Making Predictions from a Least-Squares Regression Line — Quiz
Question 5 • Statistical Reasoning
A movie production company was interested in the relationship between the budget to make a movie and how well that movie was received by the public. The company collected information on several movies and used it to obtain the regression equation widehat y is equal to 0 point 1 4 5 x plus 0 point 1 3 6 , where x represents the budget of the movie (in millions of dollars) and widehat y is the predicted score of that movie (in points from 0 to 1 ). Which statement best describes the meaning of the y - intercept of the regression line?
Answer
A
When the score of a movie is 0 points, the predicted budget is 0 dollars .
B
When the budget of a movie is 0 dollars , the predicted rating is 0 point 1 3 6 points. This interpretation is not meaningful, because a movie cannot have a budget of 0 dollars .
C
When the score of a movie is 0 points, the predicted budget is 0 point 1 3 6 dollars million.
D
When the budget of a movie is 0 dollars , the predicted rating is 0 point 1 4 5 points. This interpretation is not meaningful, because a movie cannot have a budget of 0 dollars .
Explanation
In the regression equation ŷ = 0.145x + 0.136, the y-intercept is 0.136, the predicted score when the budget x is 0 million dollars. Thus, the prediction is a rating of 0.136 points. This interpretation is not meaningful in practice because a movie cannot realistically be made with a zero-dollar budget.
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