2. Consider annual per-capita sales in tobacco (Y) and aggregate tobacco related advertisements (X) in the U.S. (the data are in millions of dollars). The sample size is n= = 49.

1 Tobacco Sales (Y) and Advertisement (X) Tobacco Sales (Y) The OLS results follows: a. 5000 4000 3000 2000 1000 0 0 200 400 600 Advertisement (X) We are interested in estimating the relationship between advertisements and sales in tobacco: Y, =B₁ + B₂X, +u, Intercept Tobbaco Ad ♦ ♦ Sum of Squares Mean Square Regression 13069027.5359 13069027.5359 Residual 27830633.2396 592141.1328 Total 40899660.7755 800 1000 OLS Estimate Standard Error 2487.5635 155:0608 2.6582 0.5658 By hand present an accurate plot of the fitted regression line, properly labeled (intercept, slope, etc.). Predict the value of tobacco sales based on advertisement outlays equal to 900./n3. b. C. a. Consider the classical hypothesis: H₁: B₂ = 0 H₁: B₂ 0 b. C. H₁: B₁=0 H₁: B, 0 Perform t-tests of the above hypotheses at the 10%, 5% and 1% levels. Comment on their outcomes, and the implications for our model of tobacco sales. Derive 95% CI's for the intercept and slope parameters. Comment on their sizes and how they relate to the test statistics computed above. Consider an alternative linear estimator of the slope: B₂- Y.-Y. X₂-X₁ where we are using only two points of data, although n >> 2 observations may be available. First, without doing any calculations, why is B, a logical estimator of ₂? Show that this new estimator is unbiased. That is, show E(B₂)=B₂. Why is this estimator not consistent? Without any derivations, provide a brief, yet complete, argument for the claim that the OLS estimator is more efficient than this new estimator. Comm Derive the R², compute the percent of the variance of Y captured by X, and comment on how well the model fits. 2