I need some help solving a statistics problem. Please attempt the
problem given below:

The problem of comparing the means of two independent samples can be
formulated as a regression problem as follows: Denote N1 independent,
identically distributed observations from a N(m1,s^2) population by
y_1,y_2,...,y_n1 and N2 I.I.D. observations from a N(m2,s^2)
population by y_n1+1,y_n1+2,...,y_n1+n2. Define an indicator variable
xi = 1 for i = 1,2,...,n1 and xi = 0 for i = n1+1, n2+2,...,n1+n2.
Thus if xi = 1, then yi comes from the first population, and if xi =
0, then yi comes from the second population. (m = mean, s = standard
dev. Underscores denote subscripts, and N(m,s^2) is a normal
distribution with mean m, variance s^2).

a. Show that the regression model (Yi = B0 + B1xi + ei, where ei =
random error) corresponds to B0 = m2 and B1 = m1-m2.
b. Apply the formulas for lease squares estimates for B0(hat) and
B1(hat) to show that B0(hat) = mean(y2) and B1(hat) = mean(y1) -
mean(y2).
c. Show that the mean squares estimate for regression is the same as
teh pooled estimate s^2 of sigma^2 with n1+n2-2 degrees of freedom.
d. Show that the regression t-test of B1 = 0 is the same as the pooled
variances t-test of m1 = m2.

Please ask any questions you may have as it is difficult to type these
types of problems. Any help would be great.