The equation of the line fitted is Metascore = -20.9 + 12.5 * imdbRating Using a linear model based on this fitted line: A group of movies that all have an imdbRating of 7.2 is estimated to have a mean Metascore of ______ (round your answer to one decimal place e.g. 32.0 or 64.1). An individual movie that has an imdbRating of 7.2 and an actual Metascore of 63.7 would have a residual/prediction error of ________ (round your answer to one decimal place e.g. 32.0 or -64.1). A prediction model was developed to generate prediction intervals for Metascore, using the line fitted and a fixed error amount of 2 x RMSE. The RMSE for this sample data is 13.3. Using this prediction model, the Metascore for a movie with an imdbRating of 7.2 is predicted to be between and (round your interval limits to one decimal place).
Question
The equation of the line fitted is Metascore = -20.9 + 12.5 * imdbRating
Using a linear model based on this fitted line:
A group of movies that all have an imdbRating of 7.2 is estimated to have a mean Metascore of ______ (round your answer to one decimal place e.g. 32.0 or 64.1). An individual movie that has an imdbRating of 7.2 and an actual Metascore of 63.7 would have a residual/prediction error of ________ (round your answer to one decimal place e.g. 32.0 or -64.1). A prediction model was developed to generate prediction intervals for Metascore, using the line fitted and a fixed error amount of 2 x RMSE. The RMSE for this sample data is 13.3.
Using this prediction model, the Metascore for a movie with an imdbRating of 7.2 is predicted to be between and (round your interval limits to one decimal place).
Solution
To answer these questions, we need to use the given linear model equation: Metascore = -20.9 + 12.5 * imdbRating.
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To find the mean Metascore for a group of movies with an imdbRating of 7.2, we substitute 7.2 into the equation:
Metascore = -20.9 + 12.5 * 7.2 Metascore = 69.3
So, a group of movies that all have an imdbRating of 7.2 is estimated to have a mean Metascore of 69.3.
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To find the residual/prediction error for an individual movie with an imdbRating of 7.2 and an actual Metascore of 63.7, we subtract the predicted Metascore from the actual Metascore:
Residual = Actual Metascore - Predicted Metascore Residual = 63.7 - 69.3 Residual = -5.6
So, an individual movie that has an imdbRating of 7.2 and an actual Metascore of 63.7 would have a residual/prediction error of -5.6.
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To find the prediction interval for a movie with an imdbRating of 7.2, we use the RMSE value of 13.3 and the fixed error amount of 2 * RMSE:
Lower limit = Predicted Metascore - 2 * RMSE Lower limit = 69.3 - 2 * 13.3 Lower limit = 42.7
Upper limit = Predicted Metascore + 2 * RMSE Upper limit = 69.3 + 2 * 13.3 Upper limit = 95.9
So, using this prediction model, the Metascore for a movie with an imdbRating of 7.2 is predicted to be between 42.7 and 95.9.
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