AP StatisticsName

Examining Relationships

  1. THE ENDANGERED MANATEE: Manatees are large, gentle sea creatures that live along the Florida coast. Many manatees are killed or injured by powerboats. The data on powerboat registrations (in thousands) and the number of manatees killed by boats in Florida in the years 1977 to 1994 can be found on statcrunch using a search for lakeStats (capitalization is important). It is listed under YMS 3.41.

a.)We want to examine the relationship between number of powerboats and number of manatees killed by boats. Which is the explanatory variable?

b.)Make a scatterplot of these data. (Be sure to label the axes with the variable names, scale the axes, and give the graph a title).

c.)Calculate the correlation coefficient for this set of data

d.)Describe the relationship between these two variables. Be sure to discuss Strength, Type, Direction in your description.

e.)Does it appear that we can predict the number of manatees killed if we know the number of powerboat registrations? If powerboat registrations remained constant at 719,000 about how many manatees would be killed by boats each year?

  1. DO HEAVIER PEOPLE BURN MORE ENERGY? Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. Data for 12 women and 7 men can be found on statcrunch (search southstats for the data set called Lean body mass and metabolic rate). The body mass measured in kilograms is the person’s weight leaving out all fat. Metabolic rate is measured in calories burned per 24 hours, the same calories used to describe the energy content of foods. The researchers believe that lean body mass is an important influence on metabolic rate.

a.)Make a scatterplot of the data for the female subjects. Which is the explanatory variable?

b.)Calculate the correlation coefficient for this set of data.

c.)Describe the relationship for these data using Strength, Type, and Direction.

d.)Create a second scatterplot that includes the males (Use a different color to indicate the difference in the data for gender) Does the pattern of relationship that you observed in (c) hold for men also? How do the male subjects as a group differ from the female subjects as a group?

  1. STRONG ASSOCIATION BUT NO CORRELATION: The gas mileage of an automobile first increases and then decreases as the speed increases. Suppose that this relationship is very regular, as shown by the following data on speed (miles per hour) and mileage (miles per gallon) (data on statcrunch---southstats YMS 3.28)

a.) Make a scatterplot of mileage versus speed. Verify that the correlation coefficient between speed and mileage is r=0. Explain why the correlation is 0 even though there is a strong relationship between speed and mileage.