11. Correlation

Which of the following statements about the correlation coefficient is true?

Which of the following best describes what it means for two variables to be positively associated?

"In Exercises 13-16, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?

16. r = 0.795"

Given the following pairs of data: $(1,1)$, $(-1,5)$, and $(10,?)$, which of the following values could represent the correlation coefficient between the $x$ and $y$ variables?

"In Exercises 13-16, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?

14.r =- 0.937"

[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.

b. Determine the linear correlation coefficient between months and percent change.

c. Does a linear relation exist between duration of the bear market and market performance?

Put the following correlation coefficients in order from weakest to strongest in terms of strength of linear association.

−1, 0.377, 0.084, −0.436, 0.444, −0.733

In Problems 3–6, use the results in the table to (b) determine the linear correlation between the observed values and expected z-scores, (c) determine the critical value in Table VI to assess the normality of the data.

Which of the following is not a property of the linear correlation coefficient $r$?

Explain, in your own words, what rs and (rho)s represent in Example 1.

In the context of the correlation coefficient $r$, which word best describes the degree of overlap between the two data sets?

Which of the following is not one of the three common errors involving $r$ (correlation)?

Given a scatterplot showing a strong negative linear relationship between two variables, which of the following is most likely the correlation coefficient for the data set?

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).

c. Does a linear relation exist between duration of the bull market and market performance?