In Problems 17–20, (a) draw a scatter diagram of the data,

True or False: If the linear correlation coefficient is close to 0, then the two variables have no relation.

In Problems 17–20, (b) by hand, compute the correlation coefficient, and (c) determine whether there is a linear relation between x and y.

[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.

[DATA] Bear Markets A bear market in the stock market is defined as a condition in which the market declines by 20% or more over the course of at least two months. The following data represent the number of months and percentage change in the S&P 500 (a group of 500 stocks) for a sample of bear markets.

a. Treating the length of the bear market as the explanatory variable, draw a scatter diagram of the data.

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.

[DATA] Credit Scores [See Problem 12 in Section 12.3] An economist wants to determine the relation between one’s FICO score, x, and the interest rate of a 36-month auto loan, y. The data represent the interest rate (in percent) a bank might offer on a 36-month auto loan for various FICO scores.

a. Draw a scatter diagram of the data treating credit score as the explanatory variable.