from math import sqrt

from matplotlib import pyplot as plot

from random import seed

from random import randrange

from csv import reader

# Step $2$: Load the csv file

def load$\_$csv$($filename$,$ skip$=$False$)$:

dataset $=$ list$()$

with open$($filename$,\text{'}$r$\text{'})$ as file:

csv$\_$reader $=$ reader$($file$)$

if skip:

next$($csv$\_$reader, None$)$

for row in csv$\_$reader:

dataset.append$($row$)$

return dataset

# Step $3$: Convert any string column to a float column

def string$\_$column$\_$to$\_$float$($dataset$,$ column$)$:

for row in dataset:

row$[$column$]=$ float$($row$[$column$].$strip$())$

# Step $4$: Calculate the mean value of a list of numbers

def mean$($values$)$:

return sum$($values$)/$ float$($len$($values$))$

# Step $5$: Calculate a regularisation value for the parameter

def regularisation$($parameter$,$ lambda$\_$value$=0\mathrm{.}01)$:

return lambda$\_$value $+$ parameter

def variance$($values$,$ mean$)$:

return sum$([($x $-$ mean$)**2$ for x in values$])$

def covariance$($x$,$ x$\_$mean, y$,$ y$\_$mean$)$:

covar $=0\mathrm{.}0$

for i in range$($len$($x$))$:

covar $+=($x$[$i$]-$ x$\_$mean$)*($y$[$i$]-$ y$\_$mean$)$

return covar

# Step $6$: Calculate least squares between x and y

def leastSquares$($dataset$)$:

x $=[$row$[0]$ for row in dataset$]$

y $=[$row$[1]$ for row in dataset$]$

x$\_$mean $=$ mean$($x$)$

y$\_$mean $=$ mean$($y$)$

b$1=$ covariance$($x$,$ x$\_$mean, y$,$ y$\_$mean$)/$ variance$($x$,$ x$\_$mean$)$

b$0=$ y$\_$mean $-$ b$1*$ x$\_$mean

return $[$b$0,$ b$1]$

# Step $7$: Calculate root mean squared error

def root$\_$mean$\_$square$\_$error$($actual$,$ predicted$)$:

sum$\_$error $=0\mathrm{.}0$

for i in range$($len$($actual$))$:

prediction$\_$error $=$ predicted$[$i$]-$ actual$[$i$]$

sum$\_$error $+=($prediction$\_$error $**2)$

mean$\_$error $=$ sum$\_$error $/$ float$($len$($actual$))$

return sqrt$($mean$\_$error$)$

# Step $8$: Make predictions

def simple$\_$linear$\_$regression$($train$,$ test$)$:

predictions $=$ list$()$

b$0,$ b$1=$ leastSquares$($train$)$

for row in test:

yhat $=$ b$0+$ b$1*$ row$[0]$

predictions.append$($yhat$)$

return predictions

# Step $9$: Split the data into training and test sets

def train$\_$test$\_$split$($dataset$,$ split$)$:

train $=$ list$()$

test $=$ list$($dataset$)$

train$\_$size $=$ split $*$ len$($dataset$)$

while len$($train$)<$ train$\_$size:

index $=$ randrange$($len$($test$))$

train.append$($test$.$pop$($index$))$

return train, test

# Seed the random value

seed$(1)$

# Load and prepare data

filename $=$ 'fertility$\_$rate$-$worker$\_$percent.csv$\text{'}$

dataset $=$ load$\_$csv$($filename$,$ skip$=$True$)$

for i in range$($len$($dataset$[0]))$:

string$\_$column$\_$to$\_$float$($dataset$,$ i$)$

# Evaluate algorithm

split $=0\mathrm{.}6$

rmse $=$ evaluate$\_$simple$\_$linear$\_$regression$($dataset$,$ split$)$

print$(\text{'}$Root Mean Square Error: $\%\mathrm{.}3$f$\text{'}\%$ rmse$)$

# Visualise the dataset

def visualise$\_$dataset$($dataset$)$:

test$\_$set $=$ list$()$

for row in dataset:

row$\_$copy $=$ list$($row$)$

row$\_$copy$[-1]=$ None

test$\_$set.append$($row$\_$copy$)$

sizes, prices $=[],[]$

for i in range$($len$($dataset$))$:

sizes.append$($dataset$[$i$][0])$

prices.append$($dataset$[$i$][1])$

plot.figure$()$

plot.plot$($sizes$,$ prices, $\text{'}$x$\text{'})$

plot.xlabel$(\text{'}$Fertility rate'$)$

plot.ylabel$(\text{'}$Worker percent'$)$

plot.grid$()$

plot.tight$\_$layout$()$

plot.show$()$

visualise$\_$dataset$($dataset$)$