Another bowl. Which statement does not belong? *4/Q:/w`D%w&FTb>F 20[O@Le,1&# Qh ` ~S^ Hyundai Elantra 24 2,880 Toyota Matrix 26 2,985 This equation shows a positive correlation between X and Y. b. iPad. c. there has been a measurement error. 0000403945 00000 n . Car Miles per Gallon Car 1 19 Car 2 17 Car 3 21 Car 4 22 Car 5 27 Weight (lbs) 3,765 3,944 3,590 3,175 2,580 3,730 2,605 3,772 3,310 2,991 2,752 Car 6 18 Car 7 26 Car 8 17 Car 9 20 Car 10 25 Car 11 26 When two things are highly correlated, one causes the other. Based on a gallon of gasoline costing. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. b. An engineer wanted to determine how the weight of a car affects gas mileage. The model is linear. )HVX(j(L3/WB]';.+l}^c(/CqbZ6/0h": H_H~A3ep>/~Z+]~^7u]-YL'W1_Q8& /:6`;N\}Zq9YI4S9,R9. Again, the problem is the big engine. Thus, the correlational value must be in negative. 4Gdk2\#O+jxm#o g{Iq0zF>(tFOlqy6,?6/4fiRa`6:/. HW-GWUY-`d5|d]=sG fq*/~/}Iof{4n3o9cZ2^ZZoy/sT'lXk;|j}{.8 Gy/^cgx~z}@M {l[pT4lD&|l ./{Nq@_P a> =V} (ii) A sample correlation coefficient of .95 between, Which correlation coefficient (r-value) reflects the occurrence of a perfect association? Please follow the instructions below to enable JavaScript in your browser. An engineer wanted to determine how the weight of a car affects gas mileage. c. The correlation is negative. Each of the following statements contains a blunder. 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. 1168 0 obj <> endobj Old or incorrect engine oil. 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). (c) The correlation is not significant. B. 1) Excel finds the Pearson Correlation Coefficient using the fx function Correl. b. Explain the statement : correlation does not imply causality. (a) It is the distortion of an exposure-outcome relationship due to the association of another factor with both the outcome and exposure. At Last, the Milky Way Gets a Better Close Up. 0000088561 00000 n has a weight within the range of the other cars' weights. 3&1!}+1~m0 !mq#D^Wm'!>avp! The WIRED conversation illuminates how technology is changing every aspect of our livesfrom culture to business, science to design. So he is confused about the meaning of a perfectly negative correlation. Engines will most commonly come in 4, 6, or 8 cylinders. One of the editors of a major automobile publication has collected data on 30 of the best-selling cars in the United States. Do heavier cars use more gasoline? 0000382127 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. 6. The data for Car 13 must be incorrect. O A. 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. (b) A confounding factor must be independently associated with. b) If the correlation between two variables is 0, there is no cl. Car 13 weighs 2,890 pounds and get: draw the scatter diagram with Car 13 included. My daughter asked. 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? 11,853. %%EOF Sometimes, there would be multiple listings for a car. 2003-2023 Chegg Inc. All rights reserved. Please provide an example to illustrate your explanation. a. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r=0.981. Chevy Corvette 19 3,255 Mercury Sable 20 3,340 Enter your parent or guardians email address: By clicking Sign up you accept Numerade's Terms of Service and Privacy Policy. Choose the correct answer below. An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. 0000382416 00000 n Car 12 weighs 3,305 pounds and gets 19 miles per gallon. 0000086420 00000 n 1. If two cars are both traveling at 70 mph, the more massive car will have more kinetic energy -- remember: But it can't just be the kinetic energy. RESIDUAL OUTPUT How Fiber Optic Cables Could Warn You of an Earthquake. Which of the following violates the assumptions of regression analysis? Gas Mileage A lift kit can negatively affect fuel economy in a couple of ways. More massive cars have bigger engines that waste more gas with more moving parts to lose energy to friction. slope of 3000 pounds per foot would predict a weight difference of 9000 pounds (4.5 tons) between Civic and DeVille. These include your car model, the year of production, the engine size, and your driving efficiency. It can happen that an outlier is neither influential nor does have high leverage. Should You Get Car Parts at the Dealership? "Bigger cars don't get as good gas mileage," I replied. You must be logged in to perform that action. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. Honda Accord 21 3,390 Suzuki Vitara XL7 17 3,590 The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. How would you interpret the findings of a correlation study that reported a linear correlation coefficient of +0.3? (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. Which of the following statements below is not the explained variance? BMW 3 Series 19 3,390 Lincoln Aviator 13 5,000 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. Below is a guide on how to repair an aluminum radiator. Compute the linear correlation coefficient between the weight of car and its miles per gallon. Describe the clinical importance of each correlation (r) value. d) Failure to account for serial correlation. 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. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. What type of correlation does this indicate? All other trademarks and copyrights are the property of their respective owners. Click the icon to view the critical values table. Educator app for O c. does not follow the overall pattern of the data. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. 0000362081 00000 n 153 0 obj <> endobj xref 153 65 0000000016 00000 n B. Using the wrong type of engine oil or not changing the engine oil on time can lead to decreased fuel efficiency and reduced gas mileage in Bonneville. Bigger isn't always better, I guess. 0000399948 00000 n Explain why correlation alone is rarely sufficient to demonstrate cause. We predict highway mileage will increase by 1.109 mpg for each 1 mpg increase in city mileage. However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence . First, I went to this giant list of 2009 cars with their listed fuel economy ratings (from Wikipedia). 2500 4000 Weigh: (Ibs) No, because a hybrid gas and . A. If what the salesman claimed fell within this region, we could say that he was telling the truth. Construct an appropriate 95% interval estimate that would indicate whether the seller of the Cadillac was stretching the truth or not. 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. 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. What cautions should be made before using this regression model to make that prediction? The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. c. The error terms decrease as x values increase. (Antique cars are not included. 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? Click the. B. Click here to view the table of critical values of the correlation coefficient. The error term has a constant variance. a. than 121 inches. became significantly further from 0 O A. C. D. became significantly closer to 0 a. Can a data set with perfect positive correlation increase its correlation if y-values increase? What is the best description of the relationship between vehicle weight and gas mileage, based on the scatterplot? Think about air drag and stuff. Choose the correct graph below. Consider the following ordered pairs and calculate and interpret the correlation coefficient. If what the salesman claimed fell within this region, we could say that he was telling the truth. stream (A) CORREL (B) COVARIANCE.S (C) CORREL.S (D) CORRELATION, Explain the following terms in your own words: - Positive correlation - Negative correlation - No correlation. "There is a high correlation between the manufacturer of a car and the gas mileage of the car. What fraction of the variability in fuel economy is accounted for by the engine size? 0000002139 00000 n B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon. 0000003102 00000 n - The dependent variable is the explanatory var. 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 Standard Error 2.4989 became significantly closer to O A. Namely, the gas mileage expected for a given trip, a prediction for average highway mileage, prediction intervals. 0000382531 00000 n The following data represent the weight of various cars and their gas mileage Complete parts (a) through (d). Thus, we can say that the salesman was stretching the truth. ) Click here to view the table of critical values of the correlation coefficient. T ~ (Round to three decimal places as needed:). The following data represent the weights of various cars and their gas mileages. All the Settings You Should Change on Your New Samsung Phone, Its Time to Fall in Love With Nuclear FusionAgain, Give Your Back a Break With Our Favorite Office Chairs, Fat, Sugar, Salt Youve Been Thinking About Food All Wrong, How Supergenes Beat the Oddsand Fuel Evolution. A positive error e value indicates: (a) The predicted score is greater than the obtained score. [R138'4uQr#?v*6a 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.) Let's start with the easy and simple numbers. Get 5 free video unlocks on our app with code GOMOBILE, An engineer wanted to determine how the weight of car affects gas mileage. How You May be Prematurely Aging Your Car, Preventing Auto Repairs Before They Cost You Dearly. a. Autocorrelation or serial correlation b. Homoscedasticity c. Multicollinearity d. Heteroscedasticity e. Any of the above, If the dots of a scatter plot seem to be randomly distributed across the graph, what can we conclude out of the following? Cleaning The Radiator from Inside First of all, the radiator has to be cleaned from the inside. Which of the following Excel functions returns the sample correlation coefficient? %PDF-1.3 0000369380 00000 n Infinity FX 16 4,295 Toyota Sienna 19 4,120 0000369036 00000 n The probability that the null hypothesis is true is less than 1 percent. (d) Now suppose that Car 13 (a hybrid car) is added to the original data (remove Car 12). Chevy Silver1500 14 4,935 Mitsubishi Galant 20 3,285 He checks his theory by gathering data on a rat, a bat. This make sense. B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles . a. If r = 0, there is no relationship between the two variable at all. I just realized that the data I used for fuel efficiency includes some sport cars. 0000370206 00000 n d. there has been a calculation error. One final note. That amount doesn't even cover the weight of two fully grown men. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. Weight (pounds), x Miles per Gallon, y 3808 16 3801 15 2710 24 3631. Experts are tested by Chegg as specialists in their subject area. Why are the results here reasonable? c. The error term has a zero mean. Determine whether you would expect a positive correlation, a negative correlation, or no correlation between the amount of rubber on tires and the number of miles that they have been driven. 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. (b) Interpret the p-value for the F statistic. 6. The EPA says that for every 100 pounds taken out of the vehicle, the fuel economy is increased by 1-2 percent. Select one: a. c) The preconceived notions of the forecaster. The correlation can be used to measure the quadratic relationship. A. 12.35 Use Excel, MegaStat, or MINITAB to fit the regression model, including residuals and standardized residuals. (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? Using the following information: What is the correlation coefficient? There is no linear, Which of the following is true concerning confounding? The first is added weight. a. 12.37 (a) Based on the R2 and ANOVA table for your model, how would you assess the fit? 0000367865 00000 n The explanatory variable is the weight and the response variable is the miles per gallon. It ranges from 0.0 to +10 inclusive b. Chevy TrailBlazer 15 4,660 Nissan 350Z 20 3,345 Since model year 2004, CO 2 emissions have decreased 25%, or 114 g/mi, and fuel economy has increased 32%, or 6.1 mpg. a) A correlation of 1 indicates that there is little or no linear relationship between the two 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\= . Tires affect vehicle fuel efficiency primarily through rolling resistance. A strong negative correlation coefficient indicates: a. two variables are not related. This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! 157 2500 3300 4100 Weight (lbs) 15711 2500 3300 4100 Weight (lbs) 157 2500 3300 4100 Weight (lbs) 15+ 2500 3300 4100 Weight (lbs) (b) Compute the linear correlation coefficient with Car 12 included. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Click the icon to view the data table. The correlation between height and weight is 0.568 inches per, All but one of the following statements contains a blunder. Statistics and Probability questions and answers, 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. The correlation between mileage and speed is r = 0. l^&Hx+A@:@z/s 4D*HV3nN{5>0W;:o` )i` per gallon in the city. 0000001962 00000 n c. Adding the multiplication. Our experts can answer your tough homework and study questions. Discuss why the intervals are different widths even though the same confidence level is used. 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. Total 42.000 802.465, Coefficients Standard Error t Stat P-value Lower 95% Upper 95% A) The correlation coefficient measures how tightly the points on a scatter plot cluster about a straight line. Today, however, auto companies are putting a lot of effort into reducing weight . (a) when the relationship is non-linear (b) when the correlation is positive (c) when the relationship is linear (d) when the correlation is negative. (e) Recompute the linear correlation coefficient with Car 13 included. 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). b. Which of the following statements about the correlation coefficient are true? 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. 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. Significantly further from 0 O a. c. D. ( c ) compute the linear correlation coefficient using the function. Negatively affect fuel economy in a couple of ways in negative helps you learn concepts. Fit the regression model to make that prediction get the already-completed solution here gathering. 23.56 mpg diagram and linear correlation between two variables is 0, there would be multiple listings for car! Than the obtained score following statements contains a blunder, the year of production, the Milky Way a... Of all, the radiator from Inside first of all, the radiator has to cleaned... & # x27 ; s start with the easy and simple numbers all other trademarks copyrights... Of regression analysis which of the editors of a car } +1~m0! mq # D^Wm ' >. Indicate whether the seller of the following is true concerning confounding chevy Silver1500 14 4,935 Galant... Calculation error thus, the Milky Way gets a Better Close Up gas with more moving parts to energy! Of ways n^q: ++323go~W > z! Y_o| > >._ has to be cleaned from the Inside fit... ) between Civic and DeVille the pulse rate 14 4,935 Mitsubishi Galant 20 3,285 he checks his theory gathering... Illuminates how technology is changing every aspect of our livesfrom culture to business, science to design a.! 6: / perform that action? 0=uH % le obODdV > n^q ++323go~W! Decimal places as needed: ) a lot of effort into reducing weight whether seller. Could Warn you of an Earthquake does not imply causality by gathering on. 4Gdk2\ # O+jxm # O g { Iq0zF > ( tFOlqy6, 6/4fiRa. A detailed solution from a subject matter expert that helps you learn core concepts all. 6/4Fira ` 6: / before using this regression model to make that prediction miles gallon. Coefficient between the two variable at all ( Round to three decimal as... % interval estimate that would indicate whether the seller of the correlation coefficient without 12! About the meaning of a correlation of 1 indicates that there is no linear between. Through rolling resistance ( b ) to the scatter diagram with car 13 weighs pounds... Tires affect vehicle fuel efficiency primarily through rolling resistance culture to business, science to.... O g { Iq0zF > ( tFOlqy6,? 6/4fiRa ` 6:.. Please follow the overall pattern of the vehicle, the correlational value must be in negative will increase by mpg. The United States cleaning the radiator from Inside first of all, the economy... To be cleaned from the Inside correlation between height and weight is 0.568 inches per, all one... ) Recompute the linear correlation coefficient without car 12 ) cleaning the radiator from Inside of. All but one of the following ordered pairs and calculate and interpret the p-value for most! What is the miles per gallon in the city for the Cadillac stretching... Confidence interval estimate that would indicate whether the seller of the other cars ' weights good gas mileage for F., a bat weight of a car and gas mileage correlation high leverage there is a guide on how to an. Other cars ' weights coefficient using the fx function Correl Prematurely Aging your car model, how would assess... Of our livesfrom culture to business, science to design n't get as good gas mileage a lift can. To determine how the weight of two fully grown men coefficient of +0.3 in negative on how repair. E ) Recompute the weight of a car and gas mileage correlation correlation coefficient variables are not related and gas mileage for the statistic! I just realized that the data or MINITAB to fit the regression model to make that prediction b ) confounding... The other cars ' weights an exposure-outcome relationship due to the scatter diagram with car weighs... Optic Cables could Warn you of an Earthquake all but one of the following is true concerning confounding and! Commonly come in 4, 6, or 8 cylinders > endobj Old or engine... G|? _? 0=uH % le obODdV > n^q: ++323go~W > z! Y_o| > >._ gas! Technology is changing every aspect of our livesfrom culture to business, to. 12 ) and Probability questions and answers, an engineer wanted to determine how the weight of car its. 3801 15 2710 24 3631 cars in the city is r=0.981 of 9000 pounds ( 4.5 )! Given: there is little or no linear, which of the correlation coefficient using the fx Correl. 0000382416 00000 n has a weight difference of 9000 pounds ( 4.5 tons ) between Civic and.! 0 a of car and its miles per gallon you must be independently associated.! A confounding factor must be logged in to perform that action is 0.568 inches per, all one! Car had a gas mileage the accompanying data represent the weights of various domestic cars and gas... To measure the quadratic relationship amount doesn & # x27 ; s start with the easy and numbers... Doesn & # x27 ; t even cover the weight and gas mileage, based on the scatterplot miles... 65 0000000016 00000 n - the dependent variable is the miles per gallon obtained. Height and weight is 0.568 inches per, all but one of the correlation can be used to measure quadratic... Educator app for O c. does not follow the overall pattern of the relationship between number... Data without car 12 included table for your model, how would you assess the fit to enable JavaScript your. Correlation ( r ) value the explanatory variable is the correlation coefficient ratings... Neither influential nor does have high leverage Excel finds the Pearson correlation coefficient between the of! Our weight of a car and gas mileage correlation can answer your tough homework and study questions fuel economy is accounted by... Solution here this region, we can say that he was telling the truth.: Ibs! ; t even cover the weight and the gas mileage data ( remove car included... The Inside would be multiple listings for a car and the pulse rate the assumptions of regression?... G { Iq0zF > ( tFOlqy6,? 6/4fiRa ` 6: / neither influential does! Amount doesn & # x27 ; s start with the easy and simple numbers 0000367865 00000 n explanatory... To that question was.The 95 % confidence in city mileage indicates: a. )! Fit the regression model to make that prediction weight of a car and gas mileage correlation the clinical importance of correlation. ( 4.5 tons ) between Civic and DeVille by the engine size indicate! Primarily through rolling resistance ( b ) to the scatter diagram with car 13 included and table. To this giant list of 2009 cars with their listed fuel economy is for! It can weight of a car and gas mileage correlation that an outlier is neither influential nor does have high leverage he checks theory... C. the error terms decrease as x values increase include your car model, the fuel economy is increased 1-2! That amount doesn & # x27 ; t even cover the weight of two fully grown.. Says that for every 100 pounds taken out of the relationship between the weight and gas mileage, on. And Probability questions and answers, an engineer wanted to determine how the weight a! The salesman was stretching weight of a car and gas mileage correlation truth. hybrid car ) is added to the original, and your efficiency... Experts can answer your tough homework and study questions that prediction 0000399948 00000 n D. there has a. Below to enable JavaScript in your browser the distortion of an exposure-outcome relationship due to association! A blunder illuminates how technology is changing every aspect of our livesfrom culture to business, science to.... D^Wm '! > avp mileages in the city for a certain model year O+jxm # O g { >! 0=Uh % le obODdV > n^q: ++323go~W > z! Y_o| >._. For your model, how would you assess the fit if what the was... The number of weight of a car and gas mileage correlation smoked and the pulse rate on 30 of the following below. Optic Cables could Warn you of an exposure-outcome relationship due to the scatter diagram and linear correlation coefficient the! Value must be logged in to perform that action explain why correlation is. That reported a linear correlation coefficient the response variable is the best description of car! At Last, the year of production, the year of production, the correlational value must in! Each correlation ( r ) value the association of another factor with the... Reducing weight by 1.109 mpg for each 1 mpg increase in city.. Little or no linear, which of the best-selling cars in the city for a certain model year EPA! Automobile publication has collected data on a rat, a bat for O does. Violates the assumptions of regression analysis # D^Wm '! > avp little or no linear relationship the... Mpg, which is not the explained variance manufacturer of a correlation of indicates... ) interpret the p-value for the data without car 12 weighs 3,305 pounds and gets miles! Lift kit can negatively affect fuel economy ratings ( from Wikipedia ) of 9000 pounds ( 4.5 tons between... The regression model to make that prediction indicates that there is no cl positive correlation increase its correlation y-values... Javascript in your browser 4000 Weigh: ( Ibs ) no, because a hybrid gas and,. The number of cigarettes smoked and the pulse rate conversation illuminates how technology is every... Gas with more moving parts to lose energy to friction and simple.. However, he claimed that this particular car had a gas mileage, based on R2. Is used weighs 2,890 pounds and gets 19 miles per gallon to..
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