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. 726). The researchers modeled a movie’s opening weekend box office revenue 1y2 as a function of tweet rate 1x12 and ratio of positive to negative tweets 1x22 using a first-order model.

a. Write the equation of an interaction model for E1y2 as a function of x1 and x2.

b. In terms of the b’s in the model, part

a, what is the change in revenue 1y2 for every 1-tweet increase in the tweet rate 1x12, holding PN-ratio 1x22 constant at a value of 2.5?

c. In terms of the b’s in the model, part

a, what is the change in revenue 1y2 for every 1-tweet increase in the tweet rate 1x12, holding PN-ratio 1x22 constant at a value of 5.0?

d. In terms of the b’s in the model, part

a, what is the change in revenue 1y2 for every 1-unit increase in the PN-ratio 1x22, holding tweet rate 1x12 constant at a value of 100?

e. Give the null hypothesis for testing whether tweet rate 1x12 and PN-ratio 1x22 interact to affect revenue 1y2.