Question

Julio distributed a survey to his fellow students asking them how many hours they spent playing sports in the past day. He also asked them to rate their mood on a scale from 0 to 10, with 10 being the happiest. Julio created the following scatterplot and regression line to show this relationship. The fitted line has a y-intercept of 5.

a) What does the y-intercept of 5 represent in the context of this scatterplot?

b) If a student spent 2 hours playing sports, according to the regression line, what would be their predicted mood rating?

c) True/False: The correlation coefficient between the hours spent playing sports and the mood rating is likely positive.

d) Fill in the blank: The regression line suggests that for every additional hour a student spends playing sports, their predicted mood rating increases by ____.

Answer 1

The y-intercept of 5 predicts the mood rating for someone who did not play sports. The correlation coefficient is likely positive, but without the exact regression equation, the increase in mood rating per hour of sports cannot be provided.

Step-by-step explanation:

The y-intercept of 5 in the context of this scatterplot represents the predicted mood rating for a student who spent 0 hours playing sports. Assuming that the regression line is accurate, if a student spent 2 hours playing sports, we would use the regression equation (which is not fully given in the question) to predict their mood rating; however, without the slope, we cannot provide the exact mood rating. The statement about the correlation coefficient being likely positive is true because the presence of a positive slope in the regression line suggests a positive relationship between hours spent playing sports and mood rating. Lastly, without the exact equation of the regression line that includes the slope, we cannot fill in the blank regarding how much the predicted mood rating increases for every additional hour spent playing sports.