Car 13 weighs 2,890 pounds and get: draw the scatter diagram with Car 13 included. 153 0 obj
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If an aluminum radiator is damaged or is experiencing problems, it can easily be fixed up by the owner. 0000383019 00000 n
Can a data set with perfect positive correlation increase its correlation if y-values increase? Suppose that we add Car 12 to the original data. a. Think about air drag and. My daughter asked. (b) The obtained score is greater than the predicted score. 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. Thus, we can say that the salesman was stretching the truth. ) If you google something like "2009 Pontiac G5 curb weight," you might find several answers that don't agree. Click the icon to view the critical values table. Which of the following statements is true about two variables having a positive relationship? 0000089897 00000 n
She is my daughter, after all. Suppose that we add Car 12 to the original data. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. My first guess was that with a larger mass, you have to use more energy to get the vehicle up to speed. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. 12.35 The results of the regression analysis done by using MS Excel are given below. The correlation between a car's engine size and its fuel economy (in mpg) is r = -0.8476. Complete parts (a) through (d) below. for Cubic Capacity. Was I just making that stuff up? Complete parts (a) through (d) below. 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. Click here to view the car data. It's crucial to know the fuel consumption of your car. Redraw the scatter diagram with Car 13 included. e)Suppose an editor for the publication wishes to predict the highway mileage of vehicles with a curb weight of 6,000 pounds. Identify any statistical errors. b. 1183 0 obj
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An engineer wanted to determine how the weight of a car affects gas mileage. 0000367741 00000 n
Give examples with your response. The correlation between mileage and speed is r = 0. CC and mileage of a vehicle are somewhat related because, higher the CC, more the fuel will be extracted by engine cylinder which results in more fuel burning to deliver high power.. 0.9184 b. Looks linear enough to fit a function. b. ), Which of the following is the best interpretation of r if n = 70 and r = - 236/305? 0000362642 00000 n
A correlation of 1 i, Which of the following is not part of the calculation process of the correlation coefficient? per gallon in the city. (ii) A sample correlation coefficient of .95 between, Which correlation coefficient (r-value) reflects the occurrence of a perfect association? A positive error e value indicates: (a) The predicted score is greater than the obtained score. 0000374718 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. Engine displacement is further reduced by 0.1% per 1% of weight reduction with a resultant improvement in fuel economy of 0.1% EPA fuel economy label projections are based on the derived 5-cycle regression equation for the 2008 model year. 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. 0000001596 00000 n
6. B. Why are the results here reasonable? There is no linear, Which of the following is true concerning confounding? Explain how the two correlations differ. 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. C. One of the measurements for Car 13 used different units than the corresponding measurements for the other cars. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. d. The error terms are independent. 11,853. Correlation only implies association not causation. A correlation of +.80 is just as strong as a correlation of -.80. b. 6. Therefore, a correlational value of 1.09 makes no sense. What type of correlation does this indicate? <> 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. Data gaps, funding cuts, and shyness about sex let gonorrhea gain drug resistance. This make sense. BMW 3 Series 19 3,390 Lincoln Aviator 13 5,000 2500 4000 Weigh: (Ibs) This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! A. 1193 0 obj
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Conclusions I. The correlation is moderate to strong. Complete parts (a) through (d). If not, what does it mean? How did this new value affect your result? The absolute value of the correlation coefficient and the sign of the correlation coefficient The results here are reasonable because Car 12 changed. The first is added weight. a. The error term has a constant variance. Describe each correlation (strength and direction). An engineer wanted to determine how the weight of a car affects gas mileage. B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles . 2003-2023 Chegg Inc. All rights reserved. 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. 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. Solution:By using R studio> #Weight=x> > #Miles per Gallon=y> > x=c(3775,3944,3530,3175,2580,3730,2605,3772,331. Intercept 36.634 1.879 19.493 0.000 32.838 40.429 Be specific and provide examples. All rights reserved. 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.) "There is a high correlation between the manufacturer of a car and the gas mileage of the car. . Sometimes I do that - but hopefully I was correct. 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. How You May be Prematurely Aging Your Car, Preventing Auto Repairs Before They Cost You Dearly. % Chrysler Pacifica 17 4,660 Nissan Pathfinder 15 4,270 1) Excel finds the Pearson Correlation Coefficient using the fx function Correl. First, I went to this giant list of 2009 cars with their listed fuel economy ratings (from Wikipedia). Using the following information: What is the correlation coefficient? Total 42.000 802.465, Coefficients Standard Error t Stat P-value Lower 95% Upper 95% b. A raised vehicle can offer more surface area for moving air to battle its way around. The x-variable explains ?25% of the variability in the y-variable. 2023 Cond Nast. Find combinations of statements that are correct. For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. 0000362028 00000 n
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. Thus, the correlational value must be in negative. An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. It describes the relationship between two variables. It is the essential source of information and ideas that make sense of a world in constant transformation. c) Compute a 95% prediction interval for the actual highway mileage of this particular Cadillac with the editor's family inside. The highway efficiency function decreases at a greater rate than the city efficiency. trailer
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A strong negative correlation coefficient indicates: a. two variables are not related. The correlation coefficient and the slope of the regression line may have opposite signs. 0000133335 00000 n
Which one could be true? Why are the results here reasonable? 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? 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? 4Gdk2\#O+jxm#o g{Iq0zF>(tFOlqy6,?6/4fiRa`6:/. did not change. Correct Answer (a) The slope is 1.109. xXM7%6.KR\!0"]`XyvH)RW~HAL{Csy_
nl!R"{^6aC4?']WTP.?^9#-a12e*}Rn:|$:.n(? d. The error term h, Which of the following is not a source of forecast bias? 0000177854 00000 n
C. Describe the error in the conclusion. If correlation does not imply causation, what does it imply? Be specific and provide examples. 0000383286 00000 n
How would you interpret the findings of a correlation study that reported a linear correlation coefficient of +0.3? (c) Would you say that your model's fit is good enough to be of practical value? Honda Odyssey 18 4,315 Toyota Celica 23 2,570 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. Chi-square analysis will tell us whether two qualitative variables are correlated. So he is confused about the meaning of a perfectly negative correlation. Click here to view the table of critical values of the correlation coefficient. Which of the following Excel functions returns the sample correlation coefficient? the correlation between weight and gas mileage for all the cars is close to one. a. Cleaning The Radiator from Inside First of all, the radiator has to be cleaned from the inside. d. Yes, there is a negative correlation. ", 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. 0000382531 00000 n
Excessive idling decreases MPG. b. endstream
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", 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.". Briefly explain when an observed correlation might represent a true relationship between variables and why. d) Failure to account for serial correlation. Stretches of DNA that lock inherited traits together often accumulate harmful mutations. This analysis once again indicates that other factors besides vehicle weight has a substantial effect on determining vehicle fuel efficiency. Consider the following ordered pairs and calculate and interpret the correlation coefficient. c. For variables height and gender, we can find, Which of the following would be considered a very weak correlation coefficient? A. Determine whether the correlation coefficient is an appropriate summary for the scatter-plot and explain your reasoning. O c. does not follow the overall pattern of the data. Select one: a. B. B. 0000002988 00000 n
Perfect negative b. Standard Error 2.4989 Aftershocks May Rock Turkey and Syria for Months, Even Years. tC/`X[*[od!&`\i"M9i#=q@A:CG]%:zk{CSQ&`?;Z3l*zFvbH &l&+;@k,L[,Q5 Do heavier cars use more gasoline? became significantly further from 0 O A. C. D. became significantly closer to 0
Cannot be seen from the table. b. a. Here is the data, if you want it. 12.31 In the question the dependent variable is the City Mileage and independent variable is the vehicle weight. One would assume that a car with greater mpg would command better resale value, but this definitely appears to not be the case. (i) Heteroskedasticity. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Find the correlation coefficient of the data. What is meant by the statement that correlation does not imply causality? |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? miles per gallon, Complete parts (a) through (d). So the question boils down to which engine has more friction per cycle, and which car has more weight to carry around. This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! 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. The explanatory variable is the miles per gallon and the response variable is the weight. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. 0000002939 00000 n
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The probability that the null hypothesis is true is less than 1 percent. The conditions under which miles per gallon were evaluated for Car 13 were different from the conditions for the other cars. The combined weight of his family is 570 lbs. This implies that mass has a bigger effect on highway efficiency. The correlation is either weak or 0. b. An engineer wanted to determine how the weight of a car affects gas mileage. The EPA city test includes idling, but more idling will lower MPG. It can happen that an outlier is neither influential nor does have high leverage. Based on a gallon of gasoline costing. Choose the correct answer below. (d) The correlation is significant. Of course the next question was, "Why do bigger cars get worse gas mileage?". Click here to view the table of critical values of the correlation coefficient. 2500 4000 Weigh: (Ibs Weight (pounds), x Miles per Gallon, y 3808 16 3801 15 2710 24 3631. 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. c. The error term does not have the normal distribution. News, Reviews, Photos, Videos delivered straight to your in-box. 0000362720 00000 n
c) The preconceived notions of the forecaster. Schizophrenia Drugs Are Finally Getting an Overhaul. In fact, 20% to 30% of a vehicle's fuel consumption and 24% of road vehicle CO2 emissions are tire-related. 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. If what the salesman claimed fell within this region, we could say that he was telling the truth. c. Adding the multiplication. 0000360698 00000 n
l^&Hx+A@:@z/s 4D*HV3nN{5>0W;:o` )i` Chevy Corvette 19 3,255 Mercury Sable 20 3,340 Which of the following statements regarding the coefficient of correlation is true? Click the icon t0 view the critical values table 0000352202 00000 n
One final note. Why? 0000367865 00000 n
GMC Envoy 15 4,660 Subaru Baja 21 3,575 (e) Recompute the linear correlation coefficient with Car 13 included. d. b. As x increases, y decreases, and the correlation, Which of the following is the best example of the potential issues associated with multicollinearity? Why? Think about air drag and stuff. What cautions should be made before using this regression model to make that prediction? Click the icon to view the data table. 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. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. 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. 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_ Describe the clinical importance of each correlation (r) value. a. Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. Dividing the sum of the Z score multiplications by the standard error. FMEP times volume = Power per cycle needed to fight friction.