Making Predictions from a Least-Squares Regression Line
Question 11 • SC-Statistical Modeling SDPC
A movie production company was interested in the relationship between a movie’s budget and how well that movie was received by the public. Information was collected on several movies and was used to obtain the regression equation ŷ = 0.145x + 0.136, where x represents the budget of the movie (in millions of dollars) and ŷ is the predicted score of that movie (in points from 0 to 1). Which statement best describes the meaning of the slope of the regression line?
Answer
A
For each increase in score by 1 point, the predicted budget increases by $0.136 million.
B
For each increase in score by 1 point, the predicted budget increases by $0.145 million.
C
For each increase in budget by $1 million, the predicted score increases by 0.136 points.
D
For each increase in budget by $1 million, the predicted score increases by 0.145 points.
Explanation
In the regression equation ŷ = 0.145x + 0.136, the slope is 0.145. Since x is the budget in millions of dollars and ŷ is the predicted score, the slope means the predicted score increases by 0.145 points for each $1 million increase in budget. So the correct statement is D.
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