. 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? 0000089897 00000 n As x increases, y decreases, and the correlation coefficient must be positive. He claimed that this particular car got 29 mpg. A coefficient of correlation equal to -0.78 shows: a. a strong correlation b. a weak correlation c. a moderate correlation d. r value is invalid, If the error (or residual) terms are correlated within themselves, we would find a Blank. (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? Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distributions under H_0)? One would assume that a car with greater mpg would command better resale value, but this definitely appears to not be the case. Explain the statement : correlation does not imply causality. 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) Define correlation and talk about how you can use correlation to determine the r, Describe the error in the conclusion. All rights reserved. a. d. The error terms are independent. What is meant by the statement that correlation does not imply causality? A correlation coefficient between two variables is 0.50, and this correlation is statistically significant at p < 0.01. The following data represent the weight of various cars and their gas mileage Complete parts (a) through (d). Answer (1 of 10): CC is abbr. Intercept 36.634 1.879 19.493 0.000 32.838 40.429 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. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. <> Here is data showing both the highway and the city fuel economy versus car mass. 0000088713 00000 n Suppose that the correlation r between two quantitative variabloes was found to be r=1. The following data represent the weights of various cars and their gas mileages. A correlation of 1 i, Which of the following is not part of the calculation process of the correlation coefficient? 0000370206 00000 n b. The short answer: yes. 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). Tires affect vehicle fuel efficiency primarily through rolling resistance. A. 0000362028 00000 n b) Incorrect model specification. A strong negative correlation coefficient indicates: a. two variables are not related. Total 42.000 802.465, Coefficients Standard Error t Stat P-value Lower 95% Upper 95% ", Which of the following would not be a correct interpretation of a correlation of r = 0.35 a) There exists a weak relationship between variables. Statistics and Probability questions and answers. Ford Expedition 13 5,900 Pontiac Vibe 28 2,805 [R138'4uQr#?v*6a for Cubic Capacity. A. Here are the fitting functions. critical values for the correlation coefficient (a . Infinity FX 16 4,295 Toyota Sienna 19 4,120 (A) CORREL (B) COVARIANCE.S (C) CORREL.S (D) CORRELATION, Explain the following terms in your own words: - Positive correlation - Negative correlation - No correlation. - The dependent variable is the explanatory var. Back to my daughter's question. The error term has a constant variance. How did this new value affect your result? 2003-2023 Chegg Inc. All rights reserved. e) All. c) The preconceived notions of the forecaster. RESIDUAL OUTPUT Car 13 weighs 2,890 pounds and get: draw the scatter diagram with Car 13 included. Are there ever any circumstances when a correlation can be interpreted as evidence for a causal connection between two variables? 0000362642 00000 n There is a negative correlation between x and y. b. The degree to which the regression equation of X and Y is better at predicting the dependent variable than the average of Y. b. (e) Did the sample support your hypothesis about the sign of the slope? did not change significantly Choose the correct answer below. 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 did not change. Schizophrenia Drugs Are Finally Getting an Overhaul. 0000086067 00000 n The material on this site may not be reproduced, distributed, transmitted, cached or otherwise used, except with the prior written permission of Cond Nast. 12.37 (a) Based on the R2 and ANOVA table for your model, how would you assess the fit? WIRED may earn a portion of sales from products that are purchased through our site as part of our Affiliate Partnerships with retailers. 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\= There is a very weak, roughly linear, negative association between vehicle weight and gas mileage. Which one could be true? Click here to view the car data. The Antibiotic Resistance Crisis Has a Troubling Twist. The values of the independent variable X are assumed to be random. C. 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. Today, however, auto companies are putting a lot of effort into reducing weight . The x-variable explains -25% of the variability in the y-variabl, The value of a correlation is reported by a researcher to be r = - 0.5. b. %PDF-1.6 % 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. 0000385398 00000 n Which of the following statements about the correlation coefficient are true? 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. 10 20 30 40 Mileage (mpg) 2,000 3,000 4,000 5,000 Weight (lbs.) stream An engineer wanted to determine how the weight of a car affects gas mileage. II. 0000367230 00000 n a. 0000362607 00000 n The EPA city test includes idling, but more idling will lower MPG. As x increases, y decreases, and the correlation, Which of the following is the best example of the potential issues associated with multicollinearity? *4/Q:/w`D%w&FTb>F 20[O@Le,1&# Qh ` ~S^ We are not mentioning the basic formula of getting the car mileage by dividing the number of kms by the quantity of fuel used, but a lot more than that through which you can smartly check the fuel efficiency. (d) The correlation is significant. . A) The correlation coefficient measures how tightly the points on a scatter plot cluster about a straight line. Briefly explain when an observed correlation might represent a true relationship between variables and why. Dot Physics blogger Rhett Allain answers his daughter's question by exploring the relationship between mass and efficiency. b. hbbd``b`v@"@CH `q3 $50&F% M & Suppose you have 50 observations with a correlation coefficient of -0.81625113. More massive cars have bigger engines that waste more gas with more moving parts to lose energy to friction. Which of the following statements below is not the explained variance? BrainMass Inc. brainmass.com December 16, 2022, 5:45 am ad1c9bdddf, Plug-In Hybrid Gasoline-Electric Vehicles, Multiple Regression Equation: Example Problems. All rights reserved. Which of the following statements is not true about regression models? c. Adding the multiplication. . Weight (pounds), x Miles per Gallon, y 3808 16 3801 15 2710 24 3631. Chrysler Pacifica 17 4,660 Nissan Pathfinder 15 4,270 Clearly, it is reasonable to suppose a cause and effect relationship as follows: An increase in the vehicle weight produces a decrease of mileage. C. One of the measurements for Car 13 used different units than the corresponding measurements for the other cars. Complete parts (a) through (f) below. Explain in each case what is wrong. My daughter asked. this giant list of 2009 cars with their listed fuel economy ratings. Conclusion: Cigarettes cause the pulse rate to inc, What's wrong with these statements? I think also, more massive cars generally have bigger cross-sectional areas leading to more air drag. Sean has a theory that the average weight of an animal has a high correlation with the number of letters in its name. AMab 0000369036 00000 n What does this say about the usefulness of the regression equation? Based on a gallon of gasoline costing. Which of the following is not an assumption of the regression model? Do the same for a car with city mileage 28 mpg. b. I made the off-hand comment that it wouldn't be fun to fill that sucker up. The x-variable explains 25% of the variability in the y-variable. Consider the following ordered pairs and calculate and interpret the correlation coefficient. B. %PDF-1.3 2500 4000 Weigh: (Ibs) 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? A) Adjusted R-squared is less than R-squared. A weightless car will get miles per gallon, on average. Was I just making that stuff up? The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. I. What is meant by the statement that correlation does not imply causality? miles per gallon, Complete parts (a) through (d). (b) The intercept is 4.62 mpg. Car 13 weighs 2,890 pounds and gets 60 miles per gallon. hb``e``AXX80,,tqq$,d%0h Idt4[ m`e(>W2v11y21d` i'c G&tS,XD&hV3132D231233,!!!AH Zlb !O2l4#x i&?`Nm.#D @ t:L endstream endobj 216 0 obj <>/Filter/FlateDecode/Index[34 119]/Length 27/Size 153/Type/XRef/W[1 1 1]>>stream FMEP times volume = Power per cycle needed to fight friction. Thus, the correlational value must be in negative. The best fit line is y = -6.93x + 43.1 where x is the weight of the car in thousands of pounds and y is the gas mileage in miles per gallon. a. 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. For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. T ~ (Round to three decimal places as needed:). Be specific and provide examples. State the hypotheses, degrees of freedom, and critical value for your test. The error term is uncorrelated with an explanatory variable. 0000264738 00000 n The signs of the correlation coefficient indicates the direction of the relationship. 0.9184 b. Complete parts (a) through (d) below. a. "We found a high correlation (r = 1.09) between the horsepower of a car and the gas mileage of the car." 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." 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) The obtained score is greater than the predicted score. We predict highway mileage will increase by 1.109 mpg for each 1 mpg increase in city mileage. 1 Through 2006, data are for passenger cars (and, through 1989, for motorcycles). 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. B) The correlation coefficient with car 12 included. Compute the linear correlation coefficient between the weight of car and its miles per gallon. (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. But is it possible that this trend happened by chance? Using Data set 'G', choose the dependent variable (the response variable to be 'explained') and the independent variable (the predictor or explanatory variable) as you judge appropriate. The model is linear. Why are the results here reasonable? 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 0000133335 00000 n 0000382127 00000 n has a weight outside the range of the other cars' weights. Explain why correlation alone is rarely sufficient to demonstrate cause. Educator app for a. 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. 6 0 obj Describe the clinical importance of each correlation (r) value. However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence interval. Why? Correlation means Causation. Think about air drag and. B. OC. What type of correlation does this indicate? I should have known it wouldn't stop there. (i) Heteroskedasticity. B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. 12.35 Use Excel, MegaStat, or MINITAB to fit the regression model, including residuals and standardized residuals. The data are in a file called Automobiles( attached). 5. 0000360698 00000 n Covid Can Boost Your Response to Flu Vaccinesif Youre a Man. Which of the following statements is not true? 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. "We found a high correlation (r = 1.09) between the horsepower of a car and the gas mileage of the car. 0000085638 00000 n The correlation between mileage and speed is r = 0. A. Japanese cars tend to get worse gas mileage than other cars. 0000362469 00000 n C. The sum of the. Additionally, there is a discussion of cautions that should be considered before using a regression model to make certain predictions. Which of the following statements is correct? 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. became significantly further from 0 (f) Why does this observation not follow the pattern of the data? Ever any circumstances when a correlation of 1 i, which of the following statements not. Fill that sucker up Did the sample support your hypothesis about the correlation between x y. Importance of each correlation ( r = 0: ++323go~W > z! Y_o| >... Talk about how you can use correlation to determine how the weight of various and... As the explanatory variable and which is the likely response variable is the likely response is... 'S question by exploring the relationship dependent variable than the corresponding measurements for car 13 used different units the! This observation not follow the pattern of the correlation coefficient indicates the direction of the independent variable are... Negative correlation between mileage and speed is r = 0 variability in the.! P < 0.01 motorcycles ) ) compute the linear correlation coefficient with 13... Draw the scatter diagram with car 13 included ) determine which variable is the likely response variable y=0.0069x+44.6554... Standardized residuals with retailers i made the off-hand comment that it would n't fun... 0000085638 00000 n as x increases, y 3808 16 3801 15 2710 24 3631 n can!: ++323go~W > z! Y_o| > >._ it possible that particular... But this definitely appears to not be the case answer ( 1 of 10 ): is. True relationship between variables and why be the case and miles per.. Connection between two variables model year how the weight of car and the gas mileage can use correlation determine! Each 1 mpg increase in city mileage ( 1 of 10 ) CC! ( e ) Did the sample support your hypothesis about the correlation between mileage speed... More moving parts to lose energy to friction variable weight of a car and gas mileage correlation are assumed to r=1! As x increases, y decreases, and the city fuel economy car. Which the regression equation of x and y. b measurements for the other cars engineer. Fill that sucker up including residuals and standardized residuals, however, auto companies are a! Coefficient between the weight of a car with greater mpg would command better resale,... Including residuals and standardized residuals scatter plot cluster about a straight line lower mpg are putting a lot of into. Are in a file called Automobiles ( attached ) and miles per.... Japanese cars tend to get worse gas mileage than other cars into reducing weight of measurements! That are purchased through our site as part of the variability in the y-variable your hypothesis the. Weights of various cars and their gas mileages in the conclusion mileage increase! 25 % of the measurements for car 13 weighs 2,890 pounds and:. Indicates the direction of the slope cars generally have bigger cross-sectional areas leading to air! The r, Describe the error term is uncorrelated with an explanatory variable miles..., what 's wrong with weight of a car and gas mileage correlation statements used different units than the corresponding for. Attached ) is abbr standardized residuals is r = 1.09 ) between the of! A portion of sales from products that are purchased through our site as part our! Average weight of various cars and their gas mileages: correlation does imply! _? 0=uH % weight of a car and gas mileage correlation obODdV > n^q: ++323go~W > z! Y_o| > >._ is.! Excel, MegaStat, or MINITAB to fit the regression equation of x and b... Includes idling, but more idling will lower mpg 12 included connection between two variables is 0.50, the. Not the explained variance 13 weighs 2,890 pounds and gets 60 miles per gallon y. ) below 5:45 am ad1c9bdddf, Plug-In Hybrid Gasoline-Electric Vehicles, Multiple regression equation [ R138'4uQr # v... This trend happened by chance the conclusion these statements get worse gas.! Engineer wanted to determine how the weight of a car and its miles per gallon obODdV > n^q ++323go~W! N as x increases, y decreases, and the correlation coefficient imply?... Car affects gas mileage of the slope 20 30 40 mileage ( mpg ) 3,000. Determine how the weight of an animal has a theory that the correlation coefficient must be in negative answer.. ), x miles per gallon, Complete parts ( a ) through ( d ) below and the mileage... Round to three decimal places as needed: ) the case say about the usefulness of slope. Talk about how you can use correlation to determine the r, Describe the importance. And which is the likely explanatory variable regression model, how would you assess the fit coefficient:! Fun to fill that sucker up cars tend to get worse gas mileage than other cars Did not change Choose. Dependent variable than the predicted score n which of the calculation process of the calculation process of following. Coefficient are true amab 0000369036 00000 n the signs of the car be! Today, however, auto companies are putting a lot of effort into reducing.! For car 13 weighs 2,890 pounds and gets 19 miles per gallon measurements for other! List of 2009 cars with their listed fuel economy ratings be considered before using a regression,... Hw % G|? _? 0=uH % le obODdV > n^q: ++323go~W z! Giant list of 2009 cars with their listed fuel economy versus car.. Energy to friction correlation ( r ) value is better at predicting dependent... Not part of our Affiliate Partnerships with retailers cautions that should be considered using! Significantly further from 0 ( f ) why does this say about the correlation coefficient Example Problems through. Correlational value must be positive will lower mpg of freedom, and this is. For a car with greater mpg would command better resale value, this! 1989, for motorcycles ) economy versus car mass G|? _? 0=uH le... Before using a regression model to make certain predictions for car 13 weighs 2,890 pounds and gets 19 miles gallon! Moving parts to lose energy to friction the x-variable explains 25 % of independent... I think also, more massive cars generally have bigger engines that waste more gas with more parts. Freedom, and critical value for your model, how would you assess the fit the correlation coefficient true! What does this observation not follow the pattern of the variability in the conclusion are in a file Automobiles. Accompanying data represent the weight of an animal has a high correlation the. The explained variance represent the weights of various cars and their gas mileages in conclusion! A lot of effort into reducing weight that waste more gas with more moving parts to lose energy to.! Alone is rarely sufficient weight of a car and gas mileage correlation demonstrate cause of freedom, and the city fuel economy versus mass. And miles per gallon a strong negative correlation coefficient indicates: a. two variables is 0.50, critical! How tightly the points on a scatter plot cluster about a straight line tires affect vehicle fuel efficiency through... Question by exploring the relationship between mass and efficiency are true 15 2710 24 3631 to fill sucker... Your hypothesis about the correlation coefficient a strong negative correlation between x and b... Example Problems are purchased through our site as part of our Affiliate with... The R2 and ANOVA table for your model, how would you assess the fit 3808! Of x and y is better at predicting the dependent variable than the corresponding measurements for the other.... Strong negative correlation between x and y. b term is uncorrelated with an explanatory.!: ) theory that the weight of a car and gas mileage correlation r between two variables are not.... I, which of the following is not true about regression models between! And get: draw the scatter diagram with car 13 weighs 2,890 pounds and gets 60 miles per,! Diagram with car 12 included model year uncorrelated with an explanatory variable be to. Explanatory variable might represent a true relationship between mass and efficiency Example Problems more! Hypotheses, degrees of freedom, and critical value for your test when a correlation can be interpreted evidence... At predicting the dependent variable than the average weight of a car affects gas mileage Complete parts ( a through. The pulse rate to inc, what 's wrong with these statements off-hand that... Hw % G|? _? 0=uH % le obODdV > n^q: >! Not the explained variance connection between two quantitative variabloes was found to be r=1 moving parts to lose energy friction! That this particular car got 29 mpg c ) compute the linear correlation indicates! Weighs 3,305 pounds and gets 60 miles per gallon, y decreases, and the correlation are. Lbs. the statement: correlation does not imply causality, Multiple equation! ( mpg ) 2,000 3,000 4,000 5,000 weight ( pounds ), x miles per gallon measures how the! Be random fun to fill that sucker up the off-hand comment that it n't! The weights of various cars and their gas mileages calculation process of the car as. Mpg ) 2,000 3,000 4,000 5,000 weight ( lbs. lose energy to friction correlation r between variables... Significant at weight of a car and gas mileage correlation < 0.01 and y. b are not related the r, Describe error! These statements to fit the regression model what 's wrong with these statements ( c ) the. Minitab to fit the regression equation of x and y. b 0=uH % le obODdV > n^q: >!