Q3 (30 points) 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 movie's tweet rate, i.e., the average number of tweets (at Twitter. com) referring to the movie per hour 1 week prior to the movie's release. The data (simulated based on information provided in the study) are in the file Homework 4 Q4.xlsx. a. Fit a linear regression model to the data in the file. How much do you estimate a movie's opening weekend revenue to change as the tweet rate for the movie increases by an average of 100 tweets per hour? b. Conduct a test to determine whether opening weekend revenue increase linearly as the tweet rate for the movie increases, write down the null and alternative hypothesis, report the p-value, and use alpha=0.05 c. Find the total variation of y (SS_yy) and SSE, and use them to calculate the Coefficient of Determination R-squared