Solved: Forecasting movie revenues with Twitter. Refer to

QUESTION:

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 11.23 (p. 617). 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 movie’s tweet rate, i.e., the average number of tweets referring to the movie per hour 1 week prior to the movie’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 (\(x_1\)) and PN-ratio (\(x_2\)).

b. Which \(\beta\) in the model, part a, represents the change in revenue (y) for every 1-tweet increase in the tweet rate (\(x_1\)), holding PN-ratio (\(x_2\)) constant?

c. Which \(\beta\) in the model, part a, represents the change in revenue (y) for every 1-unit increase in the PN-ratio (\(x_2\)), holding tweet rate (\(x_1\)) constant?

d. The following coefficients were reported: \(R^{2}=.945\) and \(R_{\mathrm{a}}^{2}=.940\). Give a practical interpretation for both \(R^{2}\) and \(R_{\mathrm{a}}^{2}\).

e. Conduct a test of the null hypothesis, \(H_{0}: \beta_{1}=\beta_{2}=0\). Use \(\alpha=.05\).

f. The researchers reported the p-values for testing \(H_{0}: \beta_{1}=0\) and \(H_{0}: \beta_{2}=0\) as both less than .0001. Interpret these results (use \(\alpha=.01\)).