Question

A movie studio wishes to determine the relationship between the revenue from the rental of comedies on DVD and the theatrical release of such movies. The studio has bivariate data from a sample of 12 comedies released on DVD. x from theatrical release (in millions of dollars) and the revenue y from DVD and videotape rentals (in millions of dollars). squares regression equation computed from the data is ? = 3.05 + 0.17x. The studio has plans for the DVD/video release of a comedy that grossed about 46.0 million dollars in theaters. this release using the regression equation and is now interested in both a prediction interval for this rental rev revenue of movies generating this same theater revenue. The studio has already computed the following for this release: • mean square error (MSE) ? 13.94; • 1/12 + (46.0 - x?)² / ?(xi - x?)² ? 0.1616, where x1, x2, ..., x12 denote the theater revenues in the sample, and x? denotes their mean. Based on this information, and assuming that the regression assumptions hold, answer the questions in the table. 1. What is the 90% prediction interval for an individual value for rental revenue (in millions of dollars) when the theater revenue is 46.0 million dollars? (Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.) Lower limit: Upper limit: 2. Choose one response to answer the question below. Consider (but do not actually compute) the 90% confidence interval for the mean rental revenue when the theater revenue is 46.0 million dollars. How would this confidence interval compare to the prediction interval computed above (assuming that both intervals are computed from the same sample data)? The confidence interval would have the same center as, but would be narrower than, the prediction interval. 3. Choose one response to answer the question below. For the theater revenue values in this sample, 23.8 million dollars is more extreme than 46.0 million dollars is, that is, 23.8 is farther from the sample mean theater revenue than 46.0 is. How would the 90% prediction interval for the mean rental revenue when the theater revenue is 46.0 million dollars compare to the 90% prediction interval for the mean rental revenue when the theater revenue is 23.8 million dollars? ? Choose one The interval computed from a theater revenue of 46.0 would be wider and have a different center. The interval computed from a theater revenue of 46.0 would be narrower but have the same center. The interval computed from a theater revenue of 46.0 would be wider but have the same center. The intervals would be identical. The interval computed from a theater revenue of 46.0 would be narrower and have a different center.

A movie studio wishes to determine the relationship between the revenue from the rental of comedies on DVD and the theatrical release of such movies. The studio has bivariate data from a sample of 12 comedies released on DVD. x from theatrical release (in millions of dollars) and the revenue y from DVD and videotape rentals (in millions of dollars). squares regression equation computed from the data is ? = 3.05 + 0.17x.

The studio has plans for the DVD/video release of a comedy that grossed about 46.0 million dollars in theaters. this release using the regression equation and is now interested in both a prediction interval for this rental rev revenue of movies generating this same theater revenue. The studio has already computed the following for this release:
• mean square error (MSE) ? 13.94;
• 1/12 + (46.0 - x?)² / ?(xi - x?)² ? 0.1616,
where x1, x2, ..., x12 denote the theater revenues in the sample, and x? denotes their mean.

Based on this information, and assuming that the regression assumptions hold, answer the questions in the table.

1. What is the 90% prediction interval for an individual value for rental revenue (in millions of dollars) when the theater revenue is 46.0 million dollars? (Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.)
Lower limit:
Upper limit:

2. Choose one response to answer the question below.
Consider (but do not actually compute) the 90% confidence interval for the mean rental revenue when the theater revenue is 46.0 million dollars. How would this confidence interval compare to the prediction interval computed above (assuming that both intervals are computed from the same sample data)?
The confidence interval would have the same center as, but would be narrower than, the prediction interval.

3. Choose one response to answer the question below.
For the theater revenue values in this sample, 23.8 million dollars is more extreme than 46.0 million dollars is, that is, 23.8 is farther from the sample mean theater revenue than 46.0 is. How would the 90% prediction interval for the mean rental revenue when the theater revenue is 46.0 million dollars compare to the 90% prediction interval for the mean rental revenue when the theater revenue is 23.8 million dollars?
? Choose one
The interval computed from a theater revenue of 46.0 would be wider and have a different center.
The interval computed from a theater revenue of 46.0 would be narrower but have the same center.
The interval computed from a theater revenue of 46.0 would be wider but have the same center.
The intervals would be identical.
The interval computed from a theater revenue of 46.0 would be narrower and have a different center.

A movie studio wishes to determine the relationship between the revenue from the rental of comedies on DVD and the theatrical release of such movies. The studio has bivariate data from a sample of 12 comedies released on DVD. x from theatrical release (in millions of dollars) and the revenue y from DVD and videotape rentals (in millions of dollars). squares regression equation computed from the data is ? = 3.05 + 0.17x.

The studio has plans for the DVD/video release of a comedy that grossed about 46.0 million dollars in theaters. this release using the regression equation and is now interested in both a prediction interval for this rental rev revenue of movies generating this same theater revenue. The studio has already computed the following for this release:
• mean square error (MSE) ? 13.94;
• 1/12 + (46.0 - x?)² / ?(xi - x?)² ? 0.1616,
where x1, x2, ..., x12 denote the theater revenues in the sample, and x? denotes their mean.

Based on this information, and assuming that the regression assumptions hold, answer the questions in the table.

1. What is the 90% prediction interval for an individual value for rental revenue (in millions of dollars) when the theater revenue is 46.0 million dollars? (Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.)
Lower limit:
Upper limit:

2. Choose one response to answer the question below.
Consider (but do not actually compute) the 90% confidence interval for the mean rental revenue when the theater revenue is 46.0 million dollars. How would this confidence interval compare to the prediction interval computed above (assuming that both intervals are computed from the same sample data)?
The confidence interval would have the same center as, but would be narrower than, the prediction interval.

3. Choose one response to answer the question below.
For the theater revenue values in this sample, 23.8 million dollars is more extreme than 46.0 million dollars is, that is, 23.8 is farther from the sample mean theater revenue than 46.0 is. How would the 90% prediction interval for the mean rental revenue when the theater revenue is 46.0 million dollars compare to the 90% prediction interval for the mean rental revenue when the theater revenue is 23.8 million dollars?
? Choose one
The interval computed from a theater revenue of 46.0 would be wider and have a different center.
The interval computed from a theater revenue of 46.0 would be narrower but have the same center.
The interval computed from a theater revenue of 46.0 would be wider but have the same center.
The intervals would be identical.
The interval computed from a theater revenue of 46.0 would be narrower and have a different center.

Added by Sonya J.

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