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# hw1 - PS 233 Intermediate Statistical Analysis Homework...

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PS 233 – Intermediate Statistical Analysis Homework 1 (Due 2/1/2002) Exercise 1 Show that: xx yy i n i i S S y y ErrorSS 2 1 2 1 ˆ ) ˆ ( β - = - = = where 2 1 ) ( y y S n i i yy - = = , 2 1 ) ( x x S n i i xx - = = , and 1 ˆ β is the slope of the regression line in a Linear Regression Model. Exercise 2 If the errors in the Linear Regression Model are NOT normally distributed, the OLS estimator is still unbiased, but it is no longer the most efficient. Is this statement true, false, or undetermined? Explain. Exercise 3 Table 1 presents data on economic growth and education for 11 East Asian countries. Ecgrowth measures the average annual growth of GDP per capita during 1965- 90. SecSch measures the log of the average number of years of secondary school in the population in 1965. We are interested in estimating the impact of education on economic growth. a) Find “by hand” the least squares line for the data in Table 1; b) Find “by hand” a 95% confidence interval for 1 ˆ β , the regression slope; c) Check the results in Stata and plot the data and the regression line.

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hw1 - PS 233 Intermediate Statistical Analysis Homework...

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