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### What does the estimated variance or standard error of the forecast error tell us about our prediction

INSTRUCTIONS TO CANDIDATES

Question 1: For Both ETF2100 and ETF5910

You will use the data file movie revenue.csv available on Moodle to answer this question. It contains data on box office revenue (i.e., revenue raised by ticket sales) and budget of movies released in the US during 2017-2019. Each observation is a movie. The variables are as follows:

• domestic revenue: box office revenue in the US (in millions dollars)

• world revenue : world-wide box office revenue (in millions dollars)

• budget: movie budget (in millions dollars) We are interested in the relationship between movie’s worldwide revenue (W) and its budget (B).

(a) Estimate the following linear regression model by least squares. Report the result in full (i.e., including s.e. and R-squared) and include your Eviews output in your answer.

Wi = β1 + β2Bi + ei

(b) Interpret the estimated slope coefficient. Is this consistent with what you would expect the relationship to be? Explain briefly.

(c) Interpret the estimated intercept. Does it make sense? Comment.

(d) Interpret the R2 you found in part (a).

(e) Construct a 95% confidence interval for β2. Interpret the confidence interval.

(f) Predict worldwide box office revenue for a movie with a budget of 180,500,000 dollars. Give both a point predictor and a 90 % prediction interval. Use Eviews to find the exact t-critical value. Show your calculation and don’t forget to interpret your answers in words.

(g) What does the estimated variance (or standard error) of the forecast error tell us about our prediction?

(h) How does each of the followings affect the size of the standard errors of the forecast error. Give a brief intuition (i.e., give an easy-to-understand explanation in words without the need of mathematical formula/proof).

(i) Smaller variance of the error term

(ii) Larger value of (B0 − B¯) 2 , where B0 is the value of the variable movie budget, for which we want to predict the corresponding value of movie revenue.

(i) Test at the 1% level of significance if “an extra million dollar spent in making a movie is associated with an increase in the movie’s worldwide box office revenue of MORE than three million dollars.” Be sure to show all the steps used to conduct your test using the t-statistics approach.

Question 2: Part 1 is for both ETF2100 and ETF5910; Part 2 is for ETF5910 ONLY

Consider the following simple regression model:

yi = β1 + β2xi + ei

where E(ei | x) = 0, var(ei | x) = σ 2 and cov(ei , ej | x) = 0 for all i 6= j. Suppose application of least squares rule to this equation with number of observations N = 35 yields b1 = 10, b2 = 2, and that we obtain SSE = 12, R2 = 0.7 and

cov c (b1, b2 | x) =  4 −0.1 −0.1 0.25 

(3) Are the following statements true or false? Clearly indicate if each statement is true or false and support your choice with a brief explanation.

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