Question

Math

Posted 4 months ago

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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 .
What is the best interpretation of this $y$-intercept?
Choose 1 answer:
(A) Students who had a mood rating of 0 must have spent 5 hours playing sports.
(B) The average mood rating was 5.
(C) The model indicates that students who had a mood rating of 0 will spend approximately 5 hours playing sports.
(D) The model indicates that students who spent 0 hours playing sports will have an average mood rating of 5 .
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 2

The $y$-intercept is the value of $y$ when $x$ is 0

step 3

In the context of the problem, $x$ represents "Hours playing sports" and $y$ represents "Mood rating"

step 4

Therefore, the $y$-intercept indicates the expected "Mood rating" for a student who spent 0 hours playing sports

D

Key Concept

$y$-intercept of a regression line

Explanation

The $y$-intercept of a regression line represents the expected value of the response variable when the explanatory variable is zero.

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