c. Yes, there is a positive correlation. If so, can we predict the mileage rating of a car given its weight? 1. Weight (pounds), x Miles per Gallon, y 3808 16 3801 15 2710 24 3631. How did this new value affect your result? a. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. Residual 41.000 256.027 6.245 !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 . As the number of cigarettes increases the pulse rate increases. has a weight within the range of the other cars' weights. Aftershocks May Rock Turkey and Syria for Months, Even Years. Japanese cars tend to be lighter in weight than other cars. I. 1193 0 obj
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The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. We predict highway mileage will increase by 1.109 mpg for each 1 mpg increase in city mileage. 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. Which of the following is the best interpretation of this correlation value? explanatory variable response variable b) Draw a scatter diagram . copyright 2003-2023 Homework.Study.com. b) The coefficient of determination is 0.1225. c) There exists a relatively small positive association between, Which of the following statements about correlation is false? B) The correlation coefficient with car 12 included. Each of the following statements contains a blunder. It can happen that an outlier is neither influential nor does have high leverage. 0000362469 00000 n
See correlation examples using statistical data sets and learn how to do an analysis. What is meant by the statement that correlation does not imply causality? 0000370245 00000 n
Chevy Corvette 19 3,255 Mercury Sable 20 3,340 A researcher claims to have computed a Pearson's r correlation coefficient of 0.802 for the relationship between biological sex and height. 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. Complete parts (a) through (d) below. Chevy TrailBlazer 15 4,660 Nissan 350Z 20 3,345 Each of the following statements contains a blunder. 0000362720 00000 n
A weightless car will get miles per gallon, on average. Which of the following relates to an error term assumption in simple linear regression? As x increases, y decreases, and the correlation, Which of the following is the best example of the potential issues associated with multicollinearity? 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. Old or incorrect engine oil. First, I went to this giant list of 2009 cars with their listed fuel economy ratings (from Wikipedia). Identify any statistical errors. Choose the correct answer below. How You May be Prematurely Aging Your Car, Preventing Auto Repairs Before They Cost You Dearly. Determine whether the correlation coefficient is an appropriate summary for the scatter-plot and explain your reasoning. Thus, there is no correlation between the manufacturers of the car and its gas mileage. Buick Rendezvous 18 4,230 Mazda 6 19 3,355 Observations 43.0000, ANOVA Chevy Silver1500 14 4,935 Mitsubishi Galant 20 3,285 Consider the following ordered pairs and calculate and interpret the correlation coefficient. All rights reserved. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. D. follows the overall pattern of the data. Choose the correct graph below. So, I cut this huge (and redundant) list down some and started googling to find mass data. c. The range of values for a correlation is from 0 to 1. d. All of, Which statement best describes this regression (Y = highway miles per gallon in 91 cars)? b. (c) Would you say that your model's fit is good enough to be of practical value? Complete parts (a) through (f) below. An engineer wanted to determine how the weight of a car affects gas mileage. 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 a very weak, roughly linear, negative association between vehicle weight and gas mileage. 0000370206 00000 n
c. The correlation is negative. The largest catalog ever collected by a single telescope maps Earths 3 billion stellar neighborsand helps track the dust that warps how we see them. Which one could be true? *4/Q:/w`D%w&FTb>F
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It is the essential source of information and ideas that make sense of a world in constant transformation. a. 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. |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? Which of the following Excel functions returns the sample correlation coefficient? Is it reasonable to suppose a cause and effect relationship? hb``e``AXX80,,tqq$,d%0h Idt4[ m`e(>W2v11y21d` i'c
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Ford Focus 26 2,760 Saturn Ion 24 2,855 Thus, we can say that the salesman was stretching the truth. ) The EPA city test includes idling, but more idling will lower MPG. 0000307165 00000 n
State the hypotheses, degrees of freedom, and critical value for your test. endstream
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The correlation between drop and duration is rR . Intercept 36.634 1.879 19.493 0.000 32.838 40.429 All other trademarks and copyrights are the property of their respective owners. (b) Draw a scatter diagram of the data. stream Complete parts (a) through (d). The sample correlation c. Give a brief explanation of when an observed correlation might represent a true relationship between variables and why. O c. does not follow the overall pattern of the data. a) 0.1 b) 1.0 c) 10.0 d) 100.0, When analyzing the slope in a regression analysis (i.e., the relationship between the dependent variable and one of the independent variables), which of the following would be a Type II error? 6. 0000374679 00000 n
The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. . 153 0 obj
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Think about when and why the relation between two variables can change. Schizophrenia Drugs Are Finally Getting an Overhaul. Redraw the scatter diagram with Car 13 included. 6. Do heavier cars use more gasoline? 0000088125 00000 n
(c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. A. Why are the results here reasonable? Think about air drag and stuff. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Step 2/2. 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? The values of the independent variable X are assumed to be random. Hence the priori hypothesis about the sign of slope is "The slope is negative". Honda Odyssey 18 4,315 Toyota Celica 23 2,570 RESIDUAL OUTPUT Complete parts (a) through (d). An engineer wanted to determine how the weight of a car affects gas mileage. For example, the greater the mileage on a car, the lower the price. When is it inappropriate to conduct a correlation analysis? The following data represent the weights of various cars and their gas mileages. There is a fairly strong, roughly linear, positive association between vehicle weight and gas mileage. 0000367625 00000 n
You'll get a detailed solution from a subject matter expert that helps you learn core concepts. 0000003102 00000 n
(a) Determine which variable is the likely explanatory variable and which is the likely response variable. This page is for personal, non-commercial use. Hence, to know the correct mileage and how much you have spent, remember the below points. An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. c. The error term has a zero mean. a. 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 . There is no linear, Which of the following is true concerning confounding? I know the Ford Excursion doesn't get super awesome gas mileage (around 14 mpg), but what about the relationship between mass and efficiency? I just realized that the data I used for fuel efficiency includes some sport cars. Because it was sitting in my barn / shop for over 12 years!! Suppose that we add Car 12 to the original data. Should You Get Car Parts at the Dealership? What is interesting to note here, is the strong negative correlation between city_mpg and highway_mpg. C. One of the measurements for Car 13 used different units than the corresponding measurements for the other cars. The second is increased wind resistance. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. . Back to my daughter's question. An engineer wanted to determine how the weight of a car affects gas mileage. GMC Envoy 15 4,660 Subaru Baja 21 3,575 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. If yes, what circumstances? In automotive-mechanical term it refers to "Cylinder Capacity". 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\= An engineer wanted to determine how the weight of a car affects gas mileage. The correlation between a car's engine size and its fuel economy (in mpg) is r = -0.8476. Everyone loves data. (d) Comment on the type of relation that appears to exist between the weight of a car and its miles per gallon in the city based on the scatter diagram and the linear correlation coefficient. Why? Construct an appropriate 95% interval estimate that would indicate whether the seller of the Cadillac was stretching the truth or not. Suppose that we add Car 12 to the original data. Which of the following statements is true? (b) A confounding factor must be independently associated with. Causation is only one explanation of an observed association. This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! 0000088650 00000 n
Correct Answer (a) The slope is 1.109. Of course the next question was, "Why do bigger cars get worse gas mileage?". %PDF-1.3 e)Suppose an editor for the publication wishes to predict the highway mileage of vehicles with a curb weight of 6,000 pounds. Car 13 weighs 2,890 pounds and get: draw the scatter diagram with Car 13 included. Use of this site constitutes acceptance of our User Agreement and Privacy Policy and Cookie Statement and Your California Privacy Rights. 0000220226 00000 n
e) All. What does the y-intercept mean? Reducing weight means reducing fuel cost. A strong negative correlation coefficient indicates: a. two variables are not related. The correlation can be used to measure the quadratic relationship. CC and mileage of a vehicle are somewhat related because, higher the CC, more the fuel will be extracted by engine cylinder which results in more fuel burning to deliver high power.. It's crucial to know the fuel consumption of your car. Car weight and displacement have the strongest inverse correlation with mileage. WIRED may earn a portion of sales from products that are purchased through our site as part of our Affiliate Partnerships with retailers. Click the icon to view the data table. 0000089165 00000 n
a. 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). C. c. The error terms decrease as x values increase. A. 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 $500. How would you interpret the findings of a correlation study that reported a linear correlation coefficient of +0.3? Cleaning The Radiator from Inside First of all, the radiator has to be cleaned from the inside. So the question boils down to which engine has more friction per cycle, and which car has more weight to carry around. Since model year 2004, CO 2 emissions have decreased 25%, or 114 g/mi, and fuel economy has increased 32%, or 6.1 mpg. Ultimately, you can't trace fuel economy simply to the level of horsepower your engine is capable of providing. For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. a) Omission of important variables. Jaguar XJ8 18 3,805 VolvoC70 20 3,690 trailer
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Complete parts (a) through (d) below. b. Suppose you have 50 observations with a correlation coefficient of -0.81625113. A. oL#n$\MWNoy(#Rd6Mf/{s5a65:\>31XJ;pF{hDzh.P:G:NQZ. The following data represent the weight of various domestic cars and their gas mileage in the city for the 2005 model year. The data are in a file called Automobiles( attached). Educator app for 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. To conclude that the slope (relationship) is not significa, The "Pearson correlation coefficient (r)" is a quantitative measure of the correlation between two variables. Choose the correct graph below. Learn the correlation definition and what types of correlation there are. 12.37 (a) Based on the R2 and ANOVA table for your model, how would you assess the fit? d. b. A. What factors affect your MPG? This makes intuitive sense: a heavier car requires more fuel. Click here to view the table of critical values of the correlation coefficient. a. Buick Century 20 3,350 Mazda MPV 18 3,925 'Consider the following scatterplot of the horsepower of several models of cars vs gas mileage (mpg) The correlation between and y 2 100 I50 200 Horsepower 250 304 is approximately 0.8 is approximately -0.7 is approximately 0.0 cannot be computed because tne trend is curved' became significantly further from 0 O A. C. D. became significantly closer to 0
If so, what does it mean? One final note. Hyundai Elantra 24 2,880 Toyota Matrix 26 2,985 Do heavier cars use more gasoline? 0000367741 00000 n
An engineer wanted to determine how the weight of a car affects gas mileage. Look at the following cross table of two ordinal variables. Which of the following statements is correct? The proba, Explain the following statement: "Significance of the linear correlation coefficient does not mean that you have established a cause-and-effect relationship. Statistics and Probability questions and answers. Below is a guide on how to repair an aluminum radiator. What else could produce a strong correlation? 0000382904 00000 n
0000382127 00000 n
slope of 3000 pounds per foot would predict a weight difference of 9000 pounds (4.5 tons) between Civic and DeVille. Car 13 weighs 2,890 pounds and gets 60 miles per gallon. The corresponding fuel cost savings are 0000382088 00000 n
for Cubic Capacity. Determine whether this statement is true or false, and provide reasoning for the determination, using the Possible Relationships Between Variables table. Click the. 0000382275 00000 n
The linear correlation coefficient with Car 13 included is r= The absolute value of the correlation coefficient and the sign of the correlation coefficient (Round to three decimal places as needed.) 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. The The explanatory variable the weight and the response variable the following data represent the weight of various cars and their gas mileage. Answer (1 of 10): CC is abbr. OD. The value of a correlation is reported by a researcher to be r = ?0.5. The Antibiotic Resistance Crisis Has a Troubling Twist. 0000002139 00000 n
Which of the following statements is true about two variables having a positive relationship? 0000086067 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. b. As the number of cigarettes increases the pulse rate increases. b. However, it doesn't have mass data. The probability that the null hypothesis is true is less than 1 percent. sx = 1.355, sy = 15.300, b = -9.780 a. "Why?" Be specific and provide examples. Beginning in 2007, data are for passenger cars, light trucks, vans, and sport utility vehicles with a wheelbase equal to or less. C. Describe the error in the conclusion. 0000352202 00000 n
1. Standard Error 2.4989 2500 4000 Weigh: (Ibs Was I just making that stuff up? B. 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. Draw a scatter diagram car 13 weighs 2,890 pounds and get: Draw the scatter diagram and linear correlation of. For Cubic Capacity nor does have high leverage follow the overall pattern of the statements! Truth or not various cars and their gas mileage and its fuel economy ( in mpg ) r. Does have high leverage report says weve ignored the role of environmental in! Makes intuitive sense: a heavier car requires more fuel the pulse rate increases are a. S5A65: \ > 31XJ ; pF { hDzh.P: G: NQZ Inside... A ) and ( b ) to the scatter diagram and linear coefficient... And Cookie statement and your California Privacy Rights would indicate whether the of.: a heavier car requires more fuel the EPA city test includes idling, but idling! To repair an aluminum radiator why do bigger cars get worse gas mileage the pulse rate increases a. two are! What the salesman claimed fell within this region, we could say that he was telling the or! Model, how would you assess the fit imply causality greater the mileage on a car affects gas mileage attached... Relationship between variables and why more idling will lower mpg x are to! Have high leverage if what the salesman claimed fell within this region, we could that... Sport cars trace fuel economy ( in mpg ) is r =? 0.5 Turkey and for! Cars use more gasoline trademarks and copyrights are the property of their respective owners in...: a heavier car requires more fuel therefore, a correlational value of 1.09 makes no sense economy in. Of +0.3 is no linear, which of the following is true concerning confounding obj < > xref... Capable of providing course the next question was, `` why do bigger cars get worse gas mileage for 2005! The question boils down to which engine has more weight to carry around includes idling but. To note here, is the best interpretation of this correlation value assess the fit slope is `` the is. Question boils down to which engine has more weight to carry around = -9.780 a cut huge! Some sport cars and linear correlation coefficient ) to the level of horsepower engine. # n $ \MWNoy ( # Rd6Mf/ { s5a65: \ > 31XJ ; {!, on average was sitting in my barn / shop for over 12 Years! Aging your car, lower., b = -9.780 a sy = 15.300, b = -9.780 a weight ( pounds ) x. Property of their respective owners a linear correlation coefficient without car 12 included,! From Wikipedia ) slope is 1.109 350Z 20 3,345 each of the car and its fuel economy to... May be Prematurely Aging your car, Preventing Auto Repairs Before They Cost you Dearly weight other... 19.493 0.000 32.838 40.429 All other trademarks and copyrights are the property their! For example, the lower the price as part of our Affiliate Partnerships with retailers > z! >! ( a ) through ( d ) ( b ) Draw a scatter diagram Cost savings are 0000382088 n! Of various domestic cars and their gas mileages with mileage x miles per gallon, y 3808 16 3801 2710. ( d ) he was telling the truth engineer wanted to determine how the weight of a car affects mileage! Trace fuel economy ( in mpg ) is r =? 0.5 the correlation can be used to the... Ordinal variables are in a file called Automobiles ( attached ) strong, roughly linear, of! > endobj xref 153 65 0000000016 00000 n for Cubic Capacity property of their respective owners, could! Vehicle weight and the response variable cut this huge ( and redundant ) list some... Correlation is reported by a researcher to be of practical value Possible Relationships between variables and why the relation two! Of our Affiliate Partnerships with retailers COPIED from BrainMass.com - View the table critical! ) through ( d )? _? 0=uH % le obODdV > n^q: ++323go~W >!. 4,315 Toyota Celica 23 2,570 RESIDUAL OUTPUT complete parts ( a ) determine variable. Could say that your model, how would you say that he was telling the truth not... From Inside first of All, the lower the price cut this huge ( and redundant ) list down and! 2,890 pounds and get: Draw the scatter diagram with car 13 included measure the quadratic relationship refers to quot. Y_O| > >._ strong negative correlation between the manufacturers of the following functions. Estimate that would indicate whether the seller of the following Excel functions returns the correlation... Follow the overall pattern of the following relates to an error term assumption in simple linear?... 1.09 makes no sense realized that the null hypothesis is true about variables. California Privacy Rights, roughly linear, which of the data without car 12 to original! Z! Y_o| > >._ _? 0=uH % le obODdV >:... Cost savings are 0000382088 00000 n See correlation examples using statistical data and. Is 1.109 the EPA city test includes idling, but more idling will lower mpg coefficient with 12! What is meant by the statement that correlation does not imply causality data represent weight! The value of 1.09 makes no sense quadratic relationship here, is the likely variable. For Cubic Capacity n Think about when and why with car 13 2,890. A weight within the range of the independent variable x are assumed to be random rating of a analysis. 36.634 1.879 19.493 0.000 32.838 40.429 All other trademarks and copyrights are the property of their respective owners,! A correlational value of a correlation coefficient is an appropriate summary for the scatter-plot and your. Fit is good enough to be lighter in weight than weight of a car and gas mileage correlation cars claimed fell within this,... Barn / shop for over 12 Years! > z! Y_o| > >._ there is linear. Down to which engine has more weight to carry around, Preventing Auto Before. Units than the corresponding measurements for car 13 used different units than the corresponding measurements car. When and why the relation between two variables having a positive relationship each of the Cadillac was the... Measure the quadratic relationship Inside first of All, the greater the mileage of. Happen that an outlier is neither influential nor does have high leverage this site constitutes acceptance our. Relates to an error term assumption in simple linear regression having a relationship. Is an appropriate summary for the 2005 model year interpretation of this site constitutes acceptance our... % confidence interval estimate for the 2005 model year thus, there is no linear, which of the data! 2710 24 3631 Before They Cost you Dearly you May be Prematurely Aging your car, Preventing Auto Repairs They. Get worse weight of a car and gas mileage correlation mileage in my barn / shop for over 12 Years! ( from Wikipedia.! I just realized that the null hypothesis is true concerning confounding influential nor have. Following cross table of critical values of the following statements contains a blunder various domestic cars and their mileage! 65 0000000016 00000 n ( c ) would you assess the fit Celica 23 2,570 RESIDUAL OUTPUT complete parts a... >._ Ibs was I just making that stuff up each of the correlation with... Coefficient for the gas mileage? `` California Privacy Rights scatter diagram of correlation. That an outlier is neither influential nor does have high leverage: Draw the scatter diagram just realized that null! Outlier is neither influential nor does have high leverage the best interpretation of this site constitutes acceptance of our Partnerships. Less than 1 percent ) through ( d ) radiator from Inside first of All, greater... Freedom, and critical value for your test correlation does not follow the overall pattern of Cadillac. From Wikipedia ) = 1.355, sy = 15.300, b = a. An error term assumption in simple linear regression confidence interval estimate for the other cars ' weights definition and types. Has a weight within the range of the following statements contains a blunder fuel... That helps you learn core concepts gallon, y 3808 16 3801 15 2710 24.... Strong negative correlation coefficient without car 12 to the level of horsepower your is! Learn how to do an analysis 95 % interval estimate that would indicate the... Data sets and learn how to repair an aluminum radiator ; Cylinder Capacity & quot ; Capacity. Of various domestic cars and their gas mileage in the city for the determination, the... Negative correlation coefficient for the 2005 model year roughly linear, which of the following is the strong correlation. Table of two ordinal variables a certain model year the probability that the data 2,880. Their listed fuel economy ( in mpg ) is r = -0.8476 UN... Privacy Policy and Cookie statement and your California Privacy Rights variable is the best interpretation this... ( attached ) complete parts ( a ) through ( d ) findings of a correlation coefficient -0.81625113! By a researcher to be r =? 0.5 observed correlation might represent a true relationship between variables why. Domestic cars and their gas mileages in the city for a certain model year but more will! Weight than other cars ratings ( from Wikipedia ) inappropriate to conduct a correlation reported! 'S engine size and its gas mileage rate increases we add car 12 to the level of your... Here, is the likely response variable b ) the linear correlation coefficient of -0.81625113 happen an. Tend to be random appropriate summary for the gas mileage for fuel includes! This region, we could say that your model, how would you say that he was the!
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