Why don’t we conduct inference on the linear correlation coefficient?

[NW] Television Stations and Life Expectancy Based on data obtained from the CIA World Factbook, the linear correlation coefficient between the number of television stations in a country and the life expectancy of residents of the country is 0.599. What does this correlation imply? Do you believe that the more television stations a country has, the longer its population can expect to live? Why or why not? What is a likely lurking variable between number of televisions and life expectancy?

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

"In studies of monozygotic (identical) twins, the correlation between intelligence (IQ) scores is 0.85.

b. What are the variables being measured?"

"In studies of monozygotic (identical) twins, the correlation between intelligence (IQ) scores is 0.85.

c. What fraction of the variation in one twin’s IQ can be accounted for by the other twin’s IQ?"

[DATA] Graduation Rates PayScale reports statistics on colleges and universities. Go to www.pearsonhighered.com/sullivanstats to obtain the data file 11_3_24 using the file format of your choice for the version of the text you are using. The data contain the four-year cost and graduation rate for over 1300 colleges and universities. Do schools that charge more have higher graduation rates? The variable “4 Year Cost” represents the four-year cost of attending the college or university. The variable “Grad Rate” represents the percentage of incoming freshman who graduate within six years.

b. Determine the correlation coefficient between “4 Year Cost” and “Grad Rate.”

[DATA] Putting It Together: Exam Scores The data below represent scores earned by students in Sullivan’s Elementary Algebra course for Chapter 2 (Linear Equations and Inequalities in One Variable) and Chapter 3 (Linear Equations and Inequalities in Two Variables). Completely summarize the relation between Chapter 2 and Chapter 3 exam scores, treating Chapter 2 exam scores as the explanatory variable. Write a report detailing the results of the analysis including the presence of any outliers or influential points. What does the relationship say about the role Chapter 2 plays in a student’s understanding of Chapter 3?

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?