12.28 Are the variables cross-sectional data or time-series data? The highway efficiency function decreases at a greater rate than the city efficiency. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. 2500 4000 Weigh: (Ibs) Intercept 36.634 1.879 19.493 0.000 32.838 40.429 Find EPA fuel economy estimates based on vehicle model or class. Ultimately, you can't trace fuel economy simply to the level of horsepower your engine is capable of providing. a. 0000088561 00000 n If there was a manual and an automatic version, I assumed that they had the same mass. (c) Interpret the p-value for the slope. 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_ 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. 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. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. 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. 0000374679 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. A positive error e value indicates: (a) The predicted score is greater than the obtained score. Sometimes I do that - but hopefully I was correct. Solution:By using R studio> #Weight=x> > #Miles per Gallon=y> > x=c(3775,3944,3530,3175,2580,3730,2605,3772,331. Test 2 (Y): 34, 31, 35, 30, 31, 28, 28, 25, 24, 24. A. Statistically, explain what is wrong with this researcher's analysis. If what the salesman claimed fell within this region, we could say that he was telling the truth. I know the Ford Excursion doesn't get super awesome gas mileage (around 14 mpg), but what about the relationship between mass and efficiency? 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. 0.866 c. -0.155 d. -0.866 e. 0.155 f. none of the above, One of the major misconceptions about correlation is that a relationship between two variables means causation, where one variable causes changes in the other variable. 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. Why are the results here reasonable? Find and compare the fuel economy, fuel costs, and safety ratings of new and used cars and trucks. Chevy TrailBlazer 15 4,660 Nissan 350Z 20 3,345 The EPA city test includes idling, but more idling will lower MPG. B. I should have known it wouldn't stop there. I removed any hybrid vehicles and vehicles that I had never heard of. CAN'T COPY THE TABLE Identify any statistical errors. 12.31 State your a priori hypothesis about the sign of the slope. For example, the Aston Martin DBS Coupe only gets 17 mpg on the highway and 11 mpg in the city even though it only has a mass of 1,695 kg. a) 0.8 to 1.0 b) 0.6 to 0.8 c) 0.2 to 0.4 d) 0 to 0.2, Consider the following regression equation between Y and X: Y = 4.622X - 100. There is a negative correlation between x and y. b. b. Excessive idling decreases MPG. Everyone loves data. e)Suppose an editor for the publication wishes to predict the highway mileage of vehicles with a curb weight of 6,000 pounds. The The explanatory variable the weight and the response variable the following data represent the weight of various cars and their gas mileage. The value of r i, The value of a correlation is reported by a researcher to be r = -0.5. Redraw the scatter diagram with Car 13 included. Regression 1.000 546.438 546.438 87.506 0.000 "There is a high correlation between the manufacturer of a car and the gas mileage of the car." B. a. Jaguar XJ8 18 3,805 VolvoC70 20 3,690 If so, can we predict the mileage rating of a car given its weight? The percentage of variance in Y that is explained by, Can you identify some situations where correlation doesn't prove causation? Stretches of DNA that lock inherited traits together often accumulate harmful mutations. 0000382088 00000 n a. (b) A confounding factor must be independently associated with. I. 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. (b) The obtained score is greater than the predicted score. 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. d. b. My daughter asked. The following problem uses a regression model to answer several questions associated with auto travel. c. there has been a measurement error. Here is the data, if you want it. Complete parts (a) through (d) below. 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 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. Acura TSX 23 3,320 Lexus IS 300 18 3,390 The first is added weight. Click the icon to view the data table. Which statement does not belong? !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 . Multiply the linked Z scores from the two variables. Educator app for b. Scientists say a mild Covid infection increased immune benefits from a later flu vaccine, but with a biological twist. If so, can we predict the mileage rating of a car given its weight? C. Describe the error in the conclusion. The explanatory variable is the miles per gallon and the response variable is the weight. II. A raised vehicle can offer more surface area for moving air to battle its way around. 0000002988 00000 n 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. However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence interval. The linear correlation coefficient with Car 12 included is r= (Round to three decimal places as needed.) a. Coefficient of determination is -1.0. b. Coefficient of correlation is 0.0. c. Sum of squares for error is 0.0. d. N, Suppose you are determining the association between the weight of a car and the miles per gallon that the car gets. What is meant by the statement that correlation does not imply causality? Be specific and provide examples. Is there a correlation between variable A and B? 0000362469 00000 n The answer to that question wasThe 95% confidence interval estimate for the gas mileage for the Cadillac is 20.68 to 23.56 mpg. HW-GWUY-`d5|d]=sG fq*/~/}Iof{4n3o9cZ2^ZZoy/sT'lXk;|j}{.8 Gy/^cgx~z}@M {l[pT4lD&|l ./{Nq@_P a> =V} 12.35 Use Excel, MegaStat, or MINITAB to fit the regression model, including residuals and standardized residuals. 0000403945 00000 n Think about when and why the relation between two variables can change. 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. 0000362607 00000 n 2023 Cond Nast. Today's cars and light trucks weigh between 1 000 to 3 800 kg. 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? It can happen that an outlier is neither influential nor does have high leverage. 1. This page is for personal, non-commercial use. We reviewed their content and use your feedback to keep the quality high. It can happen that an observation with high lev. I guess if a car had a mass of 0 kg, it would still just get 32 to 44 mpg. An engineer wanted to determine how the weight of a car affects gas mileage. did not change. In a meeting, a Senior Manager says that a negative correlation doesn't sound like a desirable result, and a perfect correlation sounds like a good thing. The following data represent the weight of various cars and their gas mileage. "We found a high correlation (r = 1.09) between the horsepower of a car and the gas mileage of the car. 0000087040 00000 n Use a spreadsheet or a statistical package (e.g., MegaStat or MINITAB) to obtain the bivariate regression and required graphs. The correlation coefficient, r = -1, implies a. Why are the results here reasonable? Choose the correct graph below. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. If r = 0, there is no relationship between the two variable at all. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Suppose that we add Car 12 to the original data. If you google something like "2009 Pontiac G5 curb weight," you might find several answers that don't agree. This equation shows a negative correlation between X and Y. c. The regression e, A linear regression analysis produces the equation y = 5.32 + (-0.846)x. It ranges from 0.0 to +10 inclusive b. The correlation is either weak or 0. b. In automotive-mechanical term it refers to "Cylinder Capacity". Complete parts (a) through (d). 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. 0000367625 00000 n The error term is correlated with an explanatory variable. 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. Hyundai Elantra 24 2,880 Toyota Matrix 26 2,985 One would assume that a car with greater mpg would command better resale value, but this definitely appears to not be the case. 4Gdk2\#O+jxm#o g{Iq0zF>(tFOlqy6,?6/4fiRa`6:/. The probability that the null hypothesis is true is less than 1 percent. a. Statistics and Probability questions and answers. 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 An engineer wanted to determine how the weight of car affects gas mileage. Find the correlation coefficient of the data b = .222; sx = 6.32; sy = 1.45. The conditions under which miles per gallon were evaluated for Car 13 were different from the conditions for the other cars. 0000177854 00000 n The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 c. Yes, there is a positive correlation. (ii) A sample correlation coefficient of .95 between, Which correlation coefficient (r-value) reflects the occurrence of a perfect association? IRS is responsible for collecting those taxes from manufacturers. Beginning in 2007, data are for passenger cars, light trucks, vans, and sport utility vehicles with a wheelbase equal to or less. An engineer wanted to determine how the weight of a car affects gas mileage. The correlation coefficient and the slope of the regression line may have opposite signs. 0000044566 00000 n B. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Which of the following statements must be true? There is a fairly strong, roughly linear, positive association between vehicle weight and gas mileage. He checks his theory by gathering data on a rat, a bat. Choose the correct graph below. . (c) The correlation is not significant. Get access to this video and our entire Q&A library, Correlation: Definition, Analysis & Examples. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. a. Cleaning The Radiator from Inside First of all, the radiator has to be cleaned from the inside. An engineer wanted to determine how the weight of a car affects gas mileage. Hence, to know the correct mileage and how much you have spent, remember the below points. 1168 0 obj <> endobj 1 Through 2006, data are for passenger cars (and, through 1989, for motorcycles). Why are the results here reasonable? The correlation is moderate to strong. (d) Which approach do you prefer, the t test or the p-value? 0000002939 00000 n The chi-square test is useful for explaining the relationship between high, Ten pairs of points yielded a correlation coefficient r of 0.790. investing millions in the production of carbon fiber. We dont have your requested question, but here is a suggested video that might help. 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). (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? Complete parts (a) through (f) below. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. But they also hold genetic benefits for species. B. B. A positive residual means that the car gets better gas mileage than the model predicts for a car with that much horsepower. 12.35 The results of the regression analysis done by using MS Excel are given below. Complete parts (a) and (b) below. Your gas consumption depends on a range of factors. AMab O c. does not follow the overall pattern of the data. I expected it would be the other way around.