Question

You are given the data in Table for the US for years 1980 to 1996. (a) Develop a suitable regression model to explain the male civilian labor force participation rate in relation to male civilian unemployment rate and real average hourly earnings. (b) Repeat part (a) for females. (c) Repeat part (a) but use current average hourly earnings. (d) Repeat part (b) but use current average hourly earnings.
Year	CLFPRM	CLFPRF	UNRM	UNRF	AHE82	AHE
1980	77.4	51.5	6.9	7.4	7.78	6.66
1981	77	52.1	7.4	7.9	7.69	7.25
1982	76.6	52.6	9.9	9.4	7.68	7.68
1983	76.4	53.9	9.9	9.2	7.79	8.02
1984	76.4	53.6	7.4	7.6	7.8	8.32
1985	76.3	54.5	7	7.4	7.77	8.57
1986	76.3	55.3	6.9	7.1	7.81	8.76
1987	76.2	56	6.2	6.2	7.73	8.98
1988	76.2	56.6	5.5	5.6	7.69	9.28
1989	76.4	57.4	5.2	5.4	7.64	9.66
1990	76.4	57.5	5.7	5.5	7.52	10.01
1991	75.8	57.4	7.2	6.4	7.45	10.32
1992	75.8	57.8	7.9	7	7.41	10.57
1993	75.4	57.9	7.2	6.6	7.39	10.83
1994	75.1	58.8	6.2	6	7.4	11.12
1995	75	58.9	5.6	5.6	7.4	11.44
1996	74.9	59.3	5.4	5.4	7.43	11.82
Key:
CLFPRM: Civilian labor force participation rate, male (%)
CLFPRF: Civilian labor force participation rate, female (%)
UNRM: Civilian unemployment rate, male (%)
UNRF: Civilian unemployment rate, female (%)
AHE82: Average hourly earnings (1982 dollars)
AHE: Average hourly earnings (current dollars)

Answer 1

Here we are given the data for the US for years 1980 to 1986. We have to develope a suitable regrssion model to explain the four different situations given.

Here we use MINITAB.

a) To find the regression model to explain the male civilian labour force participation rate in relation to male civilian unemployment rate and real average hourly earnings we perform the following steps:

1) First we enter the data in the minitab spreadsheet

2) Select stat the regression then again select regression an then select fit regression model

3) Select CLFPRM in response and select UNRM and AHE82 in the continuos predictor

4) Click OK

Hence we get the following output:

Model Summary

       S    R-sq R-sq(adj) R-sq(pred)
0.444645 63.24%     57.99%      47.88%

Coefficients

Term        Coef SE Coef T-Value P-Value   VIF
Constant   51.96     5.22     9.95    0.000
UNRM      0.0557   0.0841     0.66    0.519 1.11
AHE82      3.120    0.706     4.42    0.001 1.11

Regression Equation

CLFPRM = 51.96 + 0.0557 UNRM + 3.120 AHE82

b) To find the regression model to explain the female civilian labour force participation rate in relation to female civilian unemployment rate and real average hourly earnings we perform the following steps:

1) First we enter the data in the minitab spreadsheet

2) Select stat the regression then again select regression an then select fit regression model

3) Select CLFPRF in response and select UNRF and AHE82 in the continuos predictor

4) Click OK

Hence we get the following output:

Model Summary

      S    R-sq R-sq(adj) R-sq(pred)
1.09401 83.31%     80.93%      75.84%

Coefficients

Term        Coef SE Coef T-Value P-Value   VIF
Constant   125.2     14.0     8.95    0.000
UNRF      -1.004    0.259    -3.88    0.002 1.39
AHE82      -8.21     1.95    -4.21    0.001 1.39

Regression Equation

CLFPRF = 125.2 - 1.004 UNRF - 8.21 AHE82

c)To find the regression model to explain the male civilian labour force participation rate in relation to male civilian unemployment rate and current average hourly earnings we perform the following steps:

1) First we enter the data in the minitab spreadsheet

2) Select stat the regression then again select regression an then select fit regression model

3) Select CLFPRM in response and select UNRM and AHE in the continuos predictor

4) Click OK

Hence we get the following output:

Model Summary

       S    R-sq R-sq(adj) R-sq(pred)
0.226765 90.44%     89.07%      86.76%

Coefficients

Term         Coef SE Coef T-Value P-Value   VIF
Constant   81.065    0.642   126.35    0.000
UNRM      -0.0896   0.0475    -1.89    0.080 1.35
AHE       -0.4644   0.0433   -10.72    0.000 1.35

Regression Equation

CLFPRM = 81.065 - 0.0896 UNRM - 0.4644 AHE

d) To find the regression model to explain the female civilian labour force participation rate in relation to female civilian unemployment rate and current average hourly earnings we perform the following steps:

1) First we enter the data in the minitab spreadsheet

2) Select stat the regression then again select regression an then select fit regression model

3) Select CLFPRF in response and select UNRF and AHE in the continuos predictor

4) Click OK

Hence we get the following output:

Model Summary

       S    R-sq R-sq(adj) R-sq(pred)
0.427771 97.45%     97.08%      95.82%

Coefficients

Term        Coef SE Coef T-Value P-Value   VIF
Constant   45.35     1.65    27.52    0.000
UNRF      -0.365    0.123    -2.98    0.010 2.05
AHE        1.397    0.100    13.90    0.000 2.05

Regression Equation

CLFPRF = 45.35 - 0.365 UNRF + 1.397 AHE