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 scatterplot and regression line. The fitted line has a slope of −0.096. What does the negative slope indicate?

a) Strong positive correlation

b) Strong negative correlation

c) No correlation

d) Weak positive correlation

Answer 1

The negative slope of −0.096 in Surya's scatterplot indicates a negative correlation, meaning that as the release year of songs increases, the rankings tend to decrease.

Step-by-step explanation:

The question concerns the interpretation of the slope of a regression line in a scatterplot. Specifically, Surya gave each member of his family a different playlist of random songs to listen to and they ranked each song between 0 and 10. When comparing these rankings to the release year of each song and plotting the data on a scatterplot with a regression line, the slope of the fitted line was found to be −0.096.

A negative slope indicates a negative correlation between the two variables being compared. In this context, as the release year of the songs (x-axis) increases, the ranking scores (y-axis) tend to decrease, suggesting that newer songs might be ranked lower by the family members. Therefore, the presence of a negative slope would correspond to a negative correlation (choice b) rather than a positive correlation, no correlation, or a weak positive correlation.