https://file.aiquickdraw.com/mathbot/file/1726799286614jk614as5.jpg

The question asks for the best interpretation of the y-intercept of 5 from the regression line. Based on the image, Julio created a scatterplot that relates hours spent playing sports and mood ratings. 

The y-intercept in a regression context tells us the value of the dependent variable (in this case, "mood rating") when the independent variable (here, "hours spent playing sports") is 0.

Since the y-intercept is 5, this means when the number of hours spent playing sports is 0, the expected mood rating is 5.

Let’s review the answer choices:

- **A)** "The average mood rating was 5." – This is incorrect because the y-intercept does not describe the average mood rating but rather the mood rating when no time was spent playing sports.
  
- **B)** "Students who had a mood rating of 0 must have spent 5 hours playing sports." – Incorrect, this reverses the relationship. The intercept deals with mood ratings when hours are 0, not the other way around.

- **C)** "The model indicates that students who spent 0 hours playing sports will have an average mood rating of 5." – This is correct. The y-intercept indicates that at 0 hours, the mood rating is predicted to be 5.

- **D)** "The model indicates that students who had a mood rating of 0 will spend approximately 5 hours playing sports." – Incorrect, this is misinterpreting the relationship. The intercept talks about mood rating when the hours are 0.

The best answer is **C)**.

Would you like further details or clarifications? Here are 5 follow-up questions:

1. What is the importance of the slope in a regression line?
2. How do we calculate the y-intercept in a regression equation?
3. What does it mean when a scatterplot shows a positive correlation?
4. How can outliers affect the regression line and its interpretation?
5. Why is understanding residuals important in regression analysis?

**Tip:** In regression, the y-intercept provides the estimated value of the dependent variable when all independent variables are set to zero.

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 a scatterplot and regression line to show this relationship. The fitted line has a y-intercept of 5. What is the best interpretation of this y-intercept?

Learn how to interpret the y-intercept in a linear regression model. This problem examines the relationship between hours spent playing sports and mood rating based on a scatterplot. Suitable for students in Grades 10-12.

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