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Polinomyal-Regression-in-R/

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Polinomyal-Regression-in-R/**Task_2.R**

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set.seed(123) | |

#create the theta bias | |

constant = rep(1, times = length(y)) | |

#split X into X1 and X2 | |

X1=Dataframe[,1] | |

X2=Dataframe[,2] | |

#create the models | |

model1=cbind((X1^3), (X2^5), constant) | |

model2=cbind((X1^4), (X2^2), constant) | |

model3=cbind((X1^3), X2, X1, constant) | |

model4=cbind(X1, (X1^2),(X1^3), (X2^3), constant) | |

model5=cbind((X1^3), (X1^4), X2, constant) | |

for (i in 1:5) { | |

#get the model for every index: (model + i) | |

var_name=paste0("model", i) | |

my_model=get(var_name) | |

#estimate model parameters using least squares (task 2.1) | |

thetahat=solve(t(my_model) %*% my_model) %*% t(my_model) %*% y | |

#print(thetahat) #print thetahat to include in the report | |

#compute the models prediction | |

y_pred=my_model %*% thetahat | |

#compute model residual (error) and calculate the sum of squared errors (task 2.2) | |

residuals = y - y_pred | |

rss = sum(residuals^2) | |

print(paste0("--------------------- Model ", i," -----------------------")) | |

print(paste0("RSS for model ",i, ": ", rss)) | |

#compute the log-likelihood function (task 2.3) | |

n = length(y) | |

sigma_squared = rss/(n-1) | |

loglikelihood = -(n/2) * log(2*pi) - (n/2) * log(sigma_squared) - (1/(2*sigma_squared)) * rss | |

print(paste0("log likelihood for model ",i, ": ", loglikelihood)) | |

#define k for AIC and BIC this is the number of estimated parameters in each model | |

#K is 4 in model 1 and 2, K is 5 in model 3 and 5, K is 6 in model 4 | |

if (i == 1 || i == 2) { | |

k= 4 | |

} else if (i == 4){ | |

k= 6 | |

} else { | |

k= 5 | |

} | |

#compute AIC (task 2.4) | |

AIC = 2 * k - 2 * loglikelihood | |

print(paste0("AIC for model ",i, ": ", AIC, " info: K is equal to: ", k)) | |

#compute BIC | |

BIC = log(n) * k - 2 * loglikelihood | |

print(paste0("BIC for model ",i, ": ", BIC)) | |

#Check if the residuals are close to normal/Gaussian (task 2.5) | |

qqnorm(residuals, main=paste("Q-Q Plot for Model", i)) | |

qqline(residuals) | |

hist(residuals, col="limegreen", main=paste("Distribution of the residuals for model", i), xlab="Model prediction errors", ylab="Frequency") | |

print(shapiro.test(residuals)) | |

} |