Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

ECON 7310: ELEMENTS OF ECONOMETRICS

Tutorial 3: Linear Regression with a Single Regressor - Hypothesis Tests and Confidence Intervals, SW Ch5

E5.1 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. Carry out the following exercises.

(a) Run a regression of earnings on height.

i. Is the estimated slope statistically significant?

ii. Construct a 95% confidence interval for the slope coefficient.

(b) Repeat (a) for female observations.

(c) Repeat (a) for male observations.

(d) Test the null hypothesis that the effect of height on earnings is the same for men and women.

E5.2 Using the dataset Growth.csv, but excluding the data for Malta, run a regression of growth on tradeshare.

(a) Is the estimated regression slope statistically significant? This is, can you reject the null hypothesis

H0 : β1 = 0 vs. H1 : β1 = 0 at the 5% or 1% significance level?

(b) What is the p-value associated with the coefficient’s t-statistic?

(c) Construct a 99% confidence interval for β1.

E5.3 The data file Birthweight Smoking.csv contains data for a random sample of babies in Pennsylvania in 1989. The data include the baby’s birth weight together with various characteristics of the mother, including whether she smoked during the pregnancy. See Birthweight Smoking Description.pdf for a detailed description of the data. You will investigate the relationship between birth weight and smoking during pregnancy.

(a) In the sample:

i. What is the average value of birthweight?

ii. What is the average value of birthweight for mothers who smoke?

iii. What is the average value of birthweight for mothers who do not smoke?

(b) i. Use the data in the sample to estimate the difference in average birth weight for smoking and nonsmoking mothers.

ii. What is the standard error for the estimated difference in (b)i?

iii. Construct a 95% confidence interval for the difference in the average birth weight for smoking and nonsmoking mothers.

(c) Run a regression of birthweight on the binary variable smoker.

i. How the estimated slope and intercept are related to your answers in Parts (a) and (b)?

ii. How the SE(βˆ 1) is related to your answer in (b)ii.

iii. Construct a 95% confidence interval for the effect of smoking on birth weight.