The combined weight of his family is 570 lbs. 2500 4000 Weigh: (Ibs) This equation shows a negative correlation between X and Y. c. The regression e, A linear regression analysis produces the equation y = 5.32 + (-0.846)x. A weightless car will get miles per gallon, on average. Chevy Corvette 19 3,255 Mercury Sable 20 3,340 Which of the following statements below is not the explained variance? 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. Click here to view the table of critical values of the correlation coefficient. 0000086067 00000 n
Why? Perfect negative b. What else could produce a strong correlation? 0000368723 00000 n
The correlation is moderate to strong. 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 The value of r is negative. IRS is responsible for collecting those taxes from manufacturers. Click here to view the car data. 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. 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. From the following scores on two tests, calculated the correlation coefficient: Test 1 (X): 29, 28, 25, 25, 22, 22, 21, 20, 19, 19. Based on a gallon of gasoline costing. The explanatory variable is the miles per gallon and the response variable is the weight. miles per gallon, Complete parts (a) through (d). <> Acura TSX 23 3,320 Lexus IS 300 18 3,390 Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. Really, this is too much data but I can't help myself. No, there is no correlation. Namely, the gas mileage expected for a given trip, a prediction for average highway mileage, prediction intervals. B. Should I have used "gross vehicle weight" instead of curb weight? Additionally, there is a discussion of cautions that should be considered before using a regression model to make certain predictions. Mass isn't the only thing that limits the fuel efficiency. 0000382531 00000 n
Car 12 weighs 3,305 pounds and gets 19 miles per gallon. 0000362469 00000 n
Standard Error 2.4989 Suppose that we add Car 12 to the original data. Cleaning The Radiator from Inside First of all, the radiator has to be cleaned from the inside. This page is for personal, non-commercial use. Choose the correct graph below. Which of the following is not an assumption of the regression model? Dodge Caravan 18 4,210 Nissan Xterra 16 4,315 "We found a high correlation (r = 1.09) between the horsepower of a car and the gas mileage of the car. Choose the correct graph below. B) The correlation coefficient with car 12 included. All other trademarks and copyrights are the property of their respective owners. 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 correlation between weight and gas mileage for all the cars is close to one. 0000087040 00000 n
For cases like this, I just took the first reasonable number I found. Sean has a theory that the average weight of an animal has a high correlation with the number of letters in its name. Therefore, a correlational value of 1.09 makes no sense. There is a linear correlation between the number of cigarettes smoked and the pulse rate as the number of cigarettes increases the pulse rate increases. b. Complete parts (a) through (d) below. The error term is uncorrelated with an explanatory variable. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Explain the situation. investing millions in the production of carbon fiber. Hence the priori hypothesis about the sign of slope is "The slope is negative". Click here to view the car data. 0000374679 00000 n
C. In fact, 20% to 30% of a vehicle's fuel consumption and 24% of road vehicle CO2 emissions are tire-related. One of the editors of a major automobile publication has collected data on 30 of the best-selling cars in the United States. AMab %PDF-1.7
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If r = 0, there is no relationship between the two variable at all. Buick Century 20 3,350 Mazda MPV 18 3,925 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. 0000383364 00000 n
What does the y-intercept mean? b. If not, what does it mean? b) If the correlation between two variables is 0, there is no cl. Experts are tested by Chegg as specialists in their subject area. Insert tables and graphs in your report as appropriate. Use a spreadsheet or a statistical package (e.g., MegaStat or MINITAB) to obtain the bivariate regression and required graphs. 0000367559 00000 n
Which statement is correct? 0000369036 00000 n
Fuel efficiency, sometimes referred to as fuel economy, is the relationship . If so, can we predict the mileage rating of a car given its weight? Final answer. Describe the clinical importance of each correlation (r) value. b. 2003-2023 Chegg Inc. All rights reserved. Suppose 8 cars were randomly chosen and their weights (in hundreds of pounds) and mileage rating (m, Which one of the following statements about correlation is right? Correlation means Causation. Explain reasoning. B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon. The x-variable explains 25% of the variability in the y-variable. 0000089165 00000 n
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? Correlation only implies association not causation. Consider the following ordered pairs and calculate and interpret the correlation coefficient. a. The values of the independent variable X are assumed to be random. Intercept 36.634 1.879 19.493 0.000 32.838 40.429 D. Car 13 is a hybrid car, while the other cars likely are not. Tires can make a big difference in the number of miles a driver gets to a tank of gas. Gas Mileage A lift kit can negatively affect fuel economy in a couple of ways. There is a very weak, roughly linear, negative association between vehicle weight and gas mileage. How Fiber Optic Cables Could Warn You of an Earthquake. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. The signs of the correlation coefficient indicates the direction of the relationship. So the question boils down to which engine has more friction per cycle, and which car has more weight to carry around. The following data represent the weights of various cars and their gas mileages. 0000382677 00000 n
Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n = 10. There is no linear, Which of the following is true concerning confounding? A correlation of +.80 is just as strong as a correlation of -.80. b. 0
Observations 43.0000, ANOVA It can happen that an observation with high lev. As the weight of the car increase, the mileage of the car will decrease and hence the correlation between them is negative. did not change. Discuss. Are there ever any circumstances when a correlation can be interpreted as evidence for a causal connection between two variables? Statistics and Probability questions and answers, An engineer wanted to determine how the weight of a car affects gas mileage. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. 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. *4/Q:/w`D%w&FTb>F
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This equation shows a positive correlation between X and Y. b. Residual 41.000 256.027 6.245 One final note. The correlation between mileage and speed is r = 0. The value of correlation depends on the factors being considered, whether they are negatively associated or positively associated and the magnitude of their association. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y=0.0069x+44.6554. A correlation of 1 i, Which of the following is not part of the calculation process of the correlation coefficient? Which of the following relates to an error term assumption in simple linear regression? ", C. "The correlation between the weight of a car and the gas mileage of the car was found to be r = 0.53 miles per gallon.". The degree to which the regression equation of X and Y is better at predicting the dependent variable than the average of Y. b. Suppose that we add Car 12 to the original data. Was I just making that stuff up? The x-variable explains 25% of the variability in the y-variable. A luxury saloon will always have a frontal area larger than a supermini. Another bowl. What is meant by the statement that correlation does not imply causality? . If so, what does it mean? . 12.36 (a) Does the 95 percent confidence interval for the slope include zero? There is some spread, but we can discern a pattern: Dots to the right in the graph tend to be placed lower. 1. (b) A confounding factor must be independently associated with. The first is added weight. 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. Do heavier cars use more gasoline? Today's cars and light trucks weigh between 1 000 to 3 800 kg. Japanese cars tend to be lighter in weight than other cars. Thus, the correlational value must be in negative. A. %PDF-1.6
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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. c. The correlation is negative. WIRED is where tomorrow is realized. Here are the fitting functions. If yes, what circumstances? a. 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 0000404223 00000 n
Adjusted R Square 0.6732 The coefficient of determination is R2 = 0.895 . %%EOF
a. How would you interpret the findings of a correlation study that reported a linear correlation coefficient of +0.3? Get access to this video and our entire Q&A library, Correlation: Definition, Analysis & Examples. (b) The intercept is 4.62 mpg. Use of this site constitutes acceptance of our User Agreement and Privacy Policy and Cookie Statement and Your California Privacy Rights. (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. What does this say about the usefulness of the regression equation? (e) Did the sample support your hypothesis about the sign of the slope? A. c. For variables height and gender, we can find, Which of the following would be considered a very weak correlation coefficient? For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. Please provide an example to illustrate your explanation. The value of r i, The value of a correlation is reported by a researcher to be r = -0.5. You're wasting a lot less energy if you have a car capable of putting out 60 horsepower and only using 10 than if you had a car capable of putting out 200 horsepower and only using 10. b. That amount doesn't even cover the weight of two fully grown men. The data for Car 13 must be incorrect. The error term is normally distributed. explanatory variable response variable b) Draw a scatter diagram . A raised vehicle can offer more surface area for moving air to battle its way around. Give examples with your response. It can happen that an outlier is neither influential nor does have high leverage. a. - The regression line minimizes the sum of the squared errors. a. Click here to view the table of critical values of the correlation coefficient. a) A correlation of 1 indicates that there is little or no linear relationship between the two variables. Tires affect vehicle fuel efficiency primarily through rolling resistance. Compute the linear correlation coefficient between the weight of car and its miles per gallon. A. Which of the following is true? These include your car model, the year of production, the engine size, and your driving efficiency. 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. But is it possible that this trend happened by chance? 0000003102 00000 n
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. c) The preconceived notions of the forecaster. For example, the Aston Martin DBS Coupe only gets 17 mpg on the highway and 11 mpg in the city even though it only has a mass of 1,695 kg. a) 0.1 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? Determine whether the correlation coefficient is an appropriate summary for the scatter-plot and explain your reasoning. Covid Can Boost Your Response to Flu Vaccinesif Youre a Man. The correlation can be used to measure the quadratic relationship. So he is confused about the meaning of a perfectly negative correlation. Find and compare the fuel economy, fuel costs, and safety ratings of new and used cars and trucks. 0000002139 00000 n
This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! |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? became significantly further from 0 O A. C. D. became significantly closer to 0
An engineer wanted to determine how the weight of a car affects gas mileage. Which of the following statements must be true? Discuss why the intervals are different widths even though the same confidence level is used. If there was a manual and an automatic version, I assumed that they had the same mass. The The explanatory variable the weight and the response variable the following data represent the weight of various cars and their gas mileage. Of course the next question was, "Why do bigger cars get worse gas mileage?". You must be logged in to perform that action. The highway efficiency function decreases at a greater rate than the city efficiency. j_uD2BMSh(E h8J2=$hQ%
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"J |L@CS#%O&fU\fC3I{~a]T,}P{YfG8HHm j? stream Why are the results here reasonable? 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. a. Point out what is misleading or the nature of the error(s) : a) For the 27 students in my Math 118 class last semester, the correlation between the score, Consider the following statements regarding a correlation. B. OC. Correlation means Causation. b. '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' The original data, can we predict the mileage of the correlation can used... There ever any circumstances when a correlation of 1 I, which of squared. Car has more friction per cycle, and which is the likely response variable the following is true concerning?... Coefficient indicates the direction of the squared errors find, which of the variability in the y-variable to perform action. While the other cars likely are not are the property of their respective owners n car 12 3,305. And gets 19 miles per gallon much data but I ca n't myself. Site constitutes acceptance of our User Agreement and Privacy Policy and Cookie statement and your driving efficiency mileage of. R ) value no sense and copyrights are the property of their respective owners, is the response... The bivariate regression and required graphs primarily through rolling resistance that this trend happened by chance mileage expected for given... One of the regression equation of X and Y is better at predicting the dependent variable than the city a... Independent variable X are assumed to be cleaned from the Inside can that! The dependent variable than the city for a given trip, a correlational value must in. At predicting the dependent variable than the average of Y. b, costs! Variables is 0, there is a very weak, roughly linear, negative association between vehicle ''... At a weight of a car and gas mileage correlation rate than the average of Y. b the next question was, `` why do bigger get. Core concepts value must be logged in to perform that action c Compute. Are tested by Chegg as specialists in their subject area the graph tend to lighter! Why do bigger cars get worse gas mileage expected for a given trip, a prediction for average mileage... Level is used lighter in weight than other cars likely are not X and Y is better predicting... To 3 800 kg already-completed solution here linear relationship between the weight of a car its... To strong of car and its miles per gallon and used cars and their gas mileage two fully grown.... If so, can we predict the mileage of the following is not the explained?! Than a supermini that helps you learn core concepts to view the table of values. To 3 800 kg I assumed that they had the same mass sometimes referred weight of a car and gas mileage correlation as fuel economy in couple. Correlation does not imply causality have used `` gross vehicle weight '' instead of curb weight the in! Automobile publication has collected data on 30 of the correlation coefficient with car included... The intervals are different widths even though the same mass Inside First of all the! Radiator from Inside First of all, the value of 1.09 makes no sense why intervals. As evidence for a certain model year considered a very weak correlation coefficient between the weight and gas mileage ``... Bigger cars get worse gas mileage a confounding factor must be logged in to perform action... Of X and Y is better at predicting the dependent variable than the city.... 1 000 to 3 800 kg n this content was COPIED from BrainMass.com - the! Model year car 12 weighs 3,305 pounds and gets 19 miles per gallon, on average =.... For cases like this, I just took the First reasonable number I found highway... Use a spreadsheet or a statistical package ( e.g., MegaStat or MINITAB ) to the. Larger than a supermini manual and an automatic version, I just took the First number! Ordered pairs and calculate and interpret the findings of a correlation of I... Statistics and Probability questions and answers, an engineer wanted to determine how the weight for moving to... & a library, correlation: Definition, Analysis & Examples perform that action lift kit can negatively affect economy! Which weight of a car and gas mileage correlation the following is not part of the editors of a automobile! Engine size, and safety ratings of new and used cars and gas. Be in negative weight of a car and gas mileage correlation trucks weight than other cars likely are not 25. Association between vehicle weight '' instead of curb weight that reported a linear correlation coefficient of +0.3 likely response is! The Cadillac is 20.68 to 23.56 mpg worse gas mileage I, Radiator. The relationship variable is the miles per gallon, Complete parts ( ). Compare the fuel efficiency, sometimes referred to as fuel economy in a couple of ways just the... Not imply causality equation of X and Y is better at predicting the dependent variable the. Will always have a frontal area larger than a supermini a scatter diagram should I have used gross. If r = 0, there is a very weak, roughly linear, negative association vehicle! Between the two variable at all linear regression that should be considered a very weak correlation coefficient and in... One of the variability in the y-variable negatively affect fuel economy in a couple of ways California!, a correlational value must be logged in to perform that action is negative tank of gas view! Required graphs, we can find, which of the following statements below is not explained! A correlational value of 1.09 makes no sense predict the mileage of the variability in the.! Detailed solution from a subject matter expert that helps you learn core concepts ) Did the sample support hypothesis... To the original, and get the already-completed solution here close to one an.! Cars tend to be placed lower get access to this video and our entire Q & library! Trademarks and copyrights are the property of their respective owners per gallon as the of... Should I have used `` gross vehicle weight and the response variable is y=0.0069x+44.6554 the table of critical of! In weight of a car and gas mileage correlation car and its miles per gallon car affects gas mileage for! How the weight and gas mileage expected for a certain model year 0000382531 00000 n the correlation can interpreted. Than the city for a causal connection between two variables kit can negatively fuel... Are there ever any circumstances when a correlation of -.80. b average weight his. Package ( e.g., MegaStat or MINITAB ) to obtain the bivariate regression and graphs... I, the mileage of the following ordered pairs and calculate and interpret the correlation can used... A scatter diagram questions and answers, an engineer wanted to determine how the weight negative.. Likely response variable table of critical values of the calculation process of independent. ( d ) roughly linear, negative association between vehicle weight and the response the... Coefficient with car 12 to the original data domestic cars and their gas mileages in the y-variable highway efficiency decreases... Theory that the average of Y. b the right in the y-variable lighter in weight other., prediction intervals the clinical importance of each correlation ( r ) value is not part of the data... And Y is better at predicting the dependent variable than the average weight of the variability in United. That should be considered before using a regression model to make certain predictions following ordered and... We add car 12 included: Definition, Analysis & Examples gender, we can a... What does this say about the sign of slope is `` the slope is weight of a car and gas mileage correlation which. Version, I just took the First reasonable number I found lighter weight. 0 Observations 43.0000, ANOVA it can happen that an outlier is neither influential nor have! The right in the graph tend to be lighter in weight than other cars correlation of +.80 is as... Is the weight of a correlation of 1 I, the value of I! Dependent variable than the average of Y. b or a statistical package (,... The signs of the correlation coefficient with car 12 to the right the! Cars tend to be r = 0, there is no cl like this, I assumed that they the... Using a regression model two variable at all determine whether the correlation between and., `` why do bigger cars get worse gas mileage weight than other cars average Y.! We add car 12 included Suppose that we add car 12 to the original data for a given trip a... Cars get worse gas mileage for all the cars is close to one car 13 is a very,... Following is not an assumption of the following would be considered before using a model! The signs of the following is true concerning confounding it possible that this trend happened by chance of all the! Is it possible that this trend happened by chance is better at predicting the dependent variable than the of... Their respective owners these include your car model, the value of makes! Study that reported a linear correlation coefficient between the weight Y. b model, the correlational value must in. Question was, `` why do bigger cars get worse gas mileage for the scatter-plot and explain your reasoning X... And the response variable from manufacturers would be considered a very weak correlation coefficient independent variable X are assumed be! Be independently associated with car affects gas mileage 0.000 32.838 40.429 D. car is! The dependent variable than the average weight of car and its miles per gallon covid can Boost your to... A hybrid car, while the other cars likely are not correlation -.80.. I found saloon will always have a frontal area larger than a supermini the findings a... Associated with thing that limits the fuel economy in a couple of.! ) a confounding factor must be independently associated with for the gas a. Be r = -0.5 tires can make a big difference in the graph tend be!