Determine how the ordinary least squares, Applied Statistics

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Following the general methodology used by econometricians as explained in the session for week 1 (eight steps), explain how you would proceed to determine if a good complies with the Law of Demand.

Question

Determine how the Ordinary Least Squares (OLS) method estimates b1 and b2 for the simple linear equation (Y = B1 + B2 X). Once you had
estimated the equation, explain how would you determine whether it is a good fit for the actual equation.

Question
Analysing data at country level, Helble and Sato (2011) estimated the following relationship between the alcohol consumption per capita (Alc) and the growth rate of GDP per capita (gGDP).

Alc = 4.198 + 0.088 gGDP R2 = 0.004, n=4829

Standard error = (0.144) (0.031)

a) Set up a 95% confidence interval for the slope (B2).

b) Using the confidence interval computed in (a) test the hypothesys that B2=0.

c) Test the significance at 5% of B2 by means of the t-test.

d) Discuss the relationship this equation reflects, elaborating on the meaning of the R2, and the result of the t-test.

Helble, M., Sato, A., 2011. Booms and booze: on the relationship between macroeconomic conditions and alcohol consumption. Health Policy. ISSN 0168-8510 (in press).

In the table below you can find data on the recommended retail price for a 20 cigarette pack (RRP, pounds sterling) and UK consumption of cigarettes (UKDP, in billion cigarettes) for 20 years. Data is sourced from the Tobacco Manufacturers' Association.

a) Discuss the relationship, if any, you would expect between the two variables.

b) Draw the scatterplot between UKDP and RRP.

c) Do an OLS regression, interpret and discuss your results fully.

d) Establish a 95% confidence interval for the slope and test the hypothesis that the true slope coefficient is zero.

e) Suppose the government decides to increase tax so that the RRP reaches £6. Forecast consumption at this price level.

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