Question
Refer to the Wage data which reports information on annual wages for a sample of 100 workers. This data set includes variables relating to industry, years of education, and the gender for each worker. Determine the regression equation using annual wage as the dependent variable and year of education, gender, years of work experience, age in years, and whether or not the worker is a union member.
A.) Write out the regression equation. How much does each year of education and each year of experience add to the annual wage? (Minitab: Stat – Regression – Regression, Fit Regression Model, Responses = Wage, Continuous Predictors = Education, Female, Experience, Age, and Union) (SPSS: Analyze – Regression – Linear, Dependent = Wage, Independent(s) = Education, Female, Experience, Age, and Union)
B.) Determine the value of R-squared. Provide an interpretation of the variance R-squared represents.
C.) Develop a correlation matrix. Which independent variables have strong or weak correlations with the dependent variable (wage)? (Minitab: Stat – Basic Statistics – Correlation – Add the following variables: Wage, Education, Female, Experience, Age, and Union – Then uncheck display p-values) (SPSS: Analyze – Correlate – Bivariate – Variables = Wage, Education, Female, Experience, Age, and Union)
Wage Industry Occupation Education South Nonwh Hisp Female Experience Marr Age Union 19388 1 0 6 1 0 0 0 45 1 57 0 49898 2 0 12 0 0 0 0 33 1 51 1 28219 0 3 12 1 0 0 0 12 1 30 0 83601 0 5 17 0 0 1 0 18 1 41 0 29736 0 4 8 0 0 1 0 47 1 61 1 50235 1 0 16 0 0 0 0 12 1 34 0 45976 0 2 12 0 0 0 0 43 1 61 1 33411 1 2 12 1 0 0 0 20 1 38 0 21716 0 5 12 0 0 0 1 11 0 29 0 37664 0 5 18 0 0 0 0 19 1 43 0 26820 0 5 18 0 0 0 0 33 0 57 1 29977 0 4 16 0 1 0 1 6 1 28 0 33959 0 5 17 0 0 0 1 26 1 49 1 11780 0 2 11 0 0 0 1 33 1 50 0 10997 0 4 14 0 1 0 0 0 0 20 0 17626 0 3 12 0 0 0 1 45 1 63 0 22133 0 5 16 0 0 0 1 10 0 32 1 21994 0 1 12 0 0 0 1 24 1 42 0 29390 0 0 13 0 0 0 0 18 1 37 0 32138 0 4 14 0 0 0 0 22 1 42 1 30006 1 3 16 0 0 0 1 27 1 49 0 68573 0 5 16 1 0 0 0 14 1 36 1 17694 0 4 8 0 0 0 1 38 1 52 0 26795 0 0 7 1 0 0 0 44 1 57 0 19981 0 4 4 0 0 0 0 54 1 64 0 14476 0 5 12 0 0 0 1 3 1 21 0 19452 0 4 13 0 1 0 0 3 0 22 0 28168 1 0 13 0 0 0 0 17 0 36 0 19306 0 5 9 1 1 0 1 34 1 49 1 13318 1 0 11 1 0 0 1 25 1 42 1 25166 0 4 12 0 0 0 1 10 0 28 0 18121 1 3 12 0 0 0 1 18 1 36 0 13162 1 0 12 0 1 0 0 6 0 24 1 32094 0 3 12 1 0 0 1 14 1 32 0 16667 0 3 12 1 0 0 0 4 0 22 0 50171 0 5 12 0 0 0 0 39 1 57 1 31691 1 0 12 0 0 0 0 13 0 31 0 36178 0 3 12 0 0 0 1 40 1 58 0 15234 0 1 12 1 0 1 1 4 0 22 0 16817 0 3 12 1 0 0 1 26 0 44 0 22485 0 3 12 0 0 0 0 22 0 40 0 30308 0 4 12 0 0 0 0 10 1 28 0 11702 0 2 14 1 0 0 1 6 1 26 0 11186 0 0 12 0 0 0 0 0 0 18 0 12285 0 1 12 0 0 0 1 42 1 60 0 19284 1 4 16 0 0 0 0 3 0 25 0 11451 1 0 12 0 0 0 1 8 1 26 0 57623 0 1 15 0 0 0 0 31 1 52 0 25670 0 3 13 0 0 0 1 8 0 27 1 83443 0 5 17 0 0 0 1 5 0 28 0 49974 1 1 16 0 1 0 0 26 1 48 1 46646 2 0 5 1 0 0 0 44 1 55 0 31702 0 3 12 1 0 0 1 39 1 57 0 13312 0 4 12 1 0 0 1 9 1 27 0 44543 0 2 18 0 0 0 0 10 1 34 0 15013 0 4 16 0 0 0 0 21 1 43 0 33389 0 1 14 0 1 0 0 22 0 42 0 60626 0 5 18 0 0 0 0 7 1 31 0 24509 0 5 14 0 0 1 1 15 0 35 0 20852 1 0 12 0 0 0 1 38 1 56 0 30133 2 0 10 0 0 0 0 27 1 43 0 31799 0 3 12 0 0 0 1 25 0 43 0 16796 0 4 12 0 0 0 1 14 1 32 0 20793 0 0 12 1 0 0 1 6 0 24 0 29407 0 4 10 1 0 0 0 19 0 35 0 29191 0 0 12 0 0 0 0 9 0 27 0 15957 0 2 12 1 0 0 1 10 0 28 0 34484 0 3 13 1 0 0 1 28 0 47 0 35185 1 3 14 0 0 0 1 12 1 32 0 26614 1 0 12 0 0 0 1 19 1 37 0 41780 0 0 12 1 0 0 0 9 1 27 0 55777 0 1 14 1 0 0 0 21 1 41 0 15160 0 4 8 1 0 0 1 45 0 59 0 66738 0 0 9 1 0 0 0 29 1 44 0 33351 0 5 16 1 0 0 1 4 1 26 0 33498 0 1 10 0 0 0 0 20 1 36 0 29809 0 4 8 0 1 0 1 29 0 43 0 15193 1 0 12 0 0 0 1 15 0 33 0 23027 0 4 14 0 1 0 0 34 1 54 1 75165 0 1 15 0 0 0 0 12 1 33 0 18752 0 4 11 0 0 0 1 45 0 62 1 83569 0 1 18 0 0 0 0 29 1 53 0 32235 0 3 12 0 0 0 1 38 1 56 0 20852 0 0 12 1 0 0 0 1 0 19 0 13787 0 4 11 0 0 0 0 4 1 21 0 34746 0 3 14 1 0 0 1 15 1 35 0 17690 0 1 12 1 1 0 0 14 1 32 0 52762 0 5 18 0 0 0 0 7 1 31 0 60152 0 5 16 1 0 0 0 38 1 60 0 33461 0 1 16 0 0 1 0 7 1 29 1 13481 0 4 12 1 0 1 0 7 0 25 0 9879 0 3 12 1 0 0 1 28 1 46 0 16789 0 3 13 1 0 0 1 6 1 25 0 31304 0 1 16 0 0 0 1 26 1 48 0 37771 0 5 15 0 0 0 0 5 0 26 0 50187 0 3 12 0 0 0 1 24 1 42 0 39888 0 3 12 1 0 0 0 5 0 23 0 19227 0 3 12 0 0 0 1 15 1 33 0 32786 1 0 11 1 0 0 0 37 1 54 1 28440 0 4 12 0 0 0 1 24 1 42 0
Explanation / Answer
a) The regression ouput using SPSS is as follows
Hence the regression equation is given by
Wage = -16861.42 +(2877.16*Education) -(11674.51*Female)+(447.96*age) -(5355.33*Union)
B) The model Summary of the regression equation is given by
The R2 value is given by the model is 0.37
I.e., 37% of the variation in wages is explained by the variables Education, Female, Age and Union
c) The correlation matrix is given by
From the correlation matrix we can say that the indepenent variable education has strong positive corelation with the dependent variable wage and the variable Female also has strong but negative correlation with the dependent variable wage where as the other variables experience ,age and Union have weak positive correlation with the variable wage compare to other variables
Model Unstandardized Coefficients Standardized Coefficients t Sig. 95.0% Confidence Interval for B B Std. Error Beta Lower Bound Upper Bound 1 (Constant) -16861.42 9194.37 -1.83 0.07 -35114.54 1391.71 Education 2877.16 520.35 0.47 5.53 0.00 1844.13 3910.18 Female -11674.51 2795.61 -0.35 -4.18 0.00 -17224.50 -6124.52 Age 447.96 119.72 0.33 3.74 0.00 210.28 685.63 Union -5355.33 3812.78 -0.12 -1.40 0.16 -12924.66 2213.99 a. Dependent Variable: Wage