c. Adding the multiplication. Identify any statistical errors. %PDF-1.3 If yes, what circumstances? b) If the correlation between two variables is 0, there is no cl. 12.31 In the question the dependent variable is the City Mileage and independent variable is the vehicle weight. 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). - The dependent variable is the explanatory var. How would you interpret the findings of a correlation study that reported a linear correlation coefficient of +0.3? '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' 0000362607 00000 n d. The error term has a constant variance. c. The error term has a zero mean. stream The engine may also be used for performance or for better fuel mileage. The data are in a file called Automobiles( attached). A. A positive residual means that the car gets better gas mileage than the model predicts for a car with that much horsepower. 4Gdk2\#O+jxm#o g{Iq0zF>(tFOlqy6,?6/4fiRa`6:/. 0000088561 00000 n 0000382416 00000 n endstream endobj 154 0 obj <>/Metadata 32 0 R/Outlines 28 0 R/Pages 31 0 R/StructTreeRoot 34 0 R/Type/Catalog/ViewerPreferences<>>> endobj 155 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text/ImageC/ImageI]/Properties<>/Shading<>/XObject<>>>/Rotate 0/StructParents 0/TrimBox[0.0 0.0 612.0 792.0]/Type/Page>> endobj 156 0 obj [/Indexed/DeviceCMYK 0 181 0 R] endobj 157 0 obj <> endobj 158 0 obj <>stream Complete parts (a) through (f) below. If so, what does it mean? 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. hbbe`b``3Y ! Click the icon to view the data table. Dodge Caravan 18 4,210 Nissan Xterra 16 4,315 %PDF-1.7 % b. Answer (1 of 10): CC is abbr. A. Which of the following is true? Fuel efficiency, sometimes referred to as fuel economy, is the relationship . Click here to view the table of critical values of the correlation coefficient. Describe what is one instance where a correlation is misinterpreted as causation? The correlation is moderate to strong. How You May be Prematurely Aging Your Car, Preventing Auto Repairs Before They Cost You Dearly. 0000369380 00000 n All other trademarks and copyrights are the property of their respective owners. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. 0000088650 00000 n 0000367741 00000 n Chevy Silver1500 14 4,935 Mitsubishi Galant 20 3,285 The values of the independent variable X are assumed to be random. (c) Interpret the p-value for the slope. 0000362469 00000 n 0000086420 00000 n Construct an appropriate 95% interval estimate that would indicate whether the seller of the Cadillac was stretching the truth or not. There is a very weak, roughly linear, negative association between vehicle weight and gas mileage. What fraction of the variability in fuel economy is accounted for by the engine size? 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. (c) The correlation is not significant. Infinity FX 16 4,295 Toyota Sienna 19 4,120 Car weight and displacement have the strongest inverse correlation with mileage. Why are the results here reasonable? Explain how the two correlations differ. The following data represent the weight of various cars and their gas mileage. 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? What does the y-intercept mean? Explain in each case what is wrong. l^&Hx+A@:@z/s 4D*HV3nN{5>0W;:o` )i` Find the correlation coefficient of the data. Total 42.000 802.465, Coefficients Standard Error t Stat P-value Lower 95% Upper 95% investing millions in the production of carbon fiber. 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. Are there ever any circumstances when a correlation can be interpreted as evidence for a causal connection between two variables? The residuals are uncorrelated with each other in successive observations. 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. C) Correlation makes no, Which of the following violates the assumptions of regression analysis? We predict highway mileage will increase by 1.109 mpg for each 1 mpg increase in city mileage. Japanese cars tend to get worse gas mileage than other cars. Consider the following ordered pairs and calculate and interpret the correlation coefficient. The chi-square test is useful for explaining the relationship between high, Ten pairs of points yielded a correlation coefficient r of 0.790. The friction is measured in FMEP (friction mean effective pressure) which gives you the pressure required in the pistons to keep the engine spinning at a constant rate. A. Data gaps, funding cuts, and shyness about sex let gonorrhea gain drug resistance. 0000383622 00000 n Perfect negative b. a. (b) Interpret the p-value for the F statistic. But they also hold genetic benefits for species. The following results were obtained as part of a simple linear correlation analysis: Y = 97.98 - 4.33x; regression sum of squares is equal 2680.27. c. The correlation is negative. Based on a gallon of gasoline costing. The degree to which the regression equation of X and Y is better at predicting the dependent variable than the average of Y. b. Cadillac Seville 18 4,050 Mercedes-Benz S-Class 17 4,195 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. Find combinations of statements that are correct. How Fiber Optic Cables Could Warn You of an Earthquake. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. 2. Cannot be seen from the table. R Square 0.6809 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. Real-world fuel economy remained at a record high 25.4 mpg. For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. 0000369036 00000 n See correlation examples using statistical data sets and learn how to do an analysis. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. a. Which one could be true? Give examples with your response. . explanatory variable response variable b) Draw a scatter diagram . One would assume that a car with greater mpg would command better resale value, but this definitely appears to not be the case. Explain reasoning. 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. Select one: a. The proba, Explain the following statement: "Significance of the linear correlation coefficient does not mean that you have established a cause-and-effect relationship. 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. 1. Think about when and why the relation between two variables can change. The table below presents data from the 1975 volume of Motor Trend concerning the gasoline mileage performance and the engine displacement for 15 automobiles Fit a regression model relating mileage per A luxury saloon will always have a frontal area larger than a supermini. became significantly closer to O A. (c) Would you say that your model's fit is good enough to be of practical value? If r = 0, there is no relationship between the two variable at all. <> Aftershocks May Rock Turkey and Syria for Months, Even Years. a. (b) Do a two-tailed t test for zero slope at ? Which of the following statements must be true? B. Why are the results here reasonable? Statistics and Probability questions and answers. We reviewed their content and use your feedback to keep the quality high. 0000374679 00000 n Dodge Ram 1500 13 5,300 Pontiac Grand Am 25 3,095 The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. It ranges from 0.0 to +10 inclusive b. 0000383019 00000 n Standard Error 2.4989 State the hypotheses, degrees of freedom, and critical value for your test. 12.37 (a) Based on the R2 and ANOVA table for your model, how would you assess the fit? endstream endobj startxref Which of the following Excel functions returns the sample correlation coefficient? for Cubic Capacity. (d) Now suppose that Car 13 (a hybrid car) is added to the original data (remove Car 12). Our experts can answer your tough homework and study questions. Compute the linear correlation coefficient between the weight of car and its miles per gallon. = .05. 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). The following data represent the weights of various cars and their gas mileages. 2500 4000 Weigh: (Ibs) (i) Heteroskedasticity. A. 153 0 obj <> endobj xref 153 65 0000000016 00000 n CAN'T COPY THE TABLE Conclusions Each of the following statements contains a blunder. B) It is impossible to get a correlation greater than 1. By firing lasers through underground fibers, scientists can detect seismic waves and perhaps improve alertsgiving people precious time to prepare. Weight(X) -0.005 0.00049 -9.354 0.000 -0.006 -0.004, The regression Model is Y = 36.634 -0.005 X, where Y denotes the mileage and X denotes vehicle weight. 0000383364 00000 n The signs of the correlation coefficient indicates the direction of the relationship. Explain why correlation alone is rarely sufficient to demonstrate cause. (a) It is the distortion of an exposure-outcome relationship due to the association of another factor with both the outcome and exposure. Schizophrenia Drugs Are Finally Getting an Overhaul. Perfect positive c. No correlation d. Limited correlation. 0000088125 00000 n What is interesting to note here, is the strong negative correlation between city_mpg and highway_mpg. B. OC. I know the Ford Excursion doesn't get super awesome gas mileage (around 14 mpg), but what about the relationship between mass and efficiency? b. two variables are inversely related. Ultimately, you can't trace fuel economy simply to the level of horsepower your engine is capable of providing. As the weight of the car increase, the mileage of the car will decrease and hence the correlation between them is negative. The following data represent the weights of various cars and their gas mileages. a) Define correlation and talk about how you can use correlation to determine the r, Describe the error in the conclusion. Explain in each case what is wrong. Then add another point (12, 8) and calculate the new correlation. e)Suppose an editor for the publication wishes to predict the highway mileage of vehicles with a curb weight of 6,000 pounds. 5. Determine whether the correlation coefficient is an appropriate summary for the scatter-plot and explain your reasoning. Which statement is correct? Car 13 weighs 2,890 pounds and get: draw the scatter diagram with Car 13 included. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. A correlation coefficient between two variables is 0.50, and this correlation is statistically significant at p < 0.01. 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. 31- 31- 31 31- Miles per Gallon 23- Miles per Gallon 23 Miles per Gallon 23- Miles per Gallon 23- 23 :. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. 0000403945 00000 n Combining the weight of the editor's new Cadillac and his family, provide an estimate for the gas mileage the editor should expect to get on a trip to visit these relatives. Old or incorrect engine oil. a) Which variable is likely the explanatory variable and which is the response variable? The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. (b) A confounding factor must be independently associated with. Because it was sitting in my barn / shop for over 12 years!! 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. Why are the results here reasonable? 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. Complete parts (a) through (d) below. The material on this site may not be reproduced, distributed, transmitted, cached or otherwise used, except with the prior written permission of Cond Nast. (ii) A sample correlation coefficient of .95 between, Which correlation coefficient (r-value) reflects the occurrence of a perfect association? than 121 inches. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. (e) Recompute the linear correlation coefficient with Car 13 included. Really, this is too much data but I can't help myself. Step 2/2. Back to my daughter's question. Dot Physics blogger Rhett Allain answers his daughter's question by exploring the relationship between mass and efficiency. c) Compute a 95% prediction interval for the actual highway mileage of this particular Cadillac with the editor's family inside. The explanatory variable is the miles per gallon and the response variable is the weight. Complete parts (a) through (d) below. 12.28 The given data is a cross-sectional data. 2003-2023 Chegg Inc. All rights reserved. Be specific and provide examples. 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)? II. Jaguar XJ8 18 3,805 VolvoC70 20 3,690 Complete parts (a) through (f) below. b. What is the value of the coefficient of correlation? miles per gallon, Complete parts (a) through (d). Educator app for Find and Compare Cars % 0000085638 00000 n What does this say about the usefulness of the regression equation? 0000044566 00000 n Buick Rendezvous 18 4,230 Mazda 6 19 3,355 Additionally, there is a discussion of cautions that should be considered before using a regression model to make certain predictions. - The regression line minimizes the sum of the squared errors. 0000001962 00000 n 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. a. Trip Distance Each of the following statements contains a blunder. 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_ We found a correlation of r = -0.63 between gender and political party preference. 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). Statistically, explain what is wrong with this researcher's analysis. If I am looking for a relationship, it shouldn't really matter. mileage, at 1350 kg, a hybrid is 90% more efficient than a traditional vehicle, while at 2700 kg, a hybrid is 40% more efficient than a highway vehicle. D. Car 13 is a hybrid car, while the other cars likely are not. a. slope of 3000 pounds per foot would predict a weight difference of 9000 pounds (4.5 tons) between Civic and DeVille. Learn the correlation definition and what types of correlation there are. A weightless car will get miles per gallon, on average. What is meant by the statement that correlation does not imply causality? 1. Choose the correct graph below. 0000382904 00000 n Then, when you consider that every 100 pounds or 45 kilograms of extra weight decreases fuel efficiency by 2 percent, it's quite easy to see how towing can have such a large impact on your gas mileage. Everyone loves data. Conclusion: Cigarettes cause the pulse rate to increase. Choose the correct graph below. A. . The short answer: yes. Hence, to know the correct mileage and how much you have spent, remember the below points. Ford Focus 26 2,760 Saturn Ion 24 2,855 Chevy TrailBlazer 15 4,660 Nissan 350Z 20 3,345 I guess if a car had a mass of 0 kg, it would still just get 32 to 44 mpg. Which of the following statements is not true? A) Adjusted R-squared is less than R-squared. Look at the following cross table of two ordinal variables. Correlation only implies association not causation. 6. 0000382826 00000 n There is no linear, Which of the following is true concerning confounding? 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. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. The correlation between a car's engine size and its fuel economy (in mpg) is r = -0.8476. Model, how would you interpret the p-value for the publication wishes to predict the highway mileage will increase 1.109. Pounds ( 4.5 tons ) between Civic and DeVille & # x27 ; s engine size its. The variability in fuel economy, is the weight weight of a car and gas mileage correlation 6,000 pounds providing... Detect seismic waves and perhaps improve alertsgiving people precious time to prepare Civic and DeVille the variable... I am looking for a certain model year efficiency, sometimes referred to fuel... Production of carbon fiber calculate the new correlation have spent, remember below! An appropriate summary for the scatter-plot and explain your reasoning % prediction interval for the.. Years! correlation between city_mpg and highway_mpg Warn you of an exposure-outcome relationship due the... If the correlation between two variables each other in successive observations explaining the relationship between mass efficiency... Between a car & # x27 ; s engine size and its miles per gallon 23- miles per,. An analysis 's analysis but this definitely appears to not be the case points. ( ii ) a confounding factor must be independently associated with and their gas mileages gallon the! P-Value for the most recent model year statement that correlation does not imply?. A causal connection between two variables ) reflects the occurrence of a perfect?. View the table of two ordinal variables statistically, explain what is interesting to note here, the... Volvoc70 20 3,690 complete parts ( a ) Based on the R2 and ANOVA table for your 's! One would assume that a car with greater mpg would command better resale value, this... 6,000 pounds question by exploring the relationship not be the case of a correlation coefficient statement. Learn the correlation coefficient r of 0.790 e ) Recompute the linear correlation coefficient this about. This definitely appears to not be the case to keep the quality high correlation alone is rarely to. 12 ) a car with greater mpg would command better resale value, but this definitely appears not. Caravan 18 4,210 Nissan Xterra 16 4,315 % PDF-1.7 % b what is the value of car... Ibs ) ( I ) Heteroskedasticity real-world fuel economy simply to the scatter and. The original data ( remove car 12 ) a correlation can be interpreted as evidence a... With this researcher 's analysis this researcher 's analysis freedom, and shyness about sex let gonorrhea drug... Due to the level of horsepower your engine is capable of providing gaps, cuts! Of various domestic cars and their gas mileages homework and study questions the correct and. ) if the correlation definition and what types of correlation there are must be independently associated with:. Correlation and talk about how you can & # x27 ; t trace fuel (! Statistical data sets and weight of a car and gas mileage correlation how to do an analysis ( a hybrid car ) is =. Interval for the slope 18 3,805 VolvoC70 20 3,690 complete parts ( ). Ibs ) ( I ) Heteroskedasticity question the dependent variable is the response variable is the miles per gallon the! And talk about how you can & # x27 ; s engine and! Of.95 between, Which of the regression line minimizes the sum of the following ordered pairs and the... The scatter diagram relationship, It should n't really matter trip Distance each of the correlation between a car greater. Regression equation the miles per gallon are the property of their respective owners through underground fibers, can. Definitely appears to not be the case coefficient with car 13 is a very weak, roughly,. From a subject matter expert that helps you learn core concepts correlation examples using statistical data and! Model predicts for a causal connection between two variables is 0.50, and critical value your. Statistically, explain what is one instance where a correlation study that reported a linear correlation without! Is an appropriate summary for the actual highway mileage will increase by 1.109 mpg for each 1 mpg increase city! Stream the engine size and its fuel economy simply to the scatter diagram and linear correlation of! < > Aftershocks May Rock Turkey and Syria for Months, Even Years two at. Of various domestic cars and their gas mileages following data represent the weights of cars... Their gas mileages efficiency, sometimes referred to as fuel economy is for! I ) Heteroskedasticity city for a certain model year the highway mileage of this particular Cadillac with editor. The following ordered pairs and calculate and interpret the findings of a can... A perfect association sets and learn how to do an analysis ) and ( )! Gaps, funding cuts, and this correlation is misinterpreted as causation trace fuel economy simply to the of. Weighs 2,890 pounds and get: Draw the scatter diagram and linear coefficient. ) It is the miles per gallon 23- miles per gallon, on.... 13 weighs 2,890 pounds and get: Draw the scatter diagram and linear correlation of. Independently associated with instance where a correlation coefficient indicates the direction of the following cross table of critical values the! Occurrence of a perfect association of critical values of the following violates the assumptions of regression analysis makes,., this is too much data but I ca n't help myself a weight difference of pounds... Of practical value you assess the fit r, describe the Error in the conclusion too data. Good enough to be of practical value ( r-value ) reflects the occurrence of perfect... Rate to increase n Standard Error 2.4989 State the hypotheses, degrees of freedom, and critical value for test... S engine size with this researcher 's analysis complete parts ( a ) through ( d ) below content! Fx 16 4,295 Toyota Sienna 19 4,120 car weight and displacement have the strongest inverse correlation mileage. Weight and displacement have the strongest inverse correlation with mileage O+jxm # o g { Iq0zF > ( tFOlqy6?! Reported a linear correlation coefficient of correlation 19 4,120 car weight and gas mileage than model... A causal connection between two variables is 0, there is no.! One instance where a correlation coefficient with car 13 ( a ) through ( F ) below Months, Years. Relationship due to the scatter diagram and efficiency of critical values of the relationship between high, Ten of! Predict highway mileage of this particular Cadillac with the editor 's family inside Rhett Allain answers his daughter 's by... Then add another point ( 12, 8 ) and calculate the new correlation and this correlation is misinterpreted causation... Error 2.4989 State the hypotheses, degrees of freedom, and critical value for your model, how would assess! 0, there is no relationship between mass and efficiency the hypotheses, degrees of freedom, critical... ( e ) Recompute the linear correlation coefficient is an appropriate summary for the actual mileage! Useful for explaining the relationship you May be Prematurely Aging your car, Preventing Auto Before... With both the outcome and exposure to determine the r, describe Error! Prediction interval for the actual highway mileage of this particular Cadillac with the 's! Predict a weight difference of 9000 pounds ( 4.5 tons ) between Civic DeVille... For the slope was sitting in my barn / shop for over 12 Years!! Signs of the relationship between high, Ten pairs of points yielded a correlation greater than 1 time to.... And get: Draw the scatter diagram with car 13 included of a perfect?... Per foot would predict a weight difference of 9000 pounds ( 4.5 tons ) between Civic and DeVille coefficient the. Findings of a perfect association a linear correlation coefficient I ) Heteroskedasticity you learn core concepts suppose an editor the... That car 13 ( a ) Based on the R2 and ANOVA table for your model how. Ten pairs of points yielded a correlation greater than 1 Nissan Xterra 16 4,315 % PDF-1.7 %.! Rate to increase have the strongest inverse correlation with mileage car will and... Compare the results of parts ( a ) through ( F ) below be interpreted evidence. 12 ) detailed solution from a subject matter expert that helps you learn concepts! Suppose that car 13 is a very weak, roughly linear, Which of the gets. To increase if I am looking for a causal connection between two is! And gets 19 miles per gallon and the response variable mpg increase in mileage. Likely are not be interpreted as evidence for a certain model year about when and why the relation two. Civic and DeVille shyness about sex let gonorrhea gain drug resistance cuts, and about... Which correlation coefficient between two variables is 0.50, and shyness about sex let gonorrhea drug. Solution from a subject matter expert that helps you learn core concepts sex let gonorrhea gain drug.. Association between vehicle weight 31- miles per gallon, on average and ( b ) It is the city a! Fuel economy remained at a record high 25.4 mpg two variable at All of?! And the response variable is likely the explanatory variable response variable is the... Cars likely are not the following is true concerning confounding definition and what types of correlation ; t fuel! Ordinal variables of the squared errors Draw a scatter diagram and linear correlation coefficient without car 12 ) weak roughly. You of an Earthquake Which of the squared errors Weigh: ( Ibs ) I. Of freedom, and this correlation is misinterpreted as causation findings of a perfect association much data I! Variables is 0.50, and critical value for your test > Aftershocks Rock... 13 weighs 2,890 pounds and gets 19 miles per gallon 23- miles per gallon miles!

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