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ECON 2300: INTRODUCTORY ECONOMETRICS

Tutorial 2: Linear Regression with a Single Regressor, SW Ch4

E4.1 The file Growth.csv contains data on average growth rates from 1960 through 1995 for 65 coun-tries, along with variables that are potentially related to growth. A detailed description is given in Growth Description.pdf. You will investigate the relationship between growth and trade.

(a) Construct a scatterplot of average annual growth rate, growth, on the average trade share, tradeshare. Does there appear to be a relationship between the variables?

(b) One country, Malta, has a trade share much larger than the other countries. Find Malta on the scatterplot. Does Malta look like an outlier?

(c) Using all observations, run a regression of growth on tradeshare. What is the estimated slope? What is the estimated intercept? Use the regression to predict the growth rate for a country with a trade share of 0.5 and with a trade equal to 1.0

(d) Estimate the same regression, excluding the data from Malta. Answer the same questions in (c).

(e) Plot the estimated regression functions from (c) and (d). Using the scatterplot in (a), explain why the regression function that includes Malta is steeper than the regression function that excludes Malta.

(f) Where is Malta? Why is the Malta trade share so large? Should Malta be included or excluded from the analysis?

E4.2 The file Earnings and Height.csv contains data on earnings, height, and other characteristics of a random sample of U.S. workers. See Earnings and Height Description.pdf for a detailed description of the data. You will investigate the relationship between earnings and height.

(a) What is the median value of height in the sample?

(b) i. Estimate average earnings for workers whose height is at most 67 inches.

ii. Estimate average earnings for workers whose height is greater than 67 inches.

iii. On average, do taller workers earn more than shorter workers? How much more? What is a 95% confidence interval for the difference in average earnings?

(c) Construct a scatterplot of annual earnings, earnings, on height, height. Notice that the points on the plot fall along horizontal lines. (There are only 23 distinct values of earnings). Why? (Hint: Carefully read the detailed data description.)

(d) Run a regression of earnings on height.

i. What is the estimated slope?

ii. Use the estimated regression to predict earnings for a worker who is 67 inches tall, for a worker who is 70 inches tall, and for a worker who is 65 inches tall.

(e) Suppose height were measured in centimeters instead of inches. Answer the following questions about the earnings on height (in cm) regression.

i. What is the estimated slope of the regression?

ii. What is he estimated intercept?

iii. What is the R2 ?

iv. What is the standard error of the regression?

(f) Run a regression of earnings on height using data for female workers only.

i. What is the estimated slope?

ii. A randomly selected woman is 1 inch taller than he average woman in the sample. Would you predict her earnings to be higher or lower than the average earnings for women in the sample? By how much?

(g) Repeat (f) for male workers.

(h) Do you think that height is uncorrelated with other factors that cause earning? That is, do you think that the regression error term, say ui , has a conditional mean of zero, given height (Xi)?