11. Correlation

Rank Correlation Use the ranks from Exercise 1 to find the value of the rank correlation coefficient. Also, use a 0.05 significance level and find the critical value of the rank correlation coefficient. What do you conclude about correlation?

What does it mean to say that the linear correlation coefficient between two variables equals 1? What would the scatter diagram look like?

What is the primary goal of the correlation coefficient in statistics?

Testing for a Linear Correlation

In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of α = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.)

Powerball Jackpots and Tickets Sold Listed below are the same data from Table 10-1 in the Chapter Problem, but an additional pair of values has been added from actual Powerball results. Is there sufficient evidence to conclude that there is a linear correlation between lottery jackpots and numbers of tickets sold? Comment on the effect of the added pair of values in the last column. Compare the results to those obtained in Example 4.

Which of the following are properties of the linear correlation coefficient $r$?

Which of the following best describes what it means if there is a positive correlation $r>0$ between tests that measure different things?

A data set is found to have a linear correlation coefficient of $r=-0.92$. Which of the following graphs most likely represents the relationship between these variables?

3. What does the sample correlation coefficient r measure? Which value indicates a stronger correlation: r =0.918 or r =- 0.932? Explain your reasoning.

Which of the following values could not represent a correlation coefficient?

Which of the following types of analysis reveals association but not necessarily causation between data attributes?

$\text{Which of the following pairs of variables most likely represents a causal relationship?}$

Testing for Rank Correlation

In Exercises 7–12, use the rank correlation coefficient to test for a correlation between the two variables. Use a significance level of α = 0.05.

Colombian Coffee The following table lists quality rankings and costs (dollars) for a pound of different brands of Colombian coffee (based on data from Consumer Reports). Lower values of the quality rankings correspond to better coffee. Do the more expensive brands appear to have better quality?

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

Which of the following values of the correlation coefficient represents a weak positive correlation?