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Econ 209: End of Semester Notes - Econometrics Regression Analysis, Study notes of Probability and Statistics

Vassar College (VC)Probability and Statistics

The regression analysis results for econ 209 students, including the interpretation of coefficients for variables such as interest rate, money stock, education level, and marriage status on wage. It also includes predictions for wage based on different education levels and marital status.

Typology: Study notes

Pre 2010

Uploaded on 08/16/2009

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Econ 209 End of the semester notes
Review Problems
1. Given the variables, the interest rate, r, the stock of money, m , and
gross domestic product, y, the following is a regression on the transformed
variables
. g lnr = ln(r)
. g lnm= ln(m)
. g lny = ln(y)
. reg lnr lnm lny
Source | SS df MS Number of obs = 32
---------+------------------------------ F( 2, 29) = 8.31
Model | 1.61417643 2 .807088215 Prob > F = 0.0014
Residual | 2.81646021 29 .097119318 R-squared = 0.3643
---------+------------------------------ Adj R-squared = 0.3205
Total | 4.43063664 31 .142923763 Root MSE = .31164
------------------------------------------------------------------------------
lnr | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
lnm | -1.960497 .5225924 -3.751 0.001 -3.029318 -.8916753
lny | 5.319644 1.341171 3.966 0.000 2.576642 8.062646
_cons | -29.95116 7.923452 -3.780 0.001 -46.15644 -13.74589
------------------------------------------------------------------------------
a) How would you interpret the coefficient of lny, of lnm.
b) A 10% increase in the money stock would lead to what predicted change in r.
2. The following is output from stata.
reg wage ed
R-squared = 0.1459
------------------------------------------------------------------------------
wage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ed | .7504489 .0787299 9.53 0.000 .5957892 .9051086
_cons | -.7459421 1.045404 -0.71 0.476 -2.799568 1.307684
------------------------------------------------------------------------------
a) How would you interpret the coefficient of ed
b) What would you predict for the wage for a person with 14 years of ed.
3. The following is output from stata.
. reg lnwage ed
R-squared = 0.1447
------------------------------------------------------------------------------
lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ed | .0767605 .0080906 9.49 0.000 .0608671 .0926539
_cons | 1.059858 .1074298 9.87 0.000 .8488189 1.270896
------------------------------------------------------------------------------
a) How would you interpret the coefficient of ed
b) What would you predict for the wage for a person with 14 years of ed.
pf3

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Econ 209 End of the semester notes

Review Problems

  1. Given the variables, the interest rate, r, the stock of money, m , and gross domestic product, y, the following is a regression on the transformed variables . g lnr = ln(r) . g lnm= ln(m) . g lny = ln(y) . reg lnr lnm lny

Source | SS df MS Number of obs = 32 ---------+------------------------------ F( 2, 29) = 8. Model | 1.61417643 2 .807088215 Prob > F = 0. Residual | 2.81646021 29 .097119318 R-squared = 0. ---------+------------------------------ Adj R-squared = 0. Total | 4.43063664 31 .142923763 Root MSE =.

lnr | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- lnm | -1.960497 .5225924 -3.751 0.001 -3.029318 -. lny | 5.319644 1.341171 3.966 0.000 2.576642 8. _cons | -29.95116 7.923452 -3.780 0.001 -46.15644 -13.

a) How would you interpret the coefficient of lny, of lnm. b) A 10% increase in the money stock would lead to what predicted change in r.

  1. The following is output from stata. reg wage ed

R-squared = 0.

wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- ed | .7504489 .0787299 9.53 0.000 .5957892. _cons | -.7459421 1.045404 -0.71 0.476 -2.799568 1.

a) How would you interpret the coefficient of ed b) What would you predict for the wage for a person with 14 years of ed.

  1. The following is output from stata. . reg lnwage ed

R-squared = 0.

lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- ed | .0767605 .0080906 9.49 0.000 .0608671. _cons | 1.059858 .1074298 9.87 0.000 .8488189 1.

a) How would you interpret the coefficient of ed b) What would you predict for the wage for a person with 14 years of ed.

  1. The following is output from stata . g marfe = married*female . reg lnwage ed married female marfe

Source | SS df MS Number of obs = 534 -------------+------------------------------ F( 4, 529) = 39. Model | 34.0674714 4 8.51686785 Prob > F = 0. Residual | 114.374424 529 .21620874 R-squared = 0. -------------+------------------------------ Adj R-squared = 0. Total | 148.441895 533 .278502617 Root MSE =.

lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- ed | .0768516 .007714 9.96 0.000 .0616978. married | .2868351 .0573656 5.00 0.000 .1741428. female | -.063109 .0689404 -0.92 0.360 -.1985395. marfe | -.2601734 .0851219 -3.06 0.002 -.4273917 -. _cons | .9785543 .1103712 8.87 0.000 .7617347 1.

. test female married F( 2, 529) = 21.79 Prob > F = 0. . test female married marfe F( 3, 529) = 19.40 Prob > F = 0. . test female marfe F( 2, 529) = 21.44 Prob > F = 0. . test married marfe F( 2, 529) = 12.59 Prob > F = 0. . test married+ marfe=0 F( 1, 529) = 0.18 Prob > F = 0. . test female +marfe=0 F( 1, 529) = 42.04 Prob > F = 0. . test female+ married+ marfe=0 F( 1, 529) = 0.38 Prob > F = 0. . test female + married=0 F( 1, 529) = 4.06 Prob > F = 0. . test female = married F( 1, 529) = 32.56 Prob > F = 0.

a) Write the predicted equation for a single female b) What would you predict as a wage for a single female with 12 years of ed c) How would you interpret the coefficient of marfe. d) On the basis of this output would you say that there was evidence of discrimination against single men relative to married e) On the basis of this output would you say that there was evidence of discrimination against single men relative to married women. f) On the basis of this output would you say that there was evidence of discrimination single women relative to married men. g) On the basis of this output would you say that there was evidence of discrimination single women relative to married women. h) On the basis of this output would you say that discrimination against single persons is worse for women than for men.

  1. How would you interpret the sign of the coefficient of exp2 in the following output.

g exp2 = exp^

. reg lnwage ed exp exp

lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- ed | .0897588 .0083203 10.788 0.000 .0734139. exp | .0349377 .0056491 6.185 0.000 .0238403. exp2 | -.0005362 .0001245 -4.307 0.000 -.0007808 -. _cons | .5202983 .1236135 4.209 0.000 .2774659.

Sketch the relationship between lnwage and experience