#
#  Week7a_BLF.SSC  (updated in Week 8)
#  MATH 3330 Section B
#  Fall 2001
#
#  Analysis of salary and job evaluation data
#  from a big law firm (synthetic data based on
#  a true story)
#

# Import blf from blf.xls on the web site

# blf <- blf.orig

summary(blf)

pairs(blf, panel = panel.xyell)

pairs(blf[,-1], panel = panel.xyell)


#
# Extra sums of squares
# Testing whether Knowledge is enough to predict salary
#

fit.full <- lm( Salary ~ Knowledge + Experience + Communication, 
	blf)
summary( fit.full )
anova( fit.full )


fit.null <- lm( Salary ~ Knowledge, blf)
summary( fit.null )
anova( fit.null )

anova( fit.null, fit.full)  # compares two fits 

# 
# Extra Sums of Squares and the overall F test
#

# fit an intercept-only model

fit.int <- lm( Salary ~ 1, blf)  # 1 is there by default
summary(fit.int)		# note that S-Plus is unhappy when it
						# tries to do an overall F on this one
						
summary( fit.full )  # compare overall F with following:
anova( fit.int, fit.full)

# 
# Dummy variable for Gender
#

blf

# Define a dummy variable

blf$Female <- 1 * ( blf$Gender == 'F' )
blf

xyplot( Salary ~ Experience, blf)
xyplot( Salary ~ Experience | Gender, blf)
xyplot( Salary ~ Experience | Gender, blf, panel = panel.xyell)

fit1 <- lm( Salary ~ Experience, blf)
summary(fit1)

fit2 <- lm( Salary ~ Experience + Female, blf )
summary(fit2)

fit3 <- lm( Salary ~ Female, blf )  # regressing on a dummy variable
summary(fit3)

# Showing the fitted values

pred <- expand.grid( Experience = 1:7, Female = 0:1)
pred$Salary <- predict( fit2, newdata = pred )

xyplot( Salary ~ Experience | Female, pred, type ='l')

xyplot( Salary ~ Experience , pred, groups = Female, type = 'l',
	panel = panel.superpose) 
	
# 
#  What if the lines are not necessarily parallel (7.3)
#

fit4 <- lm( Salary ~ Experience * Female, blf )
summary(fit4)

pred$Salary4 <- predict( fit4, newdata = pred )

xyplot( Salary4 ~ Experience , pred, groups = Female, type = 'l',
	panel = panel.superpose) 
	
#
#  Using categorical variables directly (other codings)
#

# default coding for a factor:

contrasts( blf$Gender )

# fitting model directly with a factor

fit5 <- lm( Salary ~ Experience + Gender, blf )

summary( fit5 )
fit5$contrasts

# compare with 

summary( fit2 )

pred <- expand.grid( Experience = 0:7, Gender = levels(blf$Gender)) 
pred$Salary <- predict( fit5, newdata = pred )

xyplot( Salary ~ Experience , pred, groups = Gender, type = 'l',
	panel = panel.superpose,
	key = list(
		columns = 2,
		text = list( levels(pred$Gender)),
		lines = Rows( trellis.par.get('superpose.line'), 1:2 )))