# Section 2; Question 1:
#
source('chap_11_sect_2_question_1_data.R')
x = DF$Chirps_Per_Second
y = DF$Temperature
plot( x, y, type='p', pch=19, cex=1.5, xlab='Chirps per Second', ylab='Temperature' )
m = lm( y ~ x )
abline(m, col='red')
grid()

print(m)

predict( m, newdata=data.frame(x=18) )


# Section 2; Question 2:
#
source('chap_11_sect_2_question_2_data.R' )

#postscript("../../WriteUp/Graphics/Chapter11/chap_11_2_2_plot.eps", onefile=FALSE, horizontal=FALSE)
plot( DF$Age, DF$Proof, type='p', pch=19, cex=1.5, xlab='Age', ylab='Proof' )
m = lm( Proof ~ Age, data=DF )
abline(m, col='red')
grid()
#dev.off()


# Section 2; Question 3:
#
source( 'chap_11_sect_2_question_3_data.R' )
plot( DF$Temperature, DF$Parts_Dissolved, type='p', pch=19, cex=1.5, xlab='Temperature' , ylab='Parts Dissolved' )
m = lm( Parts_Dissolved ~ Temperature, data=DF )
abline(m, col='red')
grid()

r = residuals(m)

#postscript("../../WriteUp/Graphics/Chapter11/chap_11_2_3_residual_plot.eps", onefile=FALSE, horizontal=FALSE)
plot( DF$Temperature, r, type='p', pch=19, cex=1.5, main='residual plot' )
grid()
#dev.off()


# Section 2; Question 7:
#
source('chap_11_sect_2_question_7_data.R')

#postscript("../../WriteUp/Graphics/Chapter11/chap_11_2_7_plot.eps", onefile=FALSE, horizontal=FALSE)
plot( DF$Spending_Per_Pupil, DF$Graduation_Rate, type='p', pch=19, cex=1.5, xlab='Spending Per Pupil', ylab='Graduation Rate' )
m = lm( Graduation_Rate ~ Spending_Per_Pupil, data=DF )
abline(m, col='red')
grid()
#dev.off()

print( m )


# Section 2; Question 8:
#
source('../Chapter8/chap_8_sect_2_question_11_data.R')

plot( DF$Plant_Diversity, DF$Bird_Diversity, type='p', pch=19, cex=1.5, xlab='Plant Diversity', ylab='Bird Diversity' )
m = lm( Bird_Diversity ~ Plant_Diversity, data=DF )
abline(m, col='red')
grid()

print( m )

r = residuals(m)

#postscript("../../WriteUp/Graphics/Chapter11/chap_11_2_8_residual_plot.eps", onefile=FALSE, horizontal=FALSE)
plot( DF$Plant_Diversity, r, type='p', pch=19, cex=1.5, xlab='Plant Diversity', ylab='Residual' )
grid()
#dev.off()


# Section 2; Question 9:
#
source('chap_11_sect_2_question_9_data.R')

plot( DF$Index_of_Exposure, DF$Cancer_Mortality, type='p', pch=19, cex=1.5, xlab='Index of Exposure', ylab='Mortality' )
m = lm( Cancer_Mortality ~ Index_of_Exposure, data=DF )
abline(m, col='red')
grid()

print( m )

r = residuals(m)

#postscript("../../WriteUp/Graphics/Chapter11/chap_11_2_9_residual_plot.eps", onefile=FALSE, horizontal=FALSE)
plot( DF$Index_of_Exposure, r, type='p', pch=19, cex=1.5, xlab='Index of Exposure', ylab='Residual' )
grid()
#dev.off()


# Section 2; Question 10:
#
source('chap_11_sect_2_question_10_data.R')

plot( DF$x, DF$y, type='p', pch=19, cex=1.5, xlab='x', ylab='y' )
m = lm( y ~ x, data=DF )
abline(m, col='red')
grid()

print( m )

r = residuals(m)

#postscript("../../WriteUp/Graphics/Chapter11/chap_11_2_10_residual_plot.eps", onefile=FALSE, horizontal=FALSE)
plot( DF$x, r, type='p', pch=19, cex=1.5, xlab='x', ylab='Residual' )
abline(h=0, col='black', cex=1.5)
grid()
#dev.off()


# Section 2; Question 11:
#
source('chap_11_sect_2_question_11_data.R')

plot( DF$Plumage_Index, DF$Behavioral_Index, type='p', pch=19, cex=1.5, xlab='Plumage Index', ylab='Behavioral Index' )
m = lm( Behavioral_Index ~ Plumage_Index, data=DF )
abline(m, col='red')
grid()

print( m )

r = residuals(m)

plot( DF$Plumage_Index, r, type='p', pch=19, cex=1.5, xlab='Plumage_Index', ylab='Residual' )
abline(h=0, col='black', cex=1.5)
grid()


# Section 2; Question 15:
#
source('chap_11_sect_2_question_15_data.R')
d = DF$Distance
v = DF$Velocity

b = sum( d*v ) / sum( d*d )
print( b )


# Section 2; Question 17:
#
source('chap_11_sect_2_question_17_data.R')

a_star = 100
numer = sum( DF$Years * DF$Percent ) - a_star * sum( DF$Years )
denom = sum( DF$Years * DF$Years ) 
b = numer / denom
print( b )


# Section 2; Question 18:
#
source('../Chapter8/chap_8_sect_2_question_5_data.R')

plot( DF$Number_of_Suites, DF$Projected_Revenue, pch=19, cex=1.5, xlab='Number of Suites', ylab='Projected Revenue' )
m = lm( Projected_Revenue ~ Number_of_Suites - 1, data=DF )
abline(m, col='red')
grid()

print( m )


# Section 2; Question 20:
# 
source('chap_11_sect_2_question_20_data.R')
x = DF$Days_After_Injection
y = log(DF$Serum_Gold_Concentration)
plot( x, y, pch=19, cex=1.5, main='linearized data' )
m = lm( y ~ x )
abline(m, col='red')
grid()

print( m )

# Get the parameters of the model y = a exp( b x )
#
a = exp( coefficients(m)[1] )
b = coefficients(m)[2]
print( sprintf( 'Nonlinear model parameters: a= %10.6f, b= %10.6f', a, b) )

x = DF$Days_After_Injection
y = DF$Serum_Gold_Concentration
plot( x, y, pch=19, cex=1.5, main='data and model', xlab='Days After Injection', ylab='Serum Gold Concentration' )
x_grid = seq( min(x), max(x), length.out=50 )
y_hat = a * exp( b * x_grid )
lines( x_grid, y_hat, type='l', col='red' )
grid()

# Compute the halflife:
#
print( sprintf( 'halflife= %10.6f', log(1/2) / b) )


# Section 2; Question 21:
#
source('chap_11_sect_2_question_21_data.R')
x = DF$Years_After_1995
y = log(DF$Gross_Federal_Debt)
plot( x, y, pch=19, cex=1.5, main='linearized data' )
m = lm( y ~ x )
abline(m, col='red')
grid()

print( m )

# Get the parameters of the model y = a exp( b x )
#
a = exp( coefficients(m)[1] )
b = coefficients(m)[2]
print( sprintf('Nonlinear model parameters: a= %10.6f, b= %10.6f', a, b) )

x = DF$Years_After_1995
y = DF$Gross_Federal_Debt
plot( x, y, pch=19, cex=1.5, main='data and model', xlab='Years After 1995', ylab='Gross Federal Debt' )
x_grid = seq( min(x), max(x), length.out=50 )
y_hat = a * exp( b * x_grid )
lines( x_grid, y_hat, type='l', col='red' )
grid()

#
x0 = 2007 - 1995
y_hat = a * exp( b * x0 )
print( sprintf('x0= %3.0f; h_hat= %10.6f', x0, y_hat) )

# Plot the residuals of the nonlinear model:
#
#postscript("../../WriteUp/Graphics/Chapter11/chap_11_sect_2_ex_21.eps", onefile=FALSE, horizontal=FALSE)
y_hat = a * exp( b * x )
plot( x, y-y_hat, pch=19, cex=1.5, main='residual plot', xlab='Years After 1995' )
grid()
#dev.off()


# Section 2; Question 22:
# 
source('chap_11_sect_2_question_22_data.R')
x = DF$Age
y = log(DF$Suggested_Retail_Price)
plot( x, y, pch=19, cex=1.5, main='linearized data' )
m = lm( y ~ x )
abline(m, col='red')
grid()

print( m )

# Get the parameters of the model y = a exp( b x )
#
a = exp( coefficients(m)[1] )
b = coefficients(m)[2]
print( sprintf('Nonlinear model parameters: a= %10.6f, b= %10.6f', a, b) )

#postscript("../../WriteUp/Graphics/Chapter11/chap_11_sect_2_ex_22.eps", onefile=FALSE, horizontal=FALSE)
x = DF$Age
y = DF$Suggested_Retail_Price
plot( x, y, pch=19, cex=1.5, main='data and model', xlab='Age', ylab='Suggested Retail Price' )
x_grid = seq( min(x), max(x),length.out=50 )
y_hat = a * exp( b * x_grid ) 
lines( x_grid, y_hat, type='l', col='red' )
grid()
#dev.off()

#
x0 = 11
y_hat = a * exp( b * x0 )
print( sprintf('x0= %3.0f; h_hat= %10.6f', x0, y_hat) )


# Section 2; Question 23:
#
source('chap_11_sect_2_question_23_data.R')
x = DF$Years_After_1981
y = log(DF$Dow_Jones_Industrial_Average)
plot( x, y, pch=19, cex=1.5, main='linearized data' )
m = lm( y ~ x )
abline(m, col='red')
grid()

print( m )

# Get the parameters of the model y = a exp( b x )
#
a = exp( coefficients(m)[1] )
b = coefficients(m)[2]
print( sprintf('Nonlinear model parameters: a= %10.6f, b= %10.6f', a, b))

x = DF$Years_After_1981
y = DF$Dow_Jones_Industrial_Average
plot( x, y, pch=19, cex=1.5, main='data and model', xlab='Years After 1981', ylab='Dow Jones Industrial Average' )
x_grid = seq( min(x), max(x), length.out=50 )
y_hat = a * exp( b * x_grid )
lines( x_grid, y_hat, type='l', col='red' )
grid()


# Section 2; Question 25:
#
source('chap_11_sect_2_question_25_data.R')
x = log(DF$Peak_Wind_Gust)
y = log(DF$Number_of_Damaged_Homes)
plot( x, y, pch=19, cex=1.5, main='linearized data' )
m = lm( y ~ x )
abline(m, col='red')
grid()

print( m )

# Get the parameters of the model y = a x^b => log(y) = log(a) + b log(x)
#
a = exp( coefficients(m)[1] )
b = coefficients(m)[2]
print( sprintf('Nonlinear model parameters: a= %10.6f, b= %10.6f', a, b) )

x = DF$Peak_Wind_Gust
y = DF$Number_of_Damaged_Homes
plot( x, y, pch=19, cex=1.5, main='data and model', xlab='Peak Wind Gust', ylab='Number of Damaged Homes')
x_grid = seq( min(x), max(x), length.out=50 )
y_hat = a * x_grid^b
lines( x_grid, y_hat, type='l', col='red' )
grid()


# Section 2; Question 26:
#
source('chap_11_sect_2_question_26_data.R')
x = log(DF$Foraging_Size)
y = log(DF$Colony_Size)
plot( x, y, pch=19, cex=1.5, main='linearized data' )
m = lm( y ~ x )
abline(m, col='red')
grid()

print( m )

# Get the parameters of the model y = a x^b => log(y) = log(a) + b log(x)
#
a = exp( coefficients(m)[1] )
b = coefficients(m)[2]
print( sprintf('Nonlinear model parameters: a= %10.6f, b= %10.6f', a, b) )

x0 = 2500
y0 = a * x0^b
print( sprintf('x0= %10.2f, y0= %10.2f', x0, y0) )


# Section 2; Question 27:
#
source('chap_11_sect_2_question_27_data.R')
x = log(DF$Striate_Cortex)
y = log(DF$Prestriate_Cortex)
plot( x, y, pch=19, cex=1.5, main='linearized data' )
m = lm( y ~ x )
abline(m, col='red')
grid()

print( m )

# Get the parameters of the model y = a x^b => log(y) = log(a) + b log(x)
#
a = exp( coefficients(m)[1] )
b = coefficients(m)[2]
print( sprintf('Nonlinear model parameters: a= %10.6f, b= %10.6f', a, b) )

#postscript("../../WriteUp/Graphics/Chapter11/chap_11_sect_2_ex_27.eps", onefile=FALSE, horizontal=FALSE)
x = DF$Striate_Cortex
y = DF$Prestriate_Cortex
plot( x, y, pch=19, cex=1.5, main='data and model', xlab='Striate Cortex', ylab='Prestriate Cortex')
x_grid = seq( min(x), max(x), length.out=50 )
y_hat = a * x_grid^b 
lines( x_grid, y_hat, type='l', col='red' )
grid()
#dev.off()


# Section 2; Question 28:
#
source('chap_11_sect_2_question_28_data.R')
x = 1/DF$Distance_From_Center_of_City
y = DF$Value
plot( x, y, pch=19, cex=1.5, main='linearized data' )
m = lm( y ~ x )
abline(m, col='red')
grid()

print( m )

y_hat = predict( m, newdata=data.frame(x=4) )
print( sprintf('x= %.3f; y_hat= %.3f', 1/4, y_hat) )


# Section 2; Question 30:
#
source('chap_11_sect_2_question_30_data.R')
L = 1055
x = DF$Years_After_1959
y = log(L/DF$Number_of_ICBMs - 1)
plot( x, y, pch=19, cex=1.5, main='linearized data' )
m = lm( y ~ x )
abline(m, col='red')
grid()

print( m )

# Get the parameters of the model y = L / ( 1 + e^{a+b x} )
#
a = coefficients(m)[1]
b = coefficients(m)[2]
print( sprintf('Nonlinear model parameters: a= %10.6f, b= %10.6f', a, b) )

#postscript("../../WriteUp/Graphics/Chapter11/chap_11_sect_2_ex_30.eps", onefile=FALSE, horizontal=FALSE)
x = DF$Years_After_1959
y = DF$Number_of_ICBMs
plot( x, y, pch=19, cex=1.5, main='data and model', xlab='Years After 1959', ylab='Number of ICBMS')
x_grid = seq( min(x), max(x), length.out=50 )
y_hat = L / ( 1 + exp( a + b * x_grid ) )
lines( x_grid, y_hat, type='l', col='red' )
grid()
#dev.off()


# Section 2; Question 31:
#
source('chap_11_sect_2_question_31_data.R')
L = 60
x = DF$Age_Mid_Point
y = log(L/DF$Percent_Improved - 1)
plot( x, y, pch=19, cex=1.5, main='linearized data' )
m = lm( y ~ x )
abline(m, col='red')
grid()

print( m )

# Get the parameters of the model y = L / ( 1 + e^{a+b X} )
#
a = coefficients(m)[1]
b = coefficients(m)[2]
print( sprintf('Nonlinear model parameters; a= %10.6f, b= %10.6f', a, b) )

#postscript("../../WriteUp/Graphics/Chapter11/chap_11_sect_2_ex_31.eps", onefile=FALSE, horizontal=FALSE)
x = DF$Age_Mid_Point
y = DF$Percent_Improved
plot( x, y, pch=19, cex=1.5, main='data and model', xlab='Age', ylab='Percent Improved')
x_grid = seq( min(x), max(x), length.out=50 )
y_hat = L / ( 1 + exp( a + b * x_grid ) )
lines( x_grid, y_hat, type='l', col='red' )
grid()
#dev.off()