Question: A movie production company was interested in the relationship between a movie’s budget and how well…

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 \(\hat{y} = 0.145x + 0.136\), where \(x\) represents the budget of the movie (in millions of dollars) and \(\hat{y}\) 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?

• For each increase in score by 1 point, the predicted budget increases by $0.136 million.
• For each increase in score by 1 point, the predicted budget increases by $0.145 million.
• For each increase in budget by $1 million, the predicted score increases by 0.136 points.
• For each increase in budget by $1 million, the predicted score increases by 0.145 points.

Solution

The problem involves interpreting the slope of the regression line from the equation given: \(y = 0.146x + 0.136\). The equation is in the form \(y = mx + b\), where \(m\) is the slope. Here, \(m = 0.146\). The slope of \(0.146\) indicates the change in \(y\) (predicted score) for each unit increase in \(x\) (budget in millions of dollars). Therefore, for each increase in budget by $1 million, the predicted score increases by 0.146 points. The correct answer is: For each increase in budget by $1 million, the predicted score increases by 0.146 points.