A movie producer feels that the gross revenue (found in the "gross" column) is dependent on the following factors: duration, budgetInMills, director_facebook_likes, actor_1_facebook_likes, actor_2_facebook_likes, actor_3_facebook_likes, imdb_score.He does a regression analysis, and gets the regression table as shown below. From the above, he gets the regression equation:grossInMills = - 63.14206407 + 0.43862544 duration + 0.10925448 budgetInMills + 0.00102452 director_facebook_likes + 0.00013228 actor_1_facebook_likes + 0.00122819 actor_2_facebook_likes + 0.00681006 actor_3_facebook_likes + 8.07281821 imdb_scoreAssuming an alpha of 0.05, are all the variables chosen above, significant? If not, which should be eliminated first?

Question

BlackTom AI · Accepted Answer

Let’s walk through each option in turn, using the regression table values and the alpha = 0.05 criterion to judge significance.

actor_2_facebook_likes: The p-value for this coefficient is reported as < 0.0001, which is far below 0.05. This variable is statistically significant in predicting grossInMills, so it should be considered important in the model.

duration of movie: The duration coefficient has a p-value < 0.0001, indicating strong statistical significance at the 0.05 level. Therefore, duration is a significant predictor of grossInMills.

None of the above. Do not eliminate any.: This statement would imply that every listed variable is significant. However, the table shows at least one variable with p > 0.05 (see actor_1_facebook_likes), so this option cannot be correct.

actor_3_facebook_likes: The p-value for actor_3_facebook_likes is < 0.0001, well below 0.05, so this coefficient is statistically significant and contributes to the model.

actor_4_facebook_likes: This variable does not appear in the regression table at all. Since there is no coefficient, standard error, or p-value reported for actor_4_facebook_likes in the provided output, we cannot assess its significance from this model. Therefore, this option is not supported by the given information.

actor_1_facebook_likes: The p-value for actor_1_facebook_likes is 0.0653, which is larger than 0.05. This means actor_1_facebook_likes is not statistically significant at the 5% level and could be a candidate for elimination from the model (subject to model selection considerations).

Director_facebook_likes: The coefficient for director_facebook_likes has a p-value of 0.0035, which is below 0.05. This shows it is a statistically significant predictor of grossInMills in the model.

imdb_score: The imdb_score coefficient has a p-value of < 0.0001, indicating strong statistical significance. imdb_score is thus a significant predictor.

budget in millions (this is the budget column, divided by 1,000,000): The budgetInMills coefficient p-value is < 0.0001, demonstrating that budget in millions is a significant predictor.

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