Question: A movie production company was interested in the relationship between the budget to make a movie…

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. 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 a movie (in millions of dollars) and \(\hat{y}\) is the predicted score of that movie (in points from 0 to 1). What is the predicted score of a movie that has a $250,000 budget?

• 0.03625 points
• 0.17225 points
• 0.7862 points
• 1 point

Solution

The regression equation given is: \[ \hat{y} = 0.145x + 0.136 \] where \( x \) is the budget in millions of dollars. The budget given is $250,000, which is 0.25 million dollars. Substitute \( x = 0.25 \) into the equation: First, calculate \( 0.145 \times 0.25 \): \[ 0.145 \times 0.25 = 0.03625 \] Now, add 0.136 to the result: \[ 0.03625 + 0.136 = 0.17225 \] Therefore, the predicted score for a movie with a $250,000 budget is 0.17225 points.