Forecasting movie revenues with Twitter. Refer to theIEEE

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 12.10(p. 680). The researchers modeled a movie's opening weekend box office revenue (y) as a function of tweet rate \(\left(x_1\right)\) and ratio of positive to negative tweets \(\left(x_2\right)\) using a first-order model

a. Write the equation of an interaction model for E(y) as a function of \(x_1\) and \(x_2\).

b. In terms of the \(\beta\)'s in the model, part a, what is the change in revenue \((\mathbf{y})\) for every 1-tweet increase in the tweet rate \(\left(x_1\right)\), holding PN-ratio \(\left(x_2\right)\) constant at a value of 2.5?

c. In terms of the \(\beta\)'s in the model, part a, what is the change in revenue (y) for every 1-tweet increase in the tweet rate \(\left(x_1\right)\), holding PN-ratio \(\left(x_2\right)\) constant at a value of 5.0?

d. In terms of the \(\beta\)'s in the model, part a, what is the change in revenue (y) for every 1-unit increase in the PN-ratio \(\left(x_2\right)\), holding tweet rate \(\left(x_1\right)\) constant at a value of 100?

e. Give the null hypothesis for testing whether tweet rate \(\left(x_1\right)\) and PN-ratio \(\left(x_2\right)\) interact to affect revenue (y).