Earnings of Vietnamese street vendors. Detailed interviews were conducted with o

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Earnings of Vietnamese street vendors. Detailed interviews were conducted with over 1,000 street vendors in the city of Bien Hua, Vietnam, 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 gender, age, hours worked per day, annual earnings, and education level. A subset of these data appears in the accompanying Excel Spreadsheet: VENDORS.XLS SAS OUTPUT FOR VENDORS Dependent Var iable: EARNINGS finalys is of Var iance Sun of Mean Source DF Square F Value P> F 0.0053 5018232 3600196 8618428 2509116 300016 8.36 Model Error Corrected Total 12 Root MSE Dependent Mean Coeff Var 547.73748 R-Square 2577.13333 Adj R-Sq 0.5823 0.5126 21.25375 Paraneter Estinates Paraneter Estimate Standard Variable DF Error t Value Pr It 95% Confidence Limits Intercept AGE HOURS -20.35201 13.35045S 243.71446 652.74532 7.67168 63.51174 -0.03 1.74 3.84 0.9756 -1442.56189 0.1074 0.0024 -3.36470 105.33428 1401.85787 30 . 06559 382.09465 (d) Conduct a test of the global utility of the model (at = .01). Interpret the result. (e) Find and interpret the value of Ra . (f) Find and interpret s, the estimated standard deviation of the error term. (g) Is age (x) a statistically useful predictor of annual earnings? Test using = .01. (h) Find a 95% confidence interval for . Interpret the interval in the words of the problem.

Explanation / Answer

d) From SAS output,

p - Value for a global utility test = 0.0053

Since p - Value is less than 0.05, we reject Ho. Hence,

There is enough evidence to conclude that the model is useful in predicting earnings.

e) Ra2 = 0.5126

This represents that 51.26% of the variation in earnings can be explained by the independent variables that significantly affect the dependent variable.

f) s = Root MSE = 547.73748

It represents the average distance observed values fall from the regresison line.

g) p - value corresponding to age (x1) coefficient is 0.1074 which is greater than 0.01 so we do not reject Ho and hence, age (x1) is not a significant predictor of annual earnings.

h) From SAS output,

95% confidence interval for B2 is:

(105.33, 382.10)

Interpretation: We are 95% confident that the change in annual earnings for a unit change in hours worked per day will lie between $105.33 and $382.10

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