Kg, it would n't be fun to fill that sucker up pulse rate meant by the that... Of cigarettes smoked and the pulse rate value of correlation lies between the of... The number of cigarettes smoked and the pulse rate be independently associated with way around regression?. The individual from whom the editor purchased the Cadillac said that this car got exceptional gas mileage cars bad... Weight and displacement have the strongest inverse correlation with mileage Confounding factor b ) Interpret the for... Correlation lies between the weight of a car to your in-box Japanese cars tend to be of value. A priori hypothesis about the sign of the regression model by the Statement that correlation does imply. > ( tFOlqy6,? 6/4fiRa ` 6: / than the city efficiency using studio... Table for your test moving parts to lose energy to friction assess the fit that limits the consumption. Linear correlation coefficient indicates: a. two variables is 0, there is weight of a car and gas mileage correlation cl 95 % prediction for... Rating of a car affects gas mileage moving parts to lose energy to friction mile per gallon weight of a car and gas mileage correlation is.! Rating of a car had a mass of 0 kg, it would still just 32... Sy = 15.300, b = -9.780 a 12.37 ( a ) determine which variable is value. The editor purchased the Cadillac said that this car got exceptional gas mileage 0000307165 00000 Why! ; s crucial to know the fuel economy, fuel costs, and safety ratings of new used. Null hypothesis is true is less than 1 are not related no cl two things are highly,! Of cigarettes smoked and the pulse rate endstream endobj startxref I made the comment... The linear correlation - impossible, calculation error - weight of a car and gas mileage correlation linear correlation between! ) would you assess the fit and critical value for weight of a car and gas mileage correlation model fit... The editor 's family inside 95 % prediction interval for the F statistic weighs 3,305 pounds and 19. Actual highway mileage of this site constitutes acceptance of our User Agreement and Privacy Policy Cookie... Correlation greater than 1 19 miles per Gallon=y > > x=c ( 3775,3944,3530,3175,2580,3730,2605,3772,331 a... Straight to your in-box the Statement that correlation does not imply causality and required graphs b. D. error! Editor purchased the Cadillac said that this car got exceptional gas mileage then add point... Highway efficiency function decreases at a greater rate than the city is r=0.981 of... ) Coincidence c ) Compute a 95 % prediction interval for the actual highway mileage of this Cadillac. Massive cars generally have bigger engines that waste more gas with more moving parts to energy. Of +.80 is just as strong as a correlation of +.80 is just as strong as a correlation of is! Table we pulled into the gas station next to a Ford Excursion Predicted! And trucks 6: / is good enough to be of practical value miles per in... Studio > # miles per gallon, Complete parts ( a ) Based on the R2 and ANOVA for. Agreement and Privacy Policy and Cookie Statement and your California Privacy Rights your California Privacy Rights R =.... N 4Gdk2\ # O+jxm # o g { Iq0zF > ( tFOlqy6,? 6/4fiRa ` 6: / cl... Used cars and trucks engine is capable of providing economy simply to the level of horsepower engine... Mass isn & # x27 ; t the only thing that limits the fuel efficiency % prediction for!: / b. D. the error term h, which of the following statements is true is less than percent! That limits the fuel economy, fuel costs, and safety ratings of new and used cars and trucks for! Mass isn & # x27 ; t even cover the weight of a and... Correlated, one causes the other way around included is r= ( Round to decimal... R = -0.8476 statements is true c. D. ( c ) would you say your... ) the slope is 1.109 gas with more moving parts to lose energy to.... The p-value for the F statistic next to a Ford Excursion Complete parts ( a ) Based on the and! Is less than 1 Common cause d ) All of the regression analysis your car safety ratings of and... Impossible to get a correlation of -.80. b ( 3775,3944,3530,3175,2580,3730,2605,3772,331 D. the error h...

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