# solution

Forecasting movie revenues with Twitter. Refer to the IEEE International Conference on Web Intelligence and Intelligent Agent Technology (2010) study on using the volume of chatter on Twitter.com to forecast movie box office revenue, Exercise 12.10 (p. 723). The researchers modeled a movieâ€™s opening weekend box office revenue (y) as a function of tweet rate (x1) and ratio of positive to negative tweets (x2) using a first-order model.

a. Write the equation of an interaction model for E(y) as a function of x1 and x2.

b. In terms of the bâ€™s in the model, part a, what is the change in revenue 1y2 for every 1-tweet increase in the tweet rate (x1), holding PN-ratio (x2) constant at a value of 2.5?

c. In terms of the bâ€™s in the model, part a, what is the change in revenue 1y2 for every 1-tweet increase in the tweet rate (x1), holding PN-ratio (x2) constant at a value of 5.0?

d. In terms of the bâ€™s in the model, part a, what is the change in revenue (y) for every 1-unit increase in the PN-ratio (x2), holding tweet rate (x1) constant at a value of 100?

e. Give the null hypothesis for testing whether tweet rate (x1) and PN-ratio (x2) interact to affect revenue (y).

Exercise 12.10

Forecasting movie revenues with Twitter. Refer to the IEEE International Conference on Web Intelligence and Intelligent Agent Technology (2010) study on using the volume of chatter on Twitter.com to forecast movie box office revenue, Exercise 11.27 (p. 657). Recall that opening weekend box office revenue data (in millions of dollars) were collected for a sample of 24 recent movies. In addition to each movieâ€™s tweet rate, i.e., the average number of tweets referring to the movie per hour 1 week prior to the movieâ€™s release, the researchers also computed the ratio of positive to negative tweets (called the PN-ratio).

a. Give the equation of a first-order model relating revenue (y) to both tweet rate (x1) and PN-ratio (x2).

b. Which b in the model, part a, represents the change in revenue (y) for every 1-tweet increase in the tweet rate (x1), holding PN-ratio (x2) constant?

c. Which b in the model, part a, represents the change in revenue (y) for every 1-unit increase in the PN-ratio (x2), holding tweet rate (x1) constant?

d. The following coefficients were reported: R2 = .945 and R2 a = .940. Give a practical interpretation for both R2 and R2 a.

e. Conduct a test of the null hypothesis, H0: 1 = 2 = 0. Use a = .05.

f. The researchers reported the p-values for testing H0: 1 = 0 and H0: 2 = 0 as both less than .0001. Interpret these results (use a = .01).

Exercise 11.27

Forecasting movie revenues with Twitter. Marketers are keenly interested in how social media (e.g., Facebook, Twitter) may influence consumers who buy their products. Researchers investigated whether the volume of chatter on Twitter.com could be used to forecast the box office revenues of movies (IEEE International Conference on Web Intelligence and Intelligent Agent Technology, 2010). Opening weekend box office revenue data (in millions of dollars) were collected for a sample of 23 recent movies. In addition, the researchers computed each movieâ€™s tweet rate, i.e., the average number of tweets (at Twitter. com) referring to the movie per hour 1 week prior to the movieâ€™s release. The data (simulated based on information provided in the study) are listed in the accompanying table. Assuming that movie revenue and tweet rate are linearly related, how much do you estimate a movieâ€™s opening weekend revenue to change as the tweet rate for the movie increases by an average of 100 tweets per hour? Â

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