With the information below test the following hypothesis tests. Please write out the specific hypothesis test (null and alternative) and formula you use to produce the relevant test statistic and interpret the test result.

a. Test that all coefficients in the unrestricted model are equal to 0.

b. Test that height85 and heigth81 joinly have no effect on wage96.

c. Test that height85 and height81 have the same effect on wage96.

The unrestricted model is:

Wage96 = beta₀ + beta₁ height85 + beta₂height81 + beta₃athlets + beta₄clubnum + e

reg wage96 height85 height81 athlets clubnum if wage96<120

Source |SSdfMSNumber of obs =1851

-------------+------------------------------F(4,1846) =29.91

Model |16394.012244098.50306Prob > F=0.0000

Residual |252987.1141846137.046107R-squared=0.0609

-------------+------------------------------Adj R-squared =0.0588

Total |269381.1261850145.611419Root MSE=11.707

wage96 |Coef.Std. Err.tP>|t|[95% Conf. Interval]

-------------+----------------------------------------------------------------

height85 |.0340185.19546770.170.862-.3493426.4173796

height81 |.3480922.19092971.820.068-.0263687.7225531

athlets |3.017681.56293425.360.0001.9136274.121736

clubnum |1.884238.28180786.690.0001.3315432.436934

_cons |-13.568287.053586-1.920.055-27.40213.2655622

test height85 = height81 = 0

( 1)height85 - height81 = 0

( 2)height85 = 0

F(2,1846) =7.77

Prob > F =0.0004

reg wage96 athlets clubnum ifwage96<120

Number of obs =1851

R-squared=0.0530

wage96 |Coef.Std. Err.tP>|t|[95% Conf. Interval]

-------------+----------------------------------------------------------------

athlets |3.282094.560955.850.0002.1819314.382256

clubnum |1.913579.28270176.770.0001.3591312.468027

_cons |13.16901.410124232.110.00012.3646513.97336

reg wage96 clubnum athlets Height81PlusHeight85 if wage96<120

Number of obs =1851

R-squared=0.0605

Wage96 Coef. Std. Err. t-value Pr>|t|

-------------+----------------------------------------------------------------

clubnum1.889380.281726.707 2.64e-11 ***

athlets3.033510.562585.392 7.86e-08 ***

Height81PlusHeight850.193030.050113.852 0.000121 ***

Constant-13.908137.04146-1.975 0.048397 *

---

Signif. codes:0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 11.71 on 1847 degrees of freedom

Multiple R-squared:0.0605, F-statistic: 39.64 on 3 and 1847 DF