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. The $y$-intercept represents the expected value of the dependent variable when the independent variable is 0. ‖ ‖ step 2 ⋮ In this context, the dependent variable is "Mood rating" and the independent variable is "Hours playing sports." Therefore, the $y$-intercept of 5 indicates the expected mood rating for a student who spent 0 hours playing sports. ‖ ‖ step 3 ⋮ Evaluate the given answer choices in the context of the interpretation of the $y$-intercept. ‖ ∻1 Answer∻ ***D*** ∻Key Concept∻ ⚹$y$-intercept of a regression line⚹ ∻Explanation∻ ⚹The $y$-intercept of a regression line represents the expected value of the dependent variable when the independent variable is zero.⚹◊What is the significance of the $y$-intercept in the context of the scatter plot and line of best fit provided by the OCR model?⍭ Generate me a similar question◊

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