Statistically, explain what is wrong with this researcher's analysis. A correlation coefficient between two variables is 0.50, and this correlation is statistically significant at p < 0.01. (ii) A sample correlation coefficient of .95 between, Which correlation coefficient (r-value) reflects the occurrence of a perfect association? News, Reviews, Photos, Videos delivered straight to your in-box. 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. oL#n$\MWNoy(#Rd6Mf/{s5a65:\>31XJ;pF{hDzh.P:G:NQZ. In a meeting, a Senior Manager says that a negative correlation doesn't sound like a desirable result, and a perfect correlation sounds like a good thing. Step 2/2. Cannot be seen from the table. The probability that the null hypothesis is true is less than 1 percent. The correlation is either weak or 0. b. All rights reserved. b. two variables are inversely related. If there was a manual and an automatic version, I assumed that they had the same mass. All but one of these statements contain a mistake. 0000264738 00000 n Engine oil is responsible for lubricating the engine components and reducing friction, which can improve fuel efficiency. has a weight within the range of the other cars' weights. We pulled into the gas station next to a Ford Excursion. Discuss. 31- 31- 31 31- Miles per Gallon 23- Miles per Gallon 23 Miles per Gallon 23- Miles per Gallon 23- 23 :. We found a correlation of r = -0.63 between gender and political party preference. As the number of cigarettes increases the pulse rate increases. 0000087617 00000 n Combining the weight of the editor's new Cadillac and his family, provide an estimate for the gas mileage the editor should expect to get on a trip to visit these relatives. 1183 0 obj <>/Filter/FlateDecode/ID[<65005FC056CD9ECA1E949E0F09C467EE><2F11FBF979314043A7DFF02A565A76D7>]/Index[1168 26]/Info 1167 0 R/Length 82/Prev 762564/Root 1169 0 R/Size 1194/Type/XRef/W[1 2 1]>>stream This content was COPIED from - View the original, and get the already-completed solution here! Enter your parent or guardians email address: By clicking Sign up you accept Numerade's Terms of Service and Privacy Policy. Schizophrenia Drugs Are Finally Getting an Overhaul. c. The error term does not have the normal distribution. B. hb``e``AXX80,,tqq$,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 b. c. In negatively skewed distributions, the mean is usually greater than the m. Compute the correlation for the following data. Determine whether the correlation coefficient is an appropriate summary for the scatter-plot and explain your reasoning. For example, the average gas mileage of Ford Focus 1.6 produced between 1998 and 2005 amounts to 7.61/100 km. Reducing weight means reducing fuel cost. Why do big cars get bad mileage? There is a correlation of 0.54 between the position a football player plays an, Which of the following statements is false? did not change. What else could produce a strong correlation? But they also hold genetic benefits for species. 12.31 State your a priori hypothesis about the sign of the slope. When is it inappropriate to conduct a correlation analysis? "There is a high correlation between the manufacturer of a car and the gas mileage of the car. There is a very weak, roughly linear, negative association between vehicle weight and gas mileage. One final note. Jaguar XJ8 18 3,805 VolvoC70 20 3,690 (d) Now suppose that Car 13 (a hybrid car) is added to the original data (remove Car 12). 0000001596 00000 n 0000090679 00000 n Which of the following statements about the correlation coefficient are true? However, he claimed that this particular car had a gas mileage of 29 mpg, which is not within the 95% confidence interval. hbbe`b``3Y ! Look at the following cross table of two ordinal variables. c. The error term has a zero mean. this giant list of 2009 cars with their listed fuel economy ratings. For cases like this, I just took the first reasonable number I found. What fraction of the variability in fuel economy is accounted for by the engine size? You must be logged in to perform that action. became significantly further from 0 (f) Why does this observation not follow the pattern of the data? Honda Accord 21 3,390 Suzuki Vitara XL7 17 3,590 IRS is responsible for collecting those taxes from manufacturers. Total 42.000 802.465, Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Identify any statistical errors. 0000001962 00000 n 0000352202 00000 n Chi-square analysis will tell us whether two qualitative variables are correlated. Engines will most commonly come in 4, 6, or 8 cylinders. Hence, to know the correct mileage and how much you have spent, remember the below points. 0000002988 00000 n 2023 Cond Nast. The following data represent the weight of various cars and their gas mileage. Mass isn't the only thing that limits the fuel efficiency. 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). Back to my daughter's question. d. there has been a calculation error. copyright 2003-2023 xXM7%6.KR\!0"]`XyvH)RW~HAL{Csy_ nl!R"{^6aC4?']WTP.?^9#-a12e*}Rn:|$:.n(? Here is some data. The correlation between a car's engine size and its fuel economy (in mpg) is r = -0.8476. Isuzu Ascender 15 4,965 Volkswagen Jetta 34 3,045 4"E!6D1"tzP (4 The sample correlation c. Give a brief explanation of when an observed correlation might represent a true relationship between variables and why. 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. The percentage of variance in Y that is explained by, Can you identify some situations where correlation doesn't prove causation? 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 a. 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. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. 6 0 obj The correlation coefficient, r = -1, implies a. a. B. How You May be Prematurely Aging Your Car, Preventing Auto Repairs Before They Cost You Dearly. AMab 0000367741 00000 n (d) Which approach do you prefer, the t test or the p-value? Write your answers to exercises 12.28 through 12.43 (or those assigned by your instructor) in a concise report, labeling your answers to each question. Ultimately, you can't trace fuel economy simply to the level of horsepower your engine is capable of providing. No, because a hybrid gas and . Statistics and Probability questions and answers, An engineer wanted to determine how the weight of a car affects gas mileage. Discuss why the intervals are different widths even though the same confidence level is used. The error term is normally distributed. (d) The correlation is significant. (e) Recompute the linear correlation coefficient with Car 13 included. The data for Car 13 must be incorrect. 0000362607 00000 n Since model year 2004, CO 2 emissions have decreased 25%, or 114 g/mi, and fuel economy has increased 32%, or 6.1 mpg. (a) Draw the scatter diagram with Car 12 included. 0000367865 00000 n Is it reasonable to suppose a cause and effect relationship? His previous car was a Toyota Camry which weighs 3,241 pounds.. a) The editor often takes his entire family to visit relatives in a nearby state. O A. Looks linear enough to fit a function. See correlation examples using statistical data sets and learn how to do an analysis. The individual from whom the editor purchased the Cadillac said that this car got exceptional gas mileage. There are no new treatments yet. ", 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. Suppose that you are given the following results. Find the correlation coefficient of the data b = .222; sx = 6.32; sy = 1.45. The values of the independent variable X are assumed to be random. Which of the following violates the assumptions of regression analysis? (A) CORREL (B) COVARIANCE.S (C) CORREL.S (D) CORRELATION, Explain the following terms in your own words: - Positive correlation - Negative correlation - No correlation. endstream endobj startxref 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. For every pound added to the weight of the car, gas mileage in the city will decrease by .005920.00592 mile (s) per gallon, on average. The combined weight of his family is 570 lbs. Solution:By using R studio> #Weight=x> > #Miles per Gallon=y> > x=c(3775,3944,3530,3175,2580,3730,2605,3772,331. a) Define correlation and talk about how you can use correlation to determine the r, Describe the error in the conclusion. 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_ Excessive idling decreases MPG. The value of a correlation is reported by a researcher to be r = ?0.5. Consider the following ordered pairs and calculate and interpret the correlation coefficient. I should have known it wouldn't stop there. 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. = .05. Ford Focus 26 2,760 Saturn Ion 24 2,855 This implies that mass has a bigger effect on highway efficiency. Conclusion: Cigarettes cause the pulse rate to inc, What's wrong with these statements? 0000088713 00000 n The correlation between drop and duration is rR . The calculation for aerodynamic drag is a little more complex: Aerodynamic drag = Frontal Area x drag coefficient (Cd) x Air density x Speed squared Frontal area: this depends mostly on the class and type of car, and there's often nothing to be done about this. If r = 0, there is no relationship between the two variable at all. mpg = miles per gallon mpg US = miles per United States gallon mpg Imp = miles per Imperial gallon km/l = kilometers per liter l/100km = liters per 100 kilometers Odometer Readings Calculate gas mileage by odometer readings: enter your starting and ending odometer readings and the amount of fuel used for the trip. (b) Draw a scatter diagram of the data. The error term has a constant variance. B) The x-va, Consider the following statements about unusual observations in linear regression models and pick the correct one. 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? Weight (pounds), x Miles per Gallon, y 3808 16 3801 15 2710 24 3631. A. The conditions under which miles per gallon were evaluated for Car 13 were different from the conditions for the other cars. Which of the following statements is correct? a. 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.. 0000382127 00000 n Total sum of squares is equal to 2805.67. - Estimates of the slope are found from sample data. 2000 Test Car List Data (csv) (507.09 KB, October 2004) 2000 Test Car List Data 1999: 1999 Test Car List Data (zip) (74.77 KB, August 2004) 1998: 1998 Test Car . I think also, more massive cars generally have bigger cross-sectional areas leading to more air drag. Regression 1.000 546.438 546.438 87.506 0.000 Multiple R 0.8252 Car 12 weighs 3,305 pounds and gets 19 miles per gallon. Chevy Corvette 19 3,255 Mercury Sable 20 3,340 Tires can make a big difference in the number of miles a driver gets to a tank of gas. 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. 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. Stretches of DNA that lock inherited traits together often accumulate harmful mutations. Explain why correlation alone is rarely sufficient to demonstrate cause. Based on a gallon of gasoline costing. What cautions should be made before using this regression model to make that prediction? The amount of CO2 a car emits is directly related to the amount of fuel it consumes. It describes the relationship between two variables. If your vehicle weighs more after installing a lift kit, it will reduce mileage. Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. Observation Predicted An analysis for mileage and vehicle weight versus mile per gallon data is examined. 0000368723 00000 n 12.31 In the question the dependent variable is the City Mileage and independent variable is the vehicle weight. Click the icon to view the data table. An engineer wanted to determine how the weight of a car affects gas mileage. If an aluminum radiator is damaged or is experiencing problems, it can easily be fixed up by the owner. B. Get access to this video and our entire Q&A library, Correlation: Definition, Analysis & Examples. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. 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. BMW 3 Series 19 3,390 Lincoln Aviator 13 5,000 There is no correlation between x and y. c. There is a strong positive correlation between x and y. d. There is a p, Tell whether correlation is being used correctly. Hyundai Elantra 24 2,880 Toyota Matrix 26 2,985 0000383622 00000 n Complete parts (a) through (f) below. . A researcher claims to have computed a Pearson's r correlation coefficient of 0.802 for the relationship between biological sex and height. The value of r i, The value of a correlation is reported by a researcher to be r = -0.5. Observations 43.0000, ANOVA A: If the linear correlation coefficient for two variables is zero, then there is no relationship between t. How may correlation analysis be misused to explain a cause-and-effect relationship? did not change significantly Choose the correct answer below. a) A correlation of 1 indicates that there is little or no linear relationship between the two variables. 0000399948 00000 n The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r=0.981. There is some spread, but we can discern a pattern: Dots to the right in the graph tend to be placed lower. |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? There is a strong negative correlation between the displacement,horsepower,weight,and cylinders.This implies that,as any one of those variables increases,the mpg decreases. 0000369036 00000 n a. I guess if a car had a mass of 0 kg, it would still just get 32 to 44 mpg. Then add another point (12, 8) and calculate the new correlation. Adjusted R Square 0.6732 If so, can we predict the mileage rating of a car given its weight? (b) Draw a scatter diagram of the data. (e) Did the sample support your hypothesis about the sign of the slope? Do heavier cars use more gasoline? 0000362720 00000 n Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n = 10. 0.9184 b. It's crucial to know the fuel consumption of your car. *4/Q:/w`D%w&FTb>F 20[O@Le,1&# Qh ` ~S^ A) The correlation coefficient measures how tightly the points on a scatter plot cluster about a straight line. Determine the coefficient of determination. Complete parts (a) through (d). If so, what does it mean? 2003-2023 Chegg Inc. All rights reserved. The engine may also be used for performance or for better fuel mileage. Aftershocks May Rock Turkey and Syria for Months, Even Years. Chevy TrailBlazer 15 4,660 Nissan 350Z 20 3,345 The first is added weight. Chevy Silver1500 14 4,935 Mitsubishi Galant 20 3,285 12.35 Use Excel, MegaStat, or MINITAB to fit the regression model, including residuals and standardized residuals. What does the y-intercept mean? . 0000360698 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 10 20 30 40 Mileage (mpg) 2,000 3,000 4,000 5,000 Weight (lbs.) 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. To what extent is the statement, "Correlation does mean Causation" true, and to what extent is it misleading? A. Acura TSX 23 3,320 Lexus IS 300 18 3,390 trailer <<1A6862DFEDAF4A86A87609A026CF06EA>]/Prev 434047/XRefStm 1962>> startxref 0 %%EOF 217 0 obj <>stream B. c. D. (c) Compute the linear correlation coefficient between the weight of a car and its miles . As x increases, y decreases, and the correlation coefficient must be positive. b. became significantly further from 0 O A. C. D. became significantly closer to 0 By firing lasers through underground fibers, scientists can detect seismic waves and perhaps improve alertsgiving people precious time to prepare. It can happen that an observation with high lev. A. (b) A confounding factor must be independently associated with. In model year 2021, the average estimated real-world CO 2 emission rate for all new vehicles fell by 2 g/mi to 347 g/mi, the lowest ever measured. The data are in a file called Automobiles( attached). 6. Think about when and why the relation between two variables can change.