Question

1. The following sample on the level of education (measured by the number of years of schooling) and wages (hourly) earned by 15 individuals is as follows: Education Wages (S) Education Wages (S) 4.45 5.57 5.97 7.33 7.31 6.58 4.45 13.53 10 12 14 15 16 17 15 7.31 7.82 11.02 10.67 10.83 13.61 10.67 9 10 18 According to the human capital theory education increases a worker's pro- ductivity and thus leads to higher wages. Consider the economic model Wages Bo B1 Education. a. What sign would you expect ß0 and to take? Draw a rough scatter raph of the data with wages on the vertical axis and education on the horizontal axis. Does it look like the data support the human capital theory? b. Estimate WagesoEducation+u. Give a plot of Wages,. Interpret the intercept and the slope coefficient. C. Calculate the standard error of 30 and β1 d. Calculate and interpret R2 e. Explain the assumption of homoscedasticity.

Answer 1

Answer a. Considering the economic model wages-β 0 + β 1E ducation. In this model β0 represents the intercept term and βι represents the effect of education on wages. Since Education increases worker's productivity and hence the wages, therefore B1 should be positive sign. And if we assume that at 0 value of education there is some value of wages then the parameter Bo should also be positive sign A rough scatter graph of the data is given by the following 16 14 12 10 8 3 0 0.00 5.00 10.00 15.00 20.00 Education Human capital theory emphasizes how education increases the productivity and efficiency of workers by increasing the level of cognitive stock of economically productive human capability, which is a product of innate abilities and investment in human beings. To know whether this dataset support human capital theory or not, we have to estimate the regression coefficients Answer b. We can write the regression equation as we wish to obtain the least square estimate of β0 and A. Carrying out the appropriate calculation E-11.60, W-8.48, .eM-165.96, > . ei-227.60 Therefore, β1-227.60- o 8.48- (0.73) x 11.60 0.023

C. VarBo-S-58.15 SE of β07 square root of 58.15-7.63 Varß,--= 0.38 SE of β,-square root of 0.38-0.62