1. The key concept underlying regression analysis is the concept of the conditional expectation function (CEF), or population regression function (PRF). Our objective in regression analysis is to find out how the average value of the dependent variable ( or regressand) varies with the given value of the explanatory variable ( or regressor )
2. This book largely deals with linear PRFs, that is, regressions that are linear in they parameters. The may or may not be linear in the regressand or regressors.
3. For empirical purposes, its the stochastic PRF that matters. The stochastic disturbance term ui plays a critical role in estimating the PRF.
4.The PRF is an idealized concept, since in practice one rarely has access to the entire population of interest. Usually, one has a sample of observation from the population .Therefore, one uses the stochastic sample regression function (SRF) to estimate the PRF. How this actually accomplished is discussed in Chapter3.
EXERCISES
Questions
2.1 What Is the conditional expectation function or they population regression function?
2.2 What is difference between the population and sample regression functions?.Is this a distinction without difference?
2.3 What is the role of the stochastic error term ui in regresstion analysis? What in the difference between the stochastic error term and the residual ûi ?
2.4 Why do we need regression analysis ? Why not simply use the mean value of the regressand as its value?
2.5 What do we mean by a linear regression model?
2.6 Determine whether the the following models are linear in the parameters, or the variables, or both. Which of these models are linear regression model?
2.8 What is meant by an intrinsically linear regression model? If β2 in exercise 2.7d were 0.8, would be a linear or nonlinear or non linear regression model?
*2.9 Consider the following nonstochastic model (i.e.,m models without the stochastic error term). Are they linear regression models? if no, is it posible, by suitable algebraic manipulation, to convert them into lineart modela?
2.10 You are give the scattergram in Figure2.7 along with the regression line. What general conclusion do you draw from this diagram ? Is the regression line sketched in the diagram a population regression line or the sample regression line?
FIGURE 2.8 Skill intensity of exports and human capital endowment. Data are for 126 industrial and developing countries in 1985. Values along the horizontal axis are logarithms of ratio of the country's average educational attainment to is land area: vertical axis value are logarithms of tario of manufacured to primary-products exports.
Source:world Bank,World Development Report 1995,P.59. Original sources: Export data from United Nation Statistical Office COMTRADE data base; education data from UNDP 1990;land data from the world bank.
2.11. From the scattergram given Figure 2.8, what general conclusions do you draw? What is the economic theory that underlies this scattergram? (Hint: Look up any international economics textbook and read up on the Heckscher-Ohlin model of trade)
2.12. What does the scattergram Figure 2.9 reveal? On the basis of this diagram,Would you argue that minimum wage laws are good for economic well-being?
2.13 Is the regression line shown in Figure I.3 Of the Introduction the PRF or SRF ? Why? How would you interpret the scatterpoint around the re the regression line? Besides GDP, what other factors, or variables, might determine personal consumtion expenditure?
2.14 You are given the data in Table 2.7 for the United States for years 1980-1996.
2.6 Determine whether the the following models are linear in the parameters, or the variables, or both. Which of these models are linear regression model?
*2.9 Consider the following nonstochastic model (i.e.,m models without the stochastic error term). Are they linear regression models? if no, is it posible, by suitable algebraic manipulation, to convert them into lineart modela?
Source:world Bank,World Development Report 1995,P.59. Original sources: Export data from United Nation Statistical Office COMTRADE data base; education data from UNDP 1990;land data from the world bank.
2.11. From the scattergram given Figure 2.8, what general conclusions do you draw? What is the economic theory that underlies this scattergram? (Hint: Look up any international economics textbook and read up on the Heckscher-Ohlin model of trade)
2.12. What does the scattergram Figure 2.9 reveal? On the basis of this diagram,Would you argue that minimum wage laws are good for economic well-being?
2.13 Is the regression line shown in Figure I.3 Of the Introduction the PRF or SRF ? Why? How would you interpret the scatterpoint around the re the regression line? Besides GDP, what other factors, or variables, might determine personal consumtion expenditure?
2.14 You are given the data in Table 2.7 for the United States for years 1980-1996.
a. Plot the male civilian labor force participation rate against male civilian unemployment rate. Eyeball a regression line through the scatterpoints. A priori, waht is the expected relationship between the two and what is the underlying economic theory? Does the scattergram support the theory.
b.Repeat part a for females.
c.Now Plot both the male and female labor participation rates against average hourly earnings ( in 1982 dollars). (you may use separate diagrams.) Now what do you find? And how would you rationalize your finding?
d. Can you plot the labor force participation rate against the unemployment rate and the average hourly earnings simultaneously? If not, how would you verbalize the relationship among the three variables?
b.Repeat part a for females.
c.Now Plot both the male and female labor participation rates against average hourly earnings ( in 1982 dollars). (you may use separate diagrams.) Now what do you find? And how would you rationalize your finding?
d. Can you plot the labor force participation rate against the unemployment rate and the average hourly earnings simultaneously? If not, how would you verbalize the relationship among the three variables?
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