Name. City Weight Model MPG

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1 Name The following table reports the EPA s city miles per gallon rating and the weight (in lbs.) for the sports cars described in Consumer Reports 99 New Car Buying Guide. (The EPA rating for the Audii TT was not reported.) Model City City Model MPG MPG Audi TT * 55 Mazda MX-5 Miata BMW 3Ti Mercedes/Benz SLK 22 BMW Z3 29 Mercury Cougar Chev. Camaro 3545 Mitsubishi Eclipse Chev. Corvette 3295 Pontiac Firebird 3545 Ford Mustang 3270 Porsche Boxster 2905 Honda Prelude 22 Saturn SC 27 Hyundai Tiburon Toyota Celica What are the observational units? 2. How many variables are reported in the table for each observational unit? What type (categorical or quantitative) is each variable? The simplest graph for displaying two quantitative variables simultaneously is a scatterplot, which uses a vertical axis for one of the variables and a horizontal axis for the other. A dot is placed for each observational pair at the intersection of its two values. If you are interested in using the value of one variable to predict the value of another variable, the convention is to place the variable to the predicted (the response variable) on the vertical axis and the variable to do the predicting (the explanatory variable) on the horizontal axis. 3. Construct a scatterplot of miles per gallon vs. weight below 4. Does the scatterplot reveal any relationship between a car s weight and its fuel efficiency? In other words, does knowing a car s weight reveal any information about its fuel efficiency? Write a few sentences about the relationship between the two variables.

2 Two variables are said to be positively associated if larger values of one variable tend to occur with larger values of the other variable; they are said to be negatively associated if larger values of one variable tend to occur with smaller values of the other. The strength of the association depends on how closely the observations follow that relationship. In other words, the strength of the association reflects how accurately one could predict the value of one variable based on the value of the other variable. 5. Is fuel efficiency positively or negatively associated with weight? 6. Can you find an example where one car weighs more than another and still manages to have better fuel efficiency than that other car? If so, identify such a pair and circle them on the scatterplot. Clearly, the concept of association is an example of a statistical tendency. It is not always the case that a heavier car is less fuel efficient, but heavier cars certainly do tend to be. The data on 99 cars reported by Consumer Reports included not just sports cars but also classifications of small, family, luxury, and upscale. The following nine scatterplots display pairs of variables for these cars. The variables are: City MPG rating Highway MPG rating % front weight fuel capacity ¼ mile Acceleration from 0- page number on which car appeared 7. Evaluate the direction and strength of the association between the variables in each graph. Do this by arranging the associations revealed in the scatterplots from those that reveal the most strongly positive association to those that reveal virtually no association to those that reveal the most strongly negative association. Arrange them by letter in the table below. (Since you are to use each letter only once, you should probably look through all nine plots first.) Letter: Strongly Negative Mildly Negative Virtually None Mildly Positive Strongly Positive A: B: Acc0

3 C: D: PageNum E: F: G: H: FuelCapacity FuelCapacity I: 22

4 8. Indicate what you would expect for the direction (positive, negative, or none at all) and strength (none, weak, moderate, or strong) of the association between the pairs of variables listed below. Pair of variables Direction Strength Length & width of signatures SAT score & college G.P.A. Latitude & avg. January temperature of US cities Lifetime & weekly cigarette consumption Serving size & calories of fast food sandwiches Airfare & distance to destination Birth rate & death rates of US states Foot length & height The following scatterplot displays the relationship between husband s age and wife s age ( couples). The line drawn on the scatterplot is the y = x line, where husband s age would equal the wife s age. MarriageAge Husband Wife Husband = Wife 9. Does there seem to be an association between husband s age and wife s age? If so, is it positive or negative? Would you characterize it as strong, moderate, or weak? 10. Look back at the original listing of the data to determine how many of the couple s ages fall exactly on the line. In other words, how many of the couples listed the same age for both the man and the woman on their marriage license? 11. Again looking back at the data, for how may couples is the husband older than the wife? Do these couples fall above or below the line drawn in the scatterplot?

5 12. For how many couples is the husband younger than the wife? Do these couples fall above or below the line drawn in the scatterplot? 13. Summarize what one can learn about the ages of marrying couples by noting that the majority of couples produce points that fall above the y = x line. This worksheet was adapted from Workshop Statistics, 2 nd edition, by Alan Rossman, Beth Chance, J. Barr Von Oehsen.