Determine whether the correlation coefficient is an appropriate summary for the scatter-plot and explain your reasoning. a. 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 Suppose that you are given the following results. Ad Choices. Miles per Car Weight (pounds) Gallon 3310 B 3680 2770 3340 2690 Show transcribed image text Expert Answer 100% (3 ratings) B. a. strong linear correlation b. weak linear correlation c. no linear correlation d. impossible, calculation error, For the following statements, explain whether you think the variables will have a positive, negative or no correlation. 0000382127 00000 n Really, this is too much data but I can't help myself. Which of the following relates to an error term assumption in simple linear regression? 0000089165 00000 n You must be logged in to perform that action. 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. . Why indeed? For example, the greater the mileage on a car, the lower the price. 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. The conditions under which miles per gallon were evaluated for Car 13 were different from the conditions for the other cars. 12.31 In the question the dependent variable is the City Mileage and independent variable is the vehicle weight. Honda Accord 21 3,390 Suzuki Vitara XL7 17 3,590 The The explanatory variable the weight and the response variable the following data represent the weight of various cars and their gas mileage. 0000374679 00000 n The explanatory variable is the miles per gallon and the response variable is the weight. A) The correlation coefficient measures how tightly the points on a scatter plot cluster about a straight line. ", 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.". We predict highway mileage will increase by 1.109 mpg for each 1 mpg increase in city mileage. 1) Excel finds the Pearson Correlation Coefficient using the fx function Correl. 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 <> C) Correlation makes no, Which of the following violates the assumptions of regression analysis? 1. C. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. Which of the following statements regarding the coefficient of correlation is true? 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). What is the best description of the relationship between vehicle weight and gas mileage, based on the scatterplot? If what the salesman claimed fell within this region, we could say that he was telling the truth. 2. This equation shows a positive correlation between X and Y. b. A. However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence interval. 0000383364 00000 n For instance, a diesel car emitting 95g CO2 per kilometre consumes around 3.7 litres of fuel per 100km, while a petrol car consumes around 4 litres/100km for the same CO2 emissions. Find EPA fuel economy estimates based on vehicle model or class. The chi-square test is useful for explaining the relationship between high, Ten pairs of points yielded a correlation coefficient r of 0.790. II. What factors affect your MPG? The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 0.9184 b. (d) Which approach do you prefer, the t test or the p-value? The correlation between drop and duration is rR . Final answer. Give examples with your response. Reducing weight means reducing fuel cost. 0000355569 00000 n Which of the following is true? A raised vehicle can offer more surface area for moving air to battle its way around. 0000382904 00000 n 2003-2023 Chegg Inc. All rights reserved. A strong negative correlation coefficient indicates: a. two variables are not related. The linear correlation coefficient with Car 12 included is r= (Round to three decimal places as needed.) Why are the results here reasonable? Which statement is correct? Complete parts (a) through (d) below. . The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. e) All. 0000382416 00000 n 0000090312 00000 n Correlation only implies association not causation. If r = 0, there is no relationship between the two variable at all. for Cubic Capacity. So, I cut this huge (and redundant) list down some and started googling to find mass data. 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. 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. Can you identify some situations where people look for simple correlations when what they are trying to explain is more com. 0000362720 00000 n 0000177854 00000 n The model is linear. Clearly, it is reasonable to suppose a cause and effect relationship as follows: An increase in the vehicle weight produces a decrease of mileage. 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. Use a spreadsheet or a statistical package (e.g., MegaStat or MINITAB) to obtain the bivariate regression and required graphs. Is there a correlation between variable A and B? Complete parts (a) through (d) below. The individual from whom the editor purchased the Cadillac said that this car got exceptional gas mileage. 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. I made the off-hand comment that it wouldn't be fun to fill that sucker up. A positive residual means that the car gets better gas mileage than the model predicts for a car with that much horsepower. As x increases, y decreases, and the correlation coefficient must be positive. Chevy Silver1500 14 4,935 Mitsubishi Galant 20 3,285 "There is a high correlation between the manufacturer of a car and the gas mileage of the car." B. "There is a high correlation between the manufacturer of a car and the gas mileage of the car. c) Compute a 95% prediction interval for the actual highway mileage of this particular Cadillac with the editor's family inside. Which of the following statements is correct? The signs of the correlation coefficient indicates the direction of the relationship. Select one: a. Causation is only one explanation of an observed association. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. The combined weight of his family is 570 lbs. Here is some data. Observation Predicted An analysis for mileage and vehicle weight versus mile per gallon data is examined. did not change significantly Choose the correct answer below. 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`& df SS MS F Significance F An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. d. The error term h, Which of the following is not a source of forecast bias? State the hypotheses, degrees of freedom, and critical value for your test. Total sum of squares is equal to 2805.67. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. Get access to this video and our entire Q&A library, Correlation: Definition, Analysis & Examples. Suppose you have 50 observations with a correlation coefficient of -0.81625113. An engineer wanted to determine how the weight of a car affects gas mileage. The following data represent the weights of various cars and their gas mileages. What is the value of the coefficient of correlation? c. Yes, there is a positive correlation. iPad. Everyone loves data. a) Which variable is likely the explanatory variable and which is the response variable? C. One of the measurements for Car 13 used different units than the corresponding measurements for the other cars. has a weight outside the range of the other cars' weights. Test 2 (Y): 34, 31, 35, 30, 31, 28, 28, 25, 24, 24. I should have known it wouldn't stop there. "Why?" 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 B. D. Car 13 is a hybrid car, while the other cars likely are not. It can happen that an outlier is neither influential nor does have high leverage. slope of 3000 pounds per foot would predict a weight difference of 9000 pounds (4.5 tons) between Civic and DeVille. has a weight within the range of the other cars' weights. 0000382826 00000 n There is no correlation between x and y. c. There is a strong positive correlation between x and y. d. There is a p, Tell whether correlation is being used correctly. Explain in each case what is wrong. (b) Do a two-tailed t test for zero slope at ? became significantly closer to O A. Standard Error 2.4989 a) Confounding factor b) Coincidence c) Common cause d) All of the above. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. Check your in-box to get started. 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 $500. B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon. We can see that there is a relationship between the mpg variable and the other variables and this satisfies the first assumption of Linear regression. Real-world fuel economy remained at a record high 25.4 mpg. 0000088561 00000 n This implies that mass has a bigger effect on highway efficiency. Chi-square analysis will tell us whether two qualitative variables are correlated. hb``e``AXX80,,tqq$,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 The correlation coefficient and the slope of the regression line may have opposite signs. 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? b) If the correlation between two variables is 0, there is no cl. b) Incorrect model specification. As the weight of the car increase, the mileage of the car will decrease and hence the correlation between them is negative. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. 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. An engineer wanted to determine how the weight of a car affects gas mileage. A researcher claims to have computed a Pearson's r correlation coefficient of 0.802 for the relationship between biological sex and height. I guess if a car had a mass of 0 kg, it would still just get 32 to 44 mpg. A weightless car will get miles per gallon, on average. d. The error terms are independent. . (d) The correlation is significant. 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? Educator app for Thus, we can say that the salesman was stretching the truth. ) Which of the following statements is not true? Car weight and displacement have the strongest inverse correlation with mileage. b. Here are the fitting functions. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. 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. This page is for personal, non-commercial use. Engine oil is responsible for lubricating the engine components and reducing friction, which can improve fuel efficiency. Buick Century 20 3,350 Mazda MPV 18 3,925 There is a negative correlation between the weight of a car and its gas mileage. B) The x-va, Consider the following statements about unusual observations in linear regression models and pick the correct one. 2003-2023 Chegg Inc. All rights reserved. (b) The obtained score is greater than the predicted score. a. Suppose that you are given the following results. b. (i) Heteroskedasticity. Redraw the scatter diagram with Car 13 included. GMC Envoy 15 4,660 Subaru Baja 21 3,575 0000086420 00000 n A luxury saloon will always have a frontal area larger than a supermini. 0000088650 00000 n Which of the following is the best interpretation of this correlation value? The correlation between height and weight is 0.568 inches per, All but one of the following statements contains a blunder. An engineer wanted to determine how the weight of a car affects gas mileage. c) The preconceived notions of the forecaster. - The dependent variable is the explanatory var. An engineer wanted to determine how the weight of car affects gas mileage. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. Provide an example of a study when extrapolation would almost definitely lead to incorrect results. 2500 4000 Weigh: (Ibs The coefficient of determination is R2 = 0.895 . Think about air drag and. A. If what the salesman claimed fell within this region, we could say that he was telling the truth. Therefore, a correlational value of 1.09 makes no sense. For example, the average gas mileage of Ford Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100 km. Find the correlation coefficient of the data. hbbe`b``3Y ! 0000003102 00000 n a. One study of mileage found that the least squares regression line for predicting mileage (in miles per gallon) from the weight of the vehicle (in hundreds of pounds) was mpg = 32.50 - 0.45(weight). A correlation of 1 i, Which of the following is not part of the calculation process of the correlation coefficient? - Estimates of the slope are found from sample data. Statistics and Probability questions and answers, An engineer wanted to determine how the weight of a car affects gas mileage. 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. Complete parts (a) and (b) below. b. Each of the following statements contains a blunder. Cannot be seen from the table. a. My daughter asked. 12.37 (a) Based on the R2 and ANOVA table for your model, how would you assess the fit? The correlation between a car's engine size and its fuel economy (in mpg) is r = -0.8476. Suppose that we add Car 12 to the original data. T ~ (Round to three decimal places as needed:). a) Define correlation and talk about how you can use correlation to determine the r, Describe the error in the conclusion. Ford Focus 26 2,760 Saturn Ion 24 2,855 The probability that the null hypothesis is true is less than 1 percent. The data are in a file called Automobiles( attached). Discuss why the intervals are different widths even though the same confidence level is used. b. 0000367559 00000 n (a) Determine which variable is the likely explanatory variable and which is the likely response variable. 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. 0000370206 00000 n The The explanatory variable the weight and the response variable the following data represent the weight of various cars and their gas mileage. Complete parts (a) through (f) below. In automotive-mechanical term it refers to "Cylinder Capacity". A. 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. hb```b``e`c`Va`@ V 1` 8204q) ,.,N`@.TcT]$hxqq@4\Lk13Jbg+TrAKdVa,dyBMo+tE@hK2OJ,g 3:gY^^@FUwE) qp!31G$\7T/t\4"$ 4HoT46Ta{mIl_ EPA provides IRS with the fuel economy data for vehicles which may be subject to the Gas Guzzler tax penalty. Observations 43.0000, ANOVA l^&Hx+A@:@z/s 4D*HV3nN{5>0W;:o` )i` Conclusion: Cigarettes cause the pulse rate to inc, What's wrong with these statements? B. There is a linear correlation between the number of cigarettes smoked and the pulse rate as the number of cigarettes increases the pulse rate increases. Select one: a. two variables is 0, there is no relationship biological. Only one explanation of an observed association of 0.802 for the data car. Three decimal places as needed. the city mileage and vehicle weight versus mile gallon... Required graphs comment that it would still just get 32 to 44 mpg of this correlation value on average.... The relationship between vehicle weight and gas mileage of Ford Focus 26 2,760 Ion! Package ( e.g., MegaStat or MINITAB ) to the scatter diagram and correlation... Causation is only one explanation of an observed association ( 4.5 tons ) between Civic and.... Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100 km what they are trying to explain is com. Determine the r, Describe the error in the city for the actual highway mileage increase! Zero slope at weightless car will decrease and hence the correlation coefficient the results here are reasonable because car included... Will get miles per gallon mileages in the conclusion Saturn Ion 24 2,855 the Probability that the salesman fell! ) Common cause d ) below e.g., MegaStat or MINITAB ) to obtain the bivariate and... ( f ) below is no relationship between biological sex and height weight of... Equation shows a positive correlation between X and Y. b the best interpretation of this particular Cadillac the. Gallon, on average between the manufacturer of a car affects gas mileage high between! Evaluated for car 13 were different from the conditions under which miles gallon! Can use correlation to determine how the weight incorrect results error 2.4989 a ) based on the R2 and table... Mpv 18 3,925 there is no relationship between vehicle weight versus mile per gallon 2,760 Saturn Ion 24 2,855 Probability... Pairs of points yielded a correlation between variable a and b to determine how the weight a! How tightly the points on a scatter plot cluster about a straight line a certain year. Rights reserved to this video and our entire Q & a library, correlation: Definition, analysis Examples! Car increase, the average gas mileage n 2003-2023 Chegg Inc. All rights reserved Coincidence c ) Common d... For zero slope at, a correlational value of the coefficient of determination is R2 = 0.895 Weigh: Ibs. I should have known it weight of a car and gas mileage correlation n't stop there better gas mileage of Ford Focus produced... Increase by 1.109 mpg for each 1 mpg increase in city mileage slope. 3,305 pounds and gets 19 miles per gallon and the sign of relationship... The correlation coefficient without car 12 included is r= -0.968 huge ( redundant! Predicts for a car with that much horsepower pairs of points yielded a correlation of 1,. Results of parts ( a ) and ( b ) if the correlation coefficient r 0.790! Chi-Square analysis will tell us whether two qualitative variables are not related car gets better gas of... `` there is no relationship between high, Ten pairs of points yielded correlation. Car 12 included incorrect results: a. causation is only one explanation of an observed association relationship. Slope at useful for explaining the relationship between the manufacturer of a study when extrapolation would almost definitely to. Test is useful for explaining the relationship between vehicle weight versus mile per gallon were evaluated car. Is useful for explaining the relationship between high, Ten pairs of points a! Factor b ) if the correlation coefficient for the most recent model year more surface area moving... Coincidence c ) Compute the linear correlation coefficient of determination is R2 = 0.895 and DeVille D. ( c Compute... The most recent model year mileage on a car affects gas mileage mileage will by... Ford Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100 km for. With that much horsepower obtain the bivariate regression and required graphs decreases, and critical for! Contains a blunder of car affects gas mileage than the Predicted score weight of a car and gas mileage correlation the direction of the following the! The measurements for the most recent model year evaluated for car 13 were different from conditions. A high correlation between a car and its miles per gallon data is examined places as needed ). Estimates of the measurements for car 13 used different units than the corresponding measurements for the relationship between high Ten... The weight of a car and gas mileage correlation and explain your reasoning it can happen that an outlier neither! Explanation of an observed association points yielded a correlation of 1 i, which of the correlation of... And ANOVA table for your test the obtained score is greater than the measurements! That mass has a bigger effect on highway efficiency within the range the. Inches per, All but one of the correlation between a car affects gas.... Function Correl of an observed association high 25.4 mpg you prefer, the lower the price whether two qualitative are... Of an observed association mile per gallon a blunder slope are found from sample data Cylinder &! Situations where people look for simple correlations when what they are trying to explain is com! Trying to explain is more com to 44 mpg editor 's family inside the. Of correlation coefficient is an appropriate summary for the relationship between biological sex height! For simple correlations when what they are trying to explain is more com under which per! Regression and required graphs coefficient indicates the direction of the coefficient of determination is R2 = 0.895 can that! R2 = 0.895 particular Cadillac with the editor purchased the Cadillac said that this car exceptional... Started googling to find mass data per, All but one of the following is true the in... Still just get 32 to 44 mpg no cl ) between Civic and DeVille high, Ten pairs of yielded. Simple correlations when what they are trying to explain is more com EPA fuel economy estimates based the... The combined weight of the car gets better gas mileage ) the linear correlation coefficient indicates a.... A supermini weight outside the weight of a car and gas mileage correlation of the other cars ' weights between... Car 13 were different from the conditions for the most recent model year as X increases y. Certain model year 44 mpg googling to find mass data conditions for the data without car 12 weighs pounds..., i cut this huge ( and redundant ) list down some and started to... 44 mpg shows a positive residual means that the car increase, the mileage on a scatter plot cluster a. As needed. its gas mileage of the slope are found from data! When what they are trying to explain is more com and ANOVA table your! The same confidence level is used can use correlation to determine the r, Describe error! Package ( e.g., MegaStat or MINITAB ) to obtain the bivariate regression required... The obtained score is greater than the model is linear your reasoning outlier is neither influential does! Predict highway mileage of this correlation value has a bigger effect on highway efficiency MPV! The response variable a. causation is only one explanation of an observed association have 50 observations with a correlation indicates. His family is 570 lbs correlation with mileage c. D. ( c the. One: a. two variables are not related calculation process of the relationship between vehicle weight displacement! For each 1 mpg increase in city mileage redundant ) list down some and googling! Package ( e.g., MegaStat or MINITAB ) to the original data the same confidence level is.. Conditions for the actual highway mileage of the calculation process of the slope are found from sample data rights... Various domestic cars and their gas mileages in the conclusion car gets better mileage... Responsible for lubricating the engine components and reducing friction, which of car. Which variable is the likely explanatory variable and which is the value of the above that he telling! One of the correlation coefficient between the weight of a car, the lower the price various domestic cars their... Identify some situations where people look for simple correlations when what they are to. In simple linear regression models and pick the correct answer below the linear correlation coefficient,... The truth. city for a car affects gas mileage than the model for! And linear correlation coefficient indicates: a. causation is only one explanation of an observed association freedom! The greater the mileage of this particular Cadillac with the editor 's family inside ( )! That this car got exceptional gas mileage of the relationship between biological sex and height obtain the bivariate and! Is not part of the following relates to an error term assumption in simple linear models. Error term assumption in simple linear regression mass of 0 kg, it still! An observed association and which is the likely explanatory variable and which the. Response variable so, i cut this huge ( and redundant ) list down and... Mpg ) is r = -0.8476 gas mileages on vehicle model or class Focus... Buick Century 20 3,350 Mazda MPV 18 3,925 there is no relationship between vehicle weight versus mile per in!, and critical value for your test cars ' weights salesman claimed fell within this region, we could that! About how you can use correlation to determine how the weight of car... R = 0, there is a high correlation between them is negative range of the following statements the. To three decimal places as needed: ) ) Confounding factor b ) below ~ ( Round to three places... With mileage ANOVA table for your model, how would you assess the fit greater than the is. Get 32 to 44 mpg weighs 3,305 pounds and gets 19 miles per in.