4.6              Earnings of Mexican street vendors. Detailed interviews were conducted with over 1,000 street vendors in the  city  of  Puebla,  Mexico,  in order to study the factors influencing vendors’ incomes (World Development, February 1998). Vendors were defined as individuals working in the street, and included vendors with carts and stands on wheels and excluded beggars, drug dealers, and prostitutes. The researchers collected data on gen- der, age, hours worked per day, annual earnings, and education level. A subset of these data appears in the accompanying table.

(a)    Write a first-order model for mean annual earnings, E(y), as a function of age (x1) and hours worked (x2).

 

SAS output for Exercise 4.6

 

Source: Adapted from Smith, P. A., and Metzger, M. R. ‘‘The return to education: Street vendors in Mexico,’’ World  Development,  Vol.  26,  No.  2,  Feb.  1998, pp.

289 – 296.

(b)    The model was fit to the data using SAS. Find the least squares prediction equation on the printout shown below.

(c)    Interpret the estimated β coefficients in your model.

(d)    Conduct a test of the global utility of the model (at α = .01). Interpret the result.

(e)   

a

Find and interpret the value of R2.

 

(f)    Find and interpret s, the estimated standard deviation of the error term.

(g)    Is age (x1) a statistically useful predictor of annual earnings? Test using α = .01.

(h)    Find a 95% confidence interval for β2. Inter-

pret the interval in the words of the problem.