How to reduce my RMSE in my final code. My RMSE is $3\mathrm{.}513.$ Only step $2-9$ is allowed for editing.

Import the libraries.

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 coulm.

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

for row in dataset:

# The strip$()$ function remove white space

# then convert the data into a decimal number $($float$)$

# and overwrite the original data

#CONVERTING STRING TO FLOAT

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

###

$$

Step $4$

Calculate the mean value of a list of numbers.

def mean$($values$)$:

mean$\_$results $=0\mathrm{.}0$

#MEAN RESULT CALCULATION

mean$\_$results $=$ sum$($values$)/$ float$($len$($values$))$

###

return mean$\_$results

Step $5$

Calculate a regularisation value for the parameter.

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

#CALCULATION OF THE REHULARISED PARAMETER

regularised$\_$parameter $=$ parameter $*(1-$ lambda$\_$value$)$

###

$$

return parameter

Step $6$

Calculate least squares between x and y$.$

def leastSquares$($dataset$)$:

$$

x $=$ list$()$

y $=$ list$()$

for row in dataset:

x$.$append$($row$[0])$

for row in dataset:

y$.$append$($row$[1])$

$$

b$0=0$

b$1=0$

$$

# using the formula to calculate the b$1$ and b$0$

numerator $=0$

denominator $=0$

$$

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

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

#B$1$ SLOPE $-$ CALCULATION

numerator $=$ sum$(($x$[$i$]-$ x$\_$mean$)*($y$[$i$]-$ y$\_$mean$)$ for i in range $($len$($x$)))$

denominator $=$ sum$(($x$[$i$]-$ x$\_$mean$)**2$ for i in range$($len$($x$)))$

#B$0$ SLOPE $-$ CALCULATION

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

###

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

Step $7$

Calculate root mean squared error.

sum$\_$error $=$ sum$(($actual$[$i$]-$ predicted$[$i$])**2$ for i in range$($len$($actual$)))$

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

rmse $=$ sqrt$($mean$\_$error$)$

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

rmse $=0\mathrm{.}0$

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

###

sum$\_$error $=$ sum$(($actual$[$i$]-$ predicted$[$i$])**2$ for i in range$($len$($actual$)))$

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

rmse $=$ sqrt$($mean$\_$error$)$

###

return rmse

Step $8$

Make Predictions.

predictions $=$ list$()$

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

# This function takes the training data to calculate the linear regression model parameters $($b$0$ and b$1)$

# using the least squares method. Then it predicts the target values for the given test set.

# Each prediction is made using the formula yhat $=$ b$0+$ b$1*$ x$,$ where b$0$ is the intercept, b$1$ is the slope,

# and x is the independent variable. The predictions are stored in a list and returned.

for row in test:

x $=$ row$[0]$

yhat $=$ b$0+$ b$1*$ x

predictions.append$($yhat$)$

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

predictions $=$ list$()$

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

# This function takes the training data to calculate the linear regression model parameters $($b$0$ and b$1)$

# using the least squares method. Then it predicts the target values for the given test set.

# Each prediction is made using the formula yhat $=$ b$0+$ b$1*$ x$,$ where b$0$ is the intercept, b$1$ is the slope,

# and x is the independent variable. The predictions are stored in a list and returned.

$$

for row in test:

x $=$ row$[0]$

yhat $=$ b$0+$ b$1*$ x

predictions.append$($yhat$)$

return predictions

Step $9$

Split the data into training and test sets.

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

train $=$ list$()$

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

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

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

index $=$ randrange$($len$($dataset$\_$copy$))$ #$0$ to $99$

train.append$($dataset$\_$copy.pop$($index$))$

return train, dataset$\_$copy

Step $10$

Evaluate regression algorithm on training dataset.

def evaluate$\_$simple$\_$linear$\_$regression$($dataset$,$ split$=0)$:

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

train, test $=$ train$\_$test$\_$split$($dataset$,$ split$)$

for row in test:

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

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

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

predicted $=$ simple$\_$linear$\_$regression$($train$,$ test$\_$set$)$

actual $=[$row$[-1]$ for row in test$]$

rmse $=$ root$\_$mean$\_$square$\_$error$($actual$,$ predicted$)$

$$

return rmse

Step $12$

Seed the random value.

In $[69]$: seed$(1)$