4.11 Th e Longley Data; 14 well-known data originally collected to assess the computational accuracy of least-squares estimates in several computer programs. Th ey have been used to illustrate several econometric problems, such as (severe) multicollinearity, outliers (discussed in Chapter 7), and sensitivity of regression results to dropping one or more observations from the analysis. Th e data is for the years 1947–1961. Th e variables are defi ned as follows: Y = number of people employed, in thousands X1 = GNP implicit price defl ator X2 = GNP, millions of dollars X3 = number of people unemployed, in thousands X4 = number of people in the armed forces, in thousands X5 = non-institutionalized population over 16 years of age X6 = year equal to 1 in 1947, 2 in 1948, up to 15 in 1961 Th ese data are given in Table 4.13 on the companion website.

(a) Create pairwise scatterplots (scatter diagrams) of all the variables in the sample. What do these scatterplots suggest about the nature of multicollinearity in the data?

(b) Create a correlation matrix. Which variables seem to be most related to each other, not including the dependent variable Y?

(c) Develop a multiple regression to predict the number of people employed, using one or more X variables.

(d) Are there any outliers in the data? If so, present the regression results in

(c) Drop the outlying observations and compare your results with those obtained in (c).

(e) What conclusions do you draw from this exercise?