BackGraphical Analysis In Exercises 11–14, determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables.
[DATA] American Black Bears The American black bear (Ursus americanus) is one of eight bear species in the world. It is the smallest North American bear and the most common bear species on the planet. In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-term study of the population in the Great Smoky Mountains National Park. One aspect of the study was to develop a model that could be used to predict a bear’s weight (since it is not practical to weigh bears in the field). One variable thought to be related to weight is the length of the bear. The following data represent the lengths and weights of 12 American black bears.
a. Which variable is the explanatory variable based on the goals of the research?
b. Draw a scatter diagram of the data.
If the slope of a least-squares regression line is negative, what could be said about the correlation between the explanatory and response variable?
Bull Markets A bull market is defined as a market condition in which the price of a security rises for an extended period of time. A bull market in the stock market is often defined as a condition in which a market rises by 20% or more without a 20% decline. The data to the right represent the number of months and percentage change in the S&P 500 (a group of 500 stocks) during the 25 bull markets dating back to 1929 (the year of the famous market crash).
a. Treating the length of the bull market as the explanatory variable, draw a scatter diagram of the data.
Name the Relation, Part II For each of the following statements, explain whether you think the variables will have positive correlation, negative correlation, or no correlation. Support your opinion.
a. Number of cigarettes smoked by a pregnant woman each week and birth weight of her baby
b. Years of education and annual salary
c. Number of doctors on staff at a hospital and number of administrators on staff
d. Head circumference and IQ
e. Number of moviegoers and movie ticket price
"In Exercises 9 and 10, identify the explanatory variable and the response variable.
10. An actuary at an insurance company wants to determine whether the number of hours of safety driving classes can be used to predict the number of driving accidents for each
driver."
Writing Use an appropriate research source to find a real-life data set with the indicated cause-and-effect relationship. Write a paragraph describing each variable and explain why you think the variables have the indicated cause-and-effect relationship.
b. Other Factors: The relationship between the variables is caused by a third variable.
Why is it important to perform graphical as well as analytical analyses when analyzing relations between two quantitative variables?
True or False: Correlation implies causation.
Graphical Analysis In Exercises 11–14, determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables.
In Exercises 13–16, write a statement that interprets the P-value and includes a conclusion about linear correlation.
Using the data from Exercise 6 “Airport Data Speeds,” the P-value is 0.003.
Writing Use an appropriate research source to find a real-life data set with the indicated cause-and-effect relationship. Write a paragraph describing each variable and explain why you think the variables have the indicated cause-and-effect relationship.
c. Coincidence: The relationship between the variables is a coincidence.
Suppose you work a part-time job and earn \$15 per hour. Draw a scatter diagram that might represent the relation between your gross pay and hours worked. Is this a deterministic relation or a probabilistic relation?
"In studies of monozygotic (identical) twins, the correlation between intelligence (IQ) scores is 0.85.
a. Who are the individuals in this study?"
Randomization
For Exercises 33–36, repeat the indicated exercise using the resampling method of randomization.
Powerball Jackpots and Tickets Sold Exercise 14