Refer to the World Development (Feb. 1998) study of street vendors' earnings, y, Exercises 10.7 and 10.20 (pp. 573,586).The STATISTIX printout below shows both a 95% prediction interval for y (left side) and a 95% confidence interval for E(y) (right side) for a 45-year-old vendor who works 10 hours a day (i.e., for x₁ = 45 and x₂= 10).

a. Interpret the 95% prediction interval for y in the words of the problem.

b. Interpret the 95% confidence interval for E(y) in the words of the problem

c. Note that the interval of part a is wider than the interval of part b. Will this always be true? Explain.

Exercises 10.20

Refer to the World Development (Feb. 1998) study of street vendors in the city of Puebla, Mexico, Exercise 10.7 (p. 573). Recall that the vendors' mean annual earnings Eb) was modeled as a first-order function of age x₁ and hours worked x₂. Refer to the STATISTIX printout on p. 573 and answer the following

a. Interpret the value of R².

b. Interpret the value of  Explain the relationship between R² and 

c. Conduct a test of the global utility of the model at α = .01. Interpret the result

Exercise 10.7

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, Feb. 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 gender, age, hours worked per day, annual earnings, and education level. A subset of these data appear in the table on page 574

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

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

c. Interpret the estimated ß coefficients in your model.

d. Is age x₁ a statistically useful predictor of annual earnings? Test using a = .01

e. Construct a 99% confidence interval for ß₂. Interpret the interval in the words of the problem.