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. 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? Perfect positive c. No correlation d. Limited correlation. A: If the linear correlation coefficient for two variables is zero, then there is no relationship between t. How may correlation analysis be misused to explain a cause-and-effect relationship? %PDF-1.3 Which of the following statements is not true? The following statements are either misleading or contain one or more errors relating to correlation. Car weight and displacement have the strongest inverse correlation with mileage. Which of the following statements is correct? a) Omission of important variables. HW%G|?_?0=uH%le obODdV>n^q:++323go~W>z!Y_o|>>._?]O7zPCa*v}}yu>3|uW/WiA}Ol[L[,{e{+;{[*"~#]Cc[CoaQ jA 5i I{[.T6:qm `nr$.^Kd;zg.2B\= By firing lasers through underground fibers, scientists can detect seismic waves and perhaps improve alertsgiving people precious time to prepare. A strong negative correlation coefficient indicates: a. two variables are not related. did not change. There is some spread, but we can discern a pattern: Dots to the right in the graph tend to be placed lower. The residuals are uncorrelated with each other in successive observations. df SS MS F Significance F More massive cars have bigger engines that waste more gas with more moving parts to lose energy to friction. B) It is impossible to get a correlation greater than 1. has a weight outside the range of the other cars' weights. *4/Q:/w`D%w&FTb>F 20[O@Le,1&# Qh ` ~S^ The following data represent the weight of various cars and their gas mileage. Click here to view the table of critical values of the correlation coefficient. a. iPad. How would you interpret the findings of a correlation study that reported a linear correlation coefficient of +0.3? In model year 2021, the average estimated real-world CO 2 emission rate for all new vehicles fell by 2 g/mi to 347 g/mi, the lowest ever measured. 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. stream 12.35 Use Excel, MegaStat, or MINITAB to fit the regression model, including residuals and standardized residuals. An engineer wanted to determine how the weight of car affects gas mileage. 0000382088 00000 n Correlation only implies association not causation. - The regression line minimizes the sum of the squared errors. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. Find and compare the fuel economy, fuel costs, and safety ratings of new and used cars and trucks. Fuel efficiency, sometimes referred to as fuel economy, is the relationship . Experts are tested by Chegg as specialists in their subject area. 0000352202 00000 n Click here to view the table of critical values of the correlation coefficient. Our experts can answer your tough homework and study questions. Statistics and Probability questions and answers, An engineer wanted to determine how the weight of a car affects gas mileage. What is interesting to note here, is the strong negative correlation between city_mpg and highway_mpg. 12.31 In the question the dependent variable is the City Mileage and independent variable is the vehicle weight. Using the following information: What is the correlation coefficient? Tires affect vehicle fuel efficiency primarily through rolling resistance. B. Weight (pounds), x Miles per Gallon, y 3808 16 3801 15 2710 24 3631. than 121 inches. a. Because it was sitting in my barn / shop for over 12 years!! The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 did not change significantly (d) Now suppose that Car 13 (a hybrid car) is ad r 13 weighs 2,890 pounds and gets 60 miles per gallon. If an aluminum radiator is damaged or is experiencing problems, it can easily be fixed up by the owner. c. The error terms decrease as x values increase. (d) Now suppose that Car 13 (a hybrid car) is added to the original data (remove Car 12). b. 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. Scientists say a mild Covid infection increased immune benefits from a later flu vaccine, but with a biological twist. This make sense. Why are the results here reasonable? 6. Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distributions under H_0)? slope of 3000 pounds per foot would predict a weight difference of 9000 pounds (4.5 tons) between Civic and DeVille. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. b) Incorrect model specification. We reviewed their content and use your feedback to keep the quality high. Are there ever any circumstances when a correlation can be interpreted as evidence for a causal connection between two variables? 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. The following problem uses a regression model to answer several questions associated with auto travel. 0000382531 00000 n (e) Recompute the linear correlation coefficient with Car 13 included. Another bowl. a. 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. 2000 Test Car List Data (csv) (507.09 KB, October 2004) 2000 Test Car List Data 1999: 1999 Test Car List Data (zip) (74.77 KB, August 2004) 1998: 1998 Test Car . Hence, to know the correct mileage and how much you have spent, remember the below points. 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. 0000383019 00000 n See correlation examples using statistical data sets and learn how to do an analysis. Trip Distance endstream endobj startxref )HVX(j(L3/WB]';.+l}^c(/CqbZ6/0h": H_H~A3ep>/~Z+]~^7u]-YL'W1_Q8& /:6`;N\}Zq9YI4S9,R9. The value of correlation depends on the factors being considered, whether they are negatively associated or positively associated and the magnitude of their association. (ii) A sample correlation coefficient of .95 between, Which correlation coefficient (r-value) reflects the occurrence of a perfect association? Which of the following statements is correct? 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? has a weight within the range of the other cars' weights. The correlation is moderate to strong. Which of the following statements regarding the coefficient of correlation is true? 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 signs of the correlation coefficient indicates the direction of the relationship. 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`& The EPA city test includes idling, but more idling will lower MPG. 0.9184 b. Complete parts (a) through (d) below. = .05. Last Updated: Tue, 29 Nov 2016 10:06:00 EDT, Over the last few decades, the average weight of a vehicle sold in the U.S. climbed steadily after surviving the oil embargoes of the 1970s. Looks linear enough to fit a function. Miles per Car Weight (pounds) Gallon 3310 B 3680 2770 3340 2690 Show transcribed image text Expert Answer 100% (3 ratings) Was I just making that stuff up? a. c. The error term has a zero mean. Observations 43.0000, ANOVA An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. 0000086420 00000 n The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r=0.981. miles per gallon, Complete parts (a) through (d). 678. 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. Why are the results here reasonable? 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. Engines will most commonly come in 4, 6, or 8 cylinders. Should I have used "gross vehicle weight" instead of curb weight? The error term has a constant variance. An engineer wanted to determine how the weight of a car affects gas mileage. Complete parts (a) through (d) below. For cases like this, I just took the first reasonable number I found. The combined weight of his family is 570 lbs. Thus, the correlational value must be in negative. Which of the following Excel functions returns the sample correlation coefficient? 0000362028 00000 n 0000382127 00000 n The coefficient of determination is R2 = 0.895 . 0000367741 00000 n Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. D. Car 13 is a hybrid car, while the other cars likely are not. HW-GWUY-`d5|d]=sG fq*/~/}Iof{4n3o9cZ2^ZZoy/sT'lXk;|j}{.8 Gy/^cgx~z}@M {l[pT4lD&|l ./{Nq@_P a> =V} Chevy Silver1500 14 4,935 Mitsubishi Galant 20 3,285 Complete parts (a) through (f) below. d. b. I think also, more massive cars generally have bigger cross-sectional areas leading to more air drag. 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 For example, the greater the mileage on a car, the lower the price. For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. sx = 1.355, sy = 15.300, b = -9.780 a. Causation is only one explanation of an observed association. So he is confused about the meaning of a perfectly negative correlation. (b) Interpret the p-value for the F statistic. The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 While it is generally accepted that fuel consumption (gallons per mile) increases more or less in proportion to weight, a direct proportionality between fuel consumption and weight means that the unit fuel consumption, in gallons per pound-mile, will be constant. Redraw the scatter diagram with Car 13 included. j_uD2BMSh(E h8J2=$hQ% 7 R:F$ejd2o&#&t`f#fT!q|xEd#ic$@6q2!wmah,~Y;!Un?9 ^c0 $mQ+B'f};8+Ui\L> Ex0J(Vq[20B]L]D7M bQlB@I".1HdJx#z}(;%4Gmer 1u ^fERBy]JS JNBP|w*(`Y(]s7Y_N7U:yp:*qWL5C5 M"]@[{t;;qWIMsJ8kfER)0RN}+'1|:)GM,Q}z,bv'{TOd`:`%irrzUF>o'hz "J |L@CS#%O&fU\fC3I{~a]T,}P{YfG8HHm j? 0000090312 00000 n Ford Focus 26 2,760 Saturn Ion 24 2,855 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. 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