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 .

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 .
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 .

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Interpret the $y$-intercept of the regression line in the context of the problem. ‖ ‖ 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.◊What is the formula for calculating the slope of the regression line in a scatterplot?⍭ Generate me a similar question◊⚹

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