To investigate the relationship between the number of years of education of post-high school students (YRSED), their high school scores (HSSCORE), the average hourly wages (WAGES), and the unemployment rates (UNEMP), a researcher specified the estimated model:

Estimated(YRSED) = 7.4451 + 0.1104(HSSCRORE) + 0.0906(WAGES) - 0.0391(UNEMP) + 0.3361(BLACK) , R² = 0.269 , SER=1.556

Standard Errors are reported as hereunder:

SE(intercept)=0.523

SE(HSSCORE)=0.006

SE(WAGES)=0.048

SE(UNEMP)=0.022

SE(BLACK)=0.134

The definitions and units of measurement of the variables are as follows:

YRSED = the actual number of years of education (expressed in years)

HSSCORE = high school scores (expressed in %)

WAGES = average hourly wages (expressed in dollars)

UNEMP = unemployment rate (expressed in %)

BLACK = a binary variable (BLACK=1 if the person is a person of color, BLACK=0 otherwise).

a) Interpret the coefficients of UNEMP & BLACK.

b) Test, using 5% level of significant and a t-test approach, if the variable HSSCORE can be removed from the analysis.

c) Suppose that you want to verify if all slope coefficients can be significant or not. Hence, specify both null and alternative hypothesis statements for test. (Just hypothesis statements are satisfactory)

d) The researcher thinks that the variables BLACK, UNEMP & HSSCORE might not be important variables in estimating the YRSED. In that case, indicate both restricted and unrestricted population regression equations. You may use the letter B for slope and intercept coefficients on the two regressions, respectively. (Example: YRSED_i = B₀ + B₁ ... + ...). Specify the values of q & k.

e) Furthermore, specify if the researcher is right on his assumption in part (d) above. The required statistical table is attached into this question. Assume that F-statistic for part (d) is 178.86