#
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

n = 38
barY = 20
sumXSquared = 1922
SXY = 180
SXX = 60
s2 = 121     # this is an estimate of the common variance (the same for all x's)

b1 = SXY / SXX
barX = sqrt( - (SXX - sumXSquared)/n )
b0 = barY - b1 * barX

T = b0 * sqrt( n*SXX / (s2 * sumXSquared) )

ci = 0.98
alpha = 1 - ci
t = qt( 1 - alpha/2, n-2 )

# Part (c):
#
ci = 0.9
alpha = 1 - ci
t = qt( 1 - alpha/2, n-2 )

print( b1 - t * sqrt( s2 / SXX ) )
print( b1 + t * sqrt( s2 / SXX ) )