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?

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?

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

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?

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?

For which of the following scatterplots is the correlation between $x$ and $y$ closest to $0$?

Which of the following scatter plots suggests a linear relationship between two variables?

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?

A marketing researcher analyzed advertising budget vs. monthly sales revenue for small retail stores and found that typically the stores that spent more on advertising saw higher sales revenues. However, the relationship wasn't perfect - some stores advertised more but saw fewer sales due to poor location, customer preferences, or bad timing. Which of the following is the most likely value for the correlation coefficient $r$ between advertising budget and sales revenue?

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 in the last column. Is there sufficient evidence to conclude that there is a linear correlation between lottery jackpot amounts 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.

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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.)

Taxis Using the data from Exercise 15, is there sufficient evidence to support the claim that there is a linear correlation between the distance of the ride and the tip amount? Does it appear that riders base their tips on the distance of the ride?