Incomes of Mexican street vendors: Detailed interviews were conducted with over
ID: 3206368 • Letter: I
Question
Incomes of Mexican street vendors: Detailed interviews were conducted with over 1000 street vendors in the city of Pueblo, Mexico, in order to study the factors influencing the vendors' incomes. The researchers collected data on gender, age, hours worked per day, annual earnings and education level. The data are given in the file STREETVN.xls. Model the annual earnings as a function of age (x1) and hours worked (x2).
a. Fit a multiple linear first order regression model. Interpret the coefficients and check whether they are significant at =5%. Is age a useful predictor?
b. Is the overall model significant at =5%? How much of the variation in annual earnings is explained by age and hours worked?
c. Interpret R2 and Ra 2 . Explain the difference.
d. What is the estimated annual earnings when age is 30 and number of hours worked is 15?
VenNum Earnings Age Hours 21 2841 29 12 53 1876 21 8 60 2934 62 10 184 1552 18 10 263 3065 40 11 281 3670 50 11 354 2005 65 5 401 3215 44 8 515 1930 17 8 633 2010 70 6 677 3111 20 9 710 2882 29 9 800 1683 15 5 914 1817 14 7 997 4066 33 12Explanation / Answer
A) the model is given as : earnings = -20.3520 + 13.35045(age)+243.71446(hours). Interpretation of coefficients is given as: 1) if age is increased by 1 unit then earnings will be increased by 13.35 given hours is contant. 2) if hours is inclreased by 1 unit then earnings will be increaded by 243.71 given age is contant.
Significance of coefficients: Ho: beta coefficient is insignificant vs H1: beta coefficient is significant.
Since p-value for age is 0.1074 which is greater than 0.05 hence, it is insignificant while p-value for hours is 0.0024 which is less than 0.05, hence it is significant. Therefore, age is not a useful predictor.
B) p-value of F statistic gives information about overall model significance. Since p-value of F statistic is 0.0053 which is less than 0.05, hence overall model is significant. Only 58% of the variation in earnings is explained by age and hours. C) R^2 = 0.5823 and adjusted R^2 = 0.5126. Both gives model performance on the basis of variation explained by the model. While R^2 always increases as we add more variable sin the model, adjusted R^2 only increases if significant variables are added in the model else it will decrease.
D) when age =30 and hours = 15 then estimated earnings = -20.3520 + 13.35045*30 + 243.71446*15 = 4035.878.