(d) The correlation is significant. Because it was sitting in my barn / shop for over 12 years!! The values of the independent variable X are assumed to be random. All other trademarks and copyrights are the property of their respective owners. Choose the correct answer below. Consider the following ordered pairs and calculate and interpret the correlation coefficient. Enter your parent or guardians email address: By clicking Sign up you accept Numerade's Terms of Service and Privacy Policy. Chi-square analysis will tell us whether two qualitative variables are correlated. 2500 4000 Weigh: (Ibs Acura TSX 23 3,320 Lexus IS 300 18 3,390 Thus, the correlational value must be in negative. The following problem uses a regression model to answer several questions associated with auto travel. What does the y-intercept mean? What does the y-intercept mean? 10 20 30 40 Mileage (mpg) 2,000 3,000 4,000 5,000 Weight (lbs.) Click here to view the car data. (d) Now suppose that Car 13 (a hybrid car) is added to the original data (remove Car 12). WIRED may earn a portion of sales from products that are purchased through our site as part of our Affiliate Partnerships with retailers. 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? (b) Do a two-tailed t test for zero slope at ? The value of correlation lies between the values -1 and +1. Therefore, a correlational value of 1.09 makes no sense. First, I went to this giant list of 2009 cars with their listed fuel economy ratings (from Wikipedia). critical values for the correlation coefficient (a . Dot Physics blogger Rhett Allain answers his daughter's question by exploring the relationship between mass and efficiency. Which of the following statements below is not the explained variance? Then add another point (12, 8) and calculate the new correlation. c. The correlation is negative. d. there has been a calculation error. 0000369036 00000 n Which of the following is the best interpretation of this correlation value? The sample correlation c. Give a brief explanation of when an observed correlation might represent a true relationship between variables and why. There are no new treatments yet. b) Incorrect model specification. "There is a high correlation between the manufacturer of a car and the gas mileage of the car. trailer <<1A6862DFEDAF4A86A87609A026CF06EA>]/Prev 434047/XRefStm 1962>> startxref 0 %%EOF 217 0 obj <>stream 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. II. stream Suppose that we add Car 12 to the original data. The correlation between mileage and speed is r = 0. 0000264738 00000 n There is a negative correlation between the weight of a car and its gas mileage. 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. (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? Describe each correlation (strength and direction). 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. 1. Really, this is too much data but I can't help myself. The correlation coefficient and the slope of the regression line may have opposite signs. Compare the results of parts (a) and (b) to the scatter diagram and linear correlation coefficient without Car 12 included. Describe the clinical importance of each correlation (r) value. Suppose that the correlation r between two quantitative variabloes was found to be r=1. Dividing the sum of the Z score multiplications by the standard error. 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\= C. The x-variable explains ?25% of the variability in the y-variable. You must be logged in to perform that action. 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 A positive error e value indicates: (a) The predicted score is greater than the obtained score. There is a fairly strong, roughly linear, positive association between vehicle weight and gas mileage. Correct Answer (a) The slope is 1.109. )HVX(j(L3/WB]';.+l}^c(/CqbZ6/0h": H_H~A3ep>/~Z+]~^7u]-YL'W1_Q8& /:6`;N\}Zq9YI4S9,R9. I expected it would be the other way around. d. The error term h, Which of the following is not a source of forecast bias? No, because a hybrid gas and . l^&Hx+A@:@z/s 4D*HV3nN{5>0W;:o` )i` 1168 0 obj <> endobj 12.31 State your a priori hypothesis about the sign of the slope. Covid Can Boost Your Response to Flu Vaccinesif Youre a Man. 1. Question 9 30 seconds Q. AMab 0000382826 00000 n 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. A. Do heavier cars use more gasoline? News, Reviews, Photos, Videos delivered straight to your in-box. 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. BMW 3 Series 19 3,390 Lincoln Aviator 13 5,000 What else could produce a strong correlation? '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' Back to my daughter's question. A. The percentage of variance in Y that is explained by, Can you identify some situations where correlation doesn't prove causation? A luxury saloon will always have a frontal area larger than a supermini. The error term is uncorrelated with an explanatory variable. Should I have used "gross vehicle weight" instead of curb weight? Japanese cars tend to be lighter in weight than other cars. 1 Through 2006, data are for passenger cars (and, through 1989, for motorcycles). 0000086420 00000 n Think about air drag and. I removed any hybrid vehicles and vehicles that I had never heard of. B. 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. Hyundai Elantra 24 2,880 Toyota Matrix 26 2,985 Observation Predicted An analysis for mileage and vehicle weight versus mile per gallon data is examined. sx = 1.355, sy = 15.300, b = -9.780 a. A. No, there is no correlation. This implies that mass has a bigger effect on highway efficiency. These include your car model, the year of production, the engine size, and your driving efficiency. c. A value of 0.00, Which of the following statements about correlation are true? An engineer wanted to determine how the weight of a car affects gas mileage. 2003-2023 Chegg Inc. All rights reserved. Find and compare the fuel economy, fuel costs, and safety ratings of new and used cars and trucks. Find combinations of statements that are correct. Educator app for However, it doesn't have mass data. 17.5. 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. Japanese cars tend to get worse gas mileage than other cars. 0000403945 00000 n Weight (pounds), x Miles per Gallon, y 3808 16 3801 15 2710 24 3631. Which of the following statements is correct? 153 0 obj <> endobj xref 153 65 0000000016 00000 n The error term has a constant variance. (c) The linear correlation coefficient for the data without Car 12 included is r= -0.968. 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? The value of r is negative. became significantly further from 0 (f) Why does this observation not follow the pattern of the data? 0000374718 00000 n b. (b) Interpret the p-value for the F statistic. a. 0000002988 00000 n Why are the results here reasonable? What is interesting to note here, is the strong negative correlation between city_mpg and highway_mpg. <> Statistics and Probability questions and answers. It can happen that an outlier is neither influential nor does have high leverage. a. b. two variables are inversely related. Chevy Silver1500 14 4,935 Mitsubishi Galant 20 3,285 A. endstream endobj startxref An engineer wanted to determine how the weight of a car affects gas mileage. Choose the correct graph below. Looks linear enough to fit a function. 0000382088 00000 n 2. 0000002302 00000 n Statistics and Probability questions and answers, An engineer wanted to determine how the weight of a car affects gas mileage. Cadillac Seville 18 4,050 Mercedes-Benz S-Class 17 4,195 If two cars are both traveling at 70 mph, the more massive car will have more kinetic energy -- remember: But it can't just be the kinetic energy. Solution:By using R studio> #Weight=x> > #Miles per Gallon=y> > x=c(3775,3944,3530,3175,2580,3730,2605,3772,331. Oh, one more note. 6 0 obj miles per gallon, Complete parts (a) through (d). Test 2 (Y): 34, 31, 35, 30, 31, 28, 28, 25, 24, 24. 0000367741 00000 n The proba, Explain the following statement: "Significance of the linear correlation coefficient does not mean that you have established a cause-and-effect relationship. A weightless car will get miles per gallon, on average. Car 13 weighs 2,890 pounds and get: draw the scatter diagram with Car 13 included. There is some spread, but we can discern a pattern: Dots to the right in the graph tend to be placed lower. 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 for Cubic Capacity. ), Which of the following is the best interpretation of r if n = 70 and r = - 236/305? The correlation between height and weight is 0.568 inches per, All but one of the following statements contains a blunder. 0000382677 00000 n Complete parts (a) through (d). 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? The breakthroughs and innovations that we uncover lead to new ways of thinking, new connections, and new industries. 0000367230 00000 n b. B. OC. WIRED is where tomorrow is realized. % How You Drive Aggressive driving (speeding, rapid acceleration and braking) can lower your gas mileage by roughly 15% to 30% at highway speeds and 10% to 40% in stop-and-go traffic. 0000088561 00000 n Click here to view the table of critical values of the correlation coefficient. 0000383286 00000 n b. j_uD2BMSh(E h8J2=$hQ% 7 R:F$ejd2o&#&t`f#fT!q|xEd#ic$@6q2!wmah,~Y;!Un?9 ^c0 $mQ+B'f};8+Ui\L> Ex0J(Vq[20B]L]D7M bQlB@I".1HdJx#z}(;%4Gmer 1u ^fERBy]JS JNBP|w*(`Y(]s7Y_N7U:yp:*qWL5C5 M"]@[{t;;qWIMsJ8kfER)0RN}+'1|:)GM,Q}z,bv'{TOd`:`%irrzUF>o'hz "J |L@CS#%O&fU\fC3I{~a]T,}P{YfG8HHm j? This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! a. A correlation of +.80 is just as strong as a correlation of -.80. b. 2003-2023 Chegg Inc. All rights reserved. If so, can we predict the mileage rating of a car given its weight? hb```b``e`c`Va`@ V 1` 8204q) ,.,N`@.TcT]$hxqq@4\Lk13Jbg+TrAKdVa,dyBMo+tE@hK2OJ,g 3:gY^^@FUwE) qp!31G$\7T/t\4"$ 4HoT46Ta{mIl_ Which of the following Excel functions returns the sample correlation coefficient? 0000368723 00000 n 6. How did this new value affect your result? Which of the following statements is correct? Car weight and displacement have the strongest inverse correlation with mileage. 0.9184 b. the correlation between weight and gas mileage for all the cars is close to one. Which of the following is not an assumption of the regression model? This is not statistically meaningful, because this would represent the highway mileage for a car The error term is correlated with an explanatory variable. Complete parts (a) through (d). Which of the following statements is true? Perfect negative b. If so, what does it mean? Sean has a theory that the average weight of an animal has a high correlation with the number of letters in its name. 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. 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. 0000090679 00000 n c. The error term has a zero mean. Thus, we can say that the salesman was stretching the truth. ) Based on a gallon of gasoline costing. a) 0.8 to 1.0 b) 0.6 to 0.8 c) 0.2 to 0.4 d) 0 to 0.2, Consider the following regression equation between Y and X: Y = 4.622X - 100.

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