Question

surya gave each member of his family a different playlist of random songs to listen to and asked them to rank each song between 0 and 10. he compared his family’s rankings with the release year of each song and created the following scatter plot and trend line. assuming the line correctly models the trend in the data, what does this line’s slope of −0.096 mean? choose 1 answer: a) the difference in ratings for rock songs and rap songs was −0.096. b) the difference in ratings for rock songs and country songs was −0.096. c) on average, each 1 year increase in release year was associated with a −0.096 point change in score. d) on average, each 1 point increase in score was associated with a −0.096 year change in release year.

Explanation:

• Option A and B: The slope is about the relationship between release year and score, not between different song genres. So A and B are incorrect.
• Option C: The slope of a trend line in a scatter plot (with x as release year and y as score) represents the change in y (score) per unit change in x (release year). A slope of -0.096 means for each 1 - year increase in release year, the score changes by - 0.096 points on average.
• Option D: The slope is calculated as $\frac{\text{change in }y}{\text{change in }x}$. Here, x is release year and y is score. So the interpretation should be change in score per change in release year, not the other way around. So D is incorrect.

Answer:

C. On average, each 1 year increase in release year was associated with a -0.096 point change in score.