A movie studio wishes to determine the relationship between the revenue from the rental of comedies on DVD and videotape and the revenue generated from the theatrical release of such movies. The studio has bivariate data from a sample of 13 comedies released over the past five years. These data give the revenue x from theatrical release (in millions of dollars) and the revenue y from DVD and videotape rentals (in millions of dollars) for each of the 13 movies. The least- squares regression equation computed from the data is y= 3.57+0.13x. The studio has plans for the DVD/video release of a comedy that grossed about 40.5 million dollars in theaters. The studio has predicted the rental revenue from this release using the regression equation and is now interested in both a prediction interval for this rental revenue and a confidence interval for the mean rental revenue of movies generating this same theater revenue. The studio has already computed the following for their data: • mean square error (MSE) = 14.65; (40.5 – x)² 1 z 0.0977, 13 13 Σ- i= 1 where x, x2, .., x13 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 below. 1 What is the 90% confidence interval for the mnean rental revenue (in millions of dollars) when the Lower limit:

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A movie studio wishes to determine the relationship between the revenue from the rental of comedies on DVD and videotape and the revenue generated from
the theatrical release of such movies. The studio has bivariate data from a sample of 13 comedies released over the past five years. These data give the revenue
x from theatrical release (in millions of dollars) and the revenue y from DVD and videotape rentals (in millions of dollars) for each of the 13 movies. The least-
squares regression equation computed from the data is y= 3.57+0.13x.
The studio has plans for the DVD/video release of a comedy that grossed about 40.5 million dollars in theaters. The studio has predicted the rental revenue from
this release using the regression equation and is now interested in both a prediction interval for this rental revenue and a confidence interval for the mean rental
revenue of movies generating this same theater revenue. The studio has already computed the following for their data:
• mean square error (MSE) ~ 14.65;
2
(40.5 – x,
1
+
13
- 0.0977,
13
2
Σ
X;
i = 1
where x1, X2'
denote the theater revenues in the sample, and x denotes their mean.
... *13
Based on this information, and assuming that the regression assumptions hold, answer the questions in the table below.
Lower limit:
1. What is the 90% confidence interval for the mean rental revenue (in millions of dollars) when the
theater revenue is 40.5 million dollars? (Carry your intermediate computations to at least four decimal
places, and round your answer to at least one decimal place.)
Upper limit:
2. Choose one response to answer the question below.
Consider (but do not actually compute) the 90% prediction interval for an individual value for rental revenue when the theater
revenue is 40.5 million dollars. How would the confidence interval computed above compare to this prediction interval (assuming
that both intervals are computed from the same sample data)?
Transcribed Image Text:A movie studio wishes to determine the relationship between the revenue from the rental of comedies on DVD and videotape and the revenue generated from the theatrical release of such movies. The studio has bivariate data from a sample of 13 comedies released over the past five years. These data give the revenue x from theatrical release (in millions of dollars) and the revenue y from DVD and videotape rentals (in millions of dollars) for each of the 13 movies. The least- squares regression equation computed from the data is y= 3.57+0.13x. The studio has plans for the DVD/video release of a comedy that grossed about 40.5 million dollars in theaters. The studio has predicted the rental revenue from this release using the regression equation and is now interested in both a prediction interval for this rental revenue and a confidence interval for the mean rental revenue of movies generating this same theater revenue. The studio has already computed the following for their data: • mean square error (MSE) ~ 14.65; 2 (40.5 – x, 1 + 13 - 0.0977, 13 2 Σ X; i = 1 where x1, X2' denote the theater revenues in the sample, and x denotes their mean. ... *13 Based on this information, and assuming that the regression assumptions hold, answer the questions in the table below. Lower limit: 1. What is the 90% confidence interval for the mean rental revenue (in millions of dollars) when the theater revenue is 40.5 million dollars? (Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.) Upper limit: 2. Choose one response to answer the question below. Consider (but do not actually compute) the 90% prediction interval for an individual value for rental revenue when the theater revenue is 40.5 million dollars. How would the confidence interval computed above compare to this prediction interval (assuming that both intervals are computed from the same sample data)?
13
2
Σ
(+;- )
i= 1
where x1, X2:
, x13 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 below.
Lower limit:
1. What is the 90% confidence interval for the mean rental revenue (in millions of dollars) when the
theater revenue is 40.5 million dollars? (Carry your intermediate computations to at least four decimal
places, and round your answer to at least one decimal place.)
Upper limit:
2. Choose one response to answer the question below.
Consider (but do not actually compute) the 90% prediction interval for an individual value for rental revenue when the theater
revenue is 40.5 million dollars. How would the confidence interval computed above compare to this prediction interval (assuming
that both intervals are computed from the same sample data)?
Choose one
3. Choose one response to answer the question below.
For the theater revenue values in this sample, 23.3 million dollars is more extreme than 40.5 million dollars is, that is, 23.3 is
farther from the sample mean theater revenue than 40.5 is. How would the 90% confidence interval for the mean rental revenue
when the theater revenue is 23.3 million dollars compare to the 90% confidence interval for the mean rental revenue when the
theater revenue is 40.5 million dollars?
Choose one
?
13
Transcribed Image Text:13 2 Σ (+;- ) i= 1 where x1, X2: , x13 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 below. Lower limit: 1. What is the 90% confidence interval for the mean rental revenue (in millions of dollars) when the theater revenue is 40.5 million dollars? (Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.) Upper limit: 2. Choose one response to answer the question below. Consider (but do not actually compute) the 90% prediction interval for an individual value for rental revenue when the theater revenue is 40.5 million dollars. How would the confidence interval computed above compare to this prediction interval (assuming that both intervals are computed from the same sample data)? Choose one 3. Choose one response to answer the question below. For the theater revenue values in this sample, 23.3 million dollars is more extreme than 40.5 million dollars is, that is, 23.3 is farther from the sample mean theater revenue than 40.5 is. How would the 90% confidence interval for the mean rental revenue when the theater revenue is 23.3 million dollars compare to the 90% confidence interval for the mean rental revenue when the theater revenue is 40.5 million dollars? Choose one ? 13
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