AnswersStatistical ReasoningMaking Predictions from a Least-Squares Regression Line — QuizQuestion 8
8
QuizMultiple Choice

Making Predictions from a Least-Squares Regression Line — Quiz

Question 8 • Statistical Reasoning

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 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 slope of the regression line?

Answer
A
For each increase in score by 1 point, the predicted budget increases by 0 point 1 3 6 dollars million.
B
For each increase in budget by 1 dollars million, the predicted score increases by 0 point 1 4 5 points.
C
For each increase in score by 1 point, the predicted budget increases by 0 point 1 4 5 dollars million.
D
For each increase in budget by 1 dollars million, the predicted score increases by 0 point 1 3 6 points.

Explanation

In the regression equation, the slope is 0.145, the coefficient of x. Since x is the movie budget in millions of dollars and y is the predicted score, the slope means that for each $1 million increase in budget, the predicted score increases by 0.145 points. Therefore, the correct statement is “For each increase in budget by 1 dollars million, the predicted score increases by 0 point 1 4 5 points.”

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