Marketers are interested in how social media (e.g. Facebook and twitter) activity are related to the box office revenues of movies. Researchers collected the opening weekend box office revenue (in millions of dollars) for a sample of 23 recent movies. In addition, researchers obtained the tweet rate of each movie (average number of tweets referring to the movie per hour) in the week prior to the movie's release. Use the data to answer the following questions.

Tweet rate Revenue

1365.8 142

1212.8 76.9

581.5 61.8

310.1 32.5

455 31.2

290 30.2

250 21.3

680.2 18.3

150 17.9

164 17.1

113.9 16.3

144.5 15.1

418 14.2

98 13.7

100.8 12.1

115 11

74.4 9.8

87.5 8.4

127.6 7.2

52.2 9

144.1 8

41.3 2

2.75 0.3

1. Present a scatterplot of the data with the fitted line.

2. Write down a population linear regression model.

3. Use EViews to estimate the coefficients and write down the point estimate of the intercept and the slope coefficient (do not copy/paste EViews output).

4. Write down the sampling distribution of the slope coefficient using the relevant statistics. What assumptions are needed to obtain this sampling distribution?

5. From the OLS estimates, how would the revenue change (on average) if the tweet rate increases by 50?