The data set above is from the March 2012 Current Population Survey and has info
ID: 3262515 • Letter: T
Question
The data set above is from the March 2012 Current Population Survey and has information for individuals on the following variables: Their hourly wage in dollars, the number of years for which they attended school (including college and graduate education, if applicable), the number of years of job market experience, and a dummy variable which takes on the value “1” if the individual has a Bachelor’s degree and the value “0” otherwise.
Part (a) (3 points)
Run a multiple regression with “Hourly Wage” as dependent variable and the three other variables as independent variables.
You must submit your actual Excel file with the output as part of the assignment.
Part (b) (2 points)
Interpret the estimated value of the intercept, i.e., explain what the number means in this regression.
Part (c) (2 points)
Interpret the estimated value of the coefficient on the “Years of Education” variable, i.e., explain what the number means in this regression.
Part (d) (2 points)
Interpret the estimated value of the coefficient on the “Years of Experience” variable, i.e., explain what the number means in this regression.
Part (e) (2 points)
Interpret the estimated value of the coefficient on the “Bachelor’s degree” dummy variable, i.e., explain what the number means in this regression.
Part (f) (2 points)
Are there any coefficient estimates that are statistically significant? If so, name one and explain how you can tell that it is statistically significant.
Part (g) (2 points)
Are there any coefficient estimates that are not statistically significant? If so, name one and explain how you can tell that it is not statistically significant.
Part (h) (3 points)
What is the predicted hourly wage for an individual who has 14 years of education, 10 years of job market experience, and whose highest educational achievement is an Associate’s degree?
Part (i) (3 points)
If we created a new variable that measures the number of letters in the name of the town in which each individual attended 5th grade and included that variable in a new regression in addition to the other three independent variables from Part (a). What would happen to R-Squared compared to R-Squared in Part (a)? Is that a desirable outcome? Why or why not?
Part (j) (2 points)
What percentage of the variation in the dependent variable can be explained by variation in the independent variables?
Part (k) (2 points)
What percentage of the variation in the dependent variable cannot be explained by variation in the independent variables?
Hourly Wage Years of Education Years of Experience Bachelor's Degree 24.04 12 9 0 18.27 10 15 0 22.12 13 13 0 15.38 10 30 0 10.29 6 21 0 25.3 14 41 0 19.23 16 15 1 25.48 14 27 0 39.9 18 36 0 3.75 12 2 0 17.31 16 4 1 43.75 13 30 0 12.5 12 17 0 40.87 13 31 0 10.28 6 23 0 10.58 10 18 0 33.65 12 14 0 36.06 14 30 0 16.35 16 14 1 6.73 12 15 0 43.27 20 34 0 18.27 12 24 0 15.38 14 7 0 17.09 13 27 0 7.21 11 28 0 31.09 13 27 0 31.58 18 35 0 6.54 16 38 1 12.98 16 39 1 31.25 16 8 1 22.6 14 42 0 7 7 14 0 12.98 14 32 0 66.67 20 10 0 17.79 13 6 0 115.38 20 23 0 34.62 13 33 0 30.22 16 10 1 28.85 13 15 0 51.44 16 15 1 6.19 13 15 0 15.38 16 39 1 14.84 12 15 0 19.23 16 19 1 15.38 18 19 0 64.42 16 30 1 20.77 14 32 0 96.15 14 36 0 7.69 12 23 0 20.19 13 3 0 38.46 16 11 1 31.25 16 32 1 12.02 12 21 0 10.1 12 23 0 52.45 14 35 0 14.42 12 27 0 11.11 12 16 0 24.04 6 18 0 28.85 20 21 0 5.29 12 5 0 62.5 18 13 0 14.62 12 36 0 9.13 18 30 0 31.84 16 10 1 18.46 12 23 0 12.55 14 20 0 15.48 12 35 0 10.58 14 24 0 35.58 11 43 0 40.67 18 29 0 3.53 12 1 0 18.27 13 21 0 10.83 12 4 0 19.23 12 23 0 22.06 16 38 1 19.23 13 9 0 18.2 12 18 0 9.62 10 29 0 34.97 16 17 1 26.49 12 9 0 17.09 16 28 1 26.92 16 14 1 43.27 16 32 1 8.88 13 11 0 54.95 12 35 0 19.23 13 23 0 10.33 16 18 1 30.77 16 11 1 28.85 12 39 0 25 13 35 0 22.73 18 15 0 10.99 13 34 0 28.85 12 35 0 21.63 12 29 0 51.51 16 6 1 7.09 12 12 0 26.1 16 13 1 26.92 16 30 1 30 16 25 1 43.27 12 36 0 26.44 14 35 0 48.08 16 39 1 28.85 16 21 1 19.23 14 32 0 20.19 16 5 1 35.26 16 12 1 21.63 12 15 0 38.46 16 7 1 6.94 14 0 0 19.23 12 41 0 55.56 16 31 1 14.42 12 34 0 12.98 13 9 0 10.1 16 38 1 8.65 7 32 0 10.58 7 44 0 28.85 20 15 0 38.46 12 27 0 230.77 16 29 1 9.38 12 9 0 9.62 9 20 0 21.63 11 35 0 25 18 23 0 68.38 18 34 0 17.63 14 23 0 8.06 16 35 1Explanation / Answer
1) Following is the output of the multiple linear regression obtained from excel -
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b)
The parameter estimate of the intercept represents the hourly wage of a person with '0' years of education, '0' experience and no bachelors degree. Basically its the basic hourly wage given irrespective of someone's education, experience and his/her bachelor degree. As the value is '-24.03' (which practically mekes no sense) indicates that the hourly wage of such person is 0. Or in other words we can say that a person with no years of education, no experience and no bachelor's degree can't earn.
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c)
The coefficient of the parameter 'years of education' indicates the change in hourly wage with a unit change in year of education keeping all the other parameters constant. In this case, the value of the coefficient 2.998 means that the hourly wage of a person increses by almost $3 with every unit increment in number of years of education he/she has.
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d)
The coefficient of the parameter 'years of experience' indicates the change in hourly wage with a unit change in year of experience keeping all the other parameters constant. In this case, the value of the coefficient 0.366 means that the hourly wage of a person increses by almost $0.37 with every unit increment in number of years of his/her experience.
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e)
Note that the variable 'Bachelor's Degree' takes only two values that is either 1 if the person has a bachelor's degree or '0' if he/she doesn't. So, the coefficient estimate of this parameter would indicate the average difference between the hourly wage of person with bachelor degree from those without the bachelor degree. In this case, the value 2.90 indicates that those with bachelor degree earn almost $2.90 more per hour than those without the bachelor degree.
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f)
A coefficient is said to be statistically significant if the p-value of the t-statistic (obtained in the excel output) is less than the significance level which generally is assumed to be 0.05.
As we can see from the output that there are two coefficients namely the 'intercept' and the 'Years of Education' which have p-value less than 0.05, so we would say that these are statistically significant.
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g)
As the other two coefficients of parameter 'Years of Experience' and 'Bachelor's Degree' have p-value less than significance level of 0.05, so we would conclude that they are not statistically significant.
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SUMMARY OUTPUT Regression Statistics Multiple R 0.398422366 R Square 0.158740381 Adjusted R Square 0.13805367 Standard Error 23.59682266 Observations 126 ANOVA df SS MS F Significance F Regression 3 12818.11798 4272.705995 7.673543384 9.69072E-05 Residual 122 67930.82482 556.8100395 Total 125 80748.9428 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -24.03004679 11.71419996 -2.051360475 0.042372555 -47.2194756 -0.84061798 Years of Education 2.998264734 0.816202752 3.673431295 0.000356624 1.382509864 4.614019603 Years of Experience 0.366192398 0.189717943 1.930193801 0.055903794 -0.009373219 0.741758014 Bachelor's Degree 2.90342789 5.334640826 0.544259302 0.587256401 -7.657026441 13.46388222Related Questions
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