The following Probit model was estimated based on information from a subset of individuals surveyed in the a national report:

Has Plan=F(0+1Regular or poor self-assessment+2gender, dummy white color+3dummy higher school+4age+5age2)

where F is the cumulative distribution function of Normal and betas are parameters.

The variables used are as follows: Regular or poor self-assessment - 0 - if the individual indicated that their health was good or very good and 1 - if they indicated that their health was Regular, Poor or Very Bad; gender 0 = male and 1 = female; dummy higher school - 1- complete higher education and 0 = otherwise; age years; dummy color white - 0 = non-white and 1 = white; Has a Plan 0 = does not have and 1 = has a health insurance or plan. The results obtained were as follows:

dummy_plain_1	coef	Std.Err.	Z	Marginal Effects in Midpoint
Self Avaliation	-0.37	0.007	-52.857142857143
gender	0.01	0.0069
dummy_white_color	0.44	0.005	0.005
dummy_higherschool	1.18	1.18	268.18181818182
age	-0.03	0.0025
age^2	0.003	6.3E-6	-4761.9047619048
_cons	-0.96	-0.96	-87.272727272727

Consider that f(.) is equal to 0.19, where f is the probability density function of the Normal, evaluated by the midpoint method, detailed in Wooldridge's book under the concept of partial effect on the mean (Economically Active Population). Answer the following questions and use decimal point, not comma.

1. z-value for the gender variable (answer with five decimal places) :

2. If Restricted Model Log Likelihood = -13479 and Unrestricted Model Log Likelihood = -9365, the value of Pseudo R2 or McFadden R2 is (respond to five decimal places):

3. The value to fill in the column "Midpoint Marginal Effects?" for the age variable (mean = 36.1) it would be:

4.Considering a hypothetical probit model in which beta0, beta1, beta2 are parameters and the estimated model was F(beta0 + beta1 * x + beta2 * x ^2 ) = F(8 + 13 * x + 5 * x ^2 ), where F is the cumulative function and f is the density function both of the Standardized Normal, find the algebraic expression of the partial effect of the variable x. For simplicity, consider in your derivation that the point to be used for the calculation will be called x, too. Note: Moodle recognizes the following functions: + addition, - subtraction, * multiplication, / division, ^ exponential; make all operations explicit, that is, do not simplify performing any calculation on the expression to be filled. Examples of algebraic expressions: F(8+13 * x + 5 * x^2 )*f(13) or f(2*13 * x+5)