Researchers collected measurements from loblolly pines.

Calculate the mean squared errors for

$-$fold cross$-$validation with

$=10.$ Use the negative of the cross$\_$val$\_$score$()$ method with the following parameters, respectively:

the model variable

x$\_$variable

y$\_$variable

the scoring parameter set to neg$\_$mean$\_$squared$\_$error

the cv parameter set to $10$

Both x$\_$variable and y$\_$variable are from the training set.

The code provided contains all imports, loads the dataset, splits the dataset into train and test datasets, initializes the model, calculates the MSEs for

$-$fold cross$-$validation, and prints average MSE and the set of all MSEs for both $10-$fold and

$-$fold cross$-$validation.# Import packages and functions

import pandas as pd

import numpy as np

from sklearn.linear$\_$model import LinearRegression

from sklearn.preprocessing import PolynomialFeatures

from sklearn.model$\_$selection import train$\_$test$\_$split, cross$\_$val$\_$score

rng $=$ np$.$random.RandomState$(46)$

# Load the dataset

pines $=$ pd$.$read$\_$csv$(\text{'}$pinesSample$.$csv$\text{'})$

# Split dataset into training data and testing data

trainDataName, testDataName $=$ train$\_$test$\_$split$($pines$,$ test$\_$size$=0\mathrm{.}2,$ random$\_$state$=$rng$)$

# Store relevant columns as variables

X $=$ trainDataName$[[\text{'}$age$\text{'}]]$

y $=$ trainDataName$[[\text{'}$height$\text{'}]]$

# Initialize the model $--$ quadratic polynomial regression model

polyFeatures $=$ PolynomialFeatures$($degree$=2,$ include$\_$bias$=$False$)$

xPoly $=$ polyFeatures.fit$\_$transform$($X$)$

polyRegModel $=$ LinearRegression$()$

# Evaluate accuracy

# neg$\_$mean$\_$square$\_$error is the negative MSE, so append a minus so the scores are positive.

tenFoldScores $=$ # Your code goes here

print$(\text{'}$ten$-$fold average MSE $=\text{'},$ np$.$mean$($tenFoldScores$),\text{'}$

$\text{'},$ tenFoldScores$)$

# neg$\_$mean$\_$square$\_$error is the negative MSE, so append a $-$ so the scores are positive.

LOOCVScores $=-$cross$\_$val$\_$score$($polyRegModel$,$ X$,$ y$,$ scoring$=$'neg$\_$mean$\_$squared$\_$error', cv$=$len$($X$))$

print$(\text{'}$

k$-$fold average MSE $=\text{'},$ np$.$mean$($LOOCVScores$),\text{'}$

$\text{'},$ LOOCVScores$)$