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95% confidence interval for predictions (week 9 session 16) use the regression model below, which predicts lifetime gross of a movie, to answer the following question. 1. the movie avatar was released in december (winter), had a mpaa rating of pg-13, budget of $237m, and an actual lifetime gross of $760m. with 95% confidence, would you have expected the movie to make as much as it did? in other words, was the movie exceptionally successful? show all your work and explain.

User Pilpo
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Final answer:

To answer this question, we need to use the given regression model to predict the lifetime gross of the movie Avatar. The regression model is ŷ = 101.32 + 2.48x, where ŷ is the predicted lifetime gross and x is the day. Using this model, the predicted sales on day 60 are $250,120 and the predicted sales on day 90 are $324,520. The actual gross of $760m is significantly higher than the predicted gross, indicating that the movie was exceptionally successful.

Step-by-step explanation:

To answer this question, we need to use the given regression model to predict the lifetime gross of the movie Avatar. The regression model is ŷ = 101.32 + 2.48x, where ŷ is the predicted lifetime gross and x is the day. Since we are interested in predicting the lifetime gross at a specific time (week 9 session 16), we need to substitute the corresponding value of x into the equation.

According to the given information, the movie Avatar was released in December, had a MPAA rating of PG-13, a budget of $237m, and an actual lifetime gross of $760m. We can assume that week 9 session 16 corresponds to day 60. So, to predict the sales on day 60, we substitute x=60 into the equation: ŷ = 101.32 + 2.48(60) = 101.32 + 148.8 = 250.12 (thousands of dollars). Therefore, we would predict the sales to be $250,120 on day 60.

To predict the sales on day 90, we substitute x=90 into the equation: ŷ = 101.32 + 2.48(90) = 101.32 + 223.2 = 324.52 (thousands of dollars). Therefore, we would predict the sales to be $324,520 on day 90.

Based on the prediction for the lifetime gross of the movie Avatar, we can see that the actual gross of $760m is significantly higher than the predicted gross. This indicates that the movie was exceptionally successful, as it exceeded expectations.

User Isopach
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