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Polinomyal-Regression-in-R/Task_2.7.R
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set.seed(123) | |
#split the matrix of data 70% training data and 30% testing data | |
data = sort(sample(nrow(X), nrow(X)*.7)) | |
train_data<-Dataframe[data,] | |
test_data<-Dataframe[-data,] | |
#task 2.7.1 | |
#create the theta bias of length X1 in training data. | |
const = rep(1, times=length(train_data$x1)) | |
#create the theta bias of length X1 in training data. | |
const_test = rep(1, times=length(test_data$x1)) | |
#create the model | |
model3=cbind((train_data$x1^3), train_data$x2, train_data$x1, const) | |
model3_test_data=cbind((test_data$x1^3), test_data$x2, test_data$x1, const_test) | |
#estimate model parameters using least squares (training data) | |
thetahat=solve(t(model3) %*% model3) %*% t(model3) %*% train_data$y | |
#compute model prediction using test data | |
y_pred=model3_test_data %*% thetahat | |
#plot 95% confidence interval | |
residuals = test_data$y - y_pred | |
rss = sum(residuals^2) | |
n = length(test_data$y) | |
#calculate variance of the residuals | |
sigma_squared = rss/(n-1) | |
#compute the estimated covariance matrix of the model parameters | |
cov_thetaHat = sigma_squared * (solve(t(model3_test_data) %*% model3_test_data)) | |
var_y_hat = matrix(0 , n , 1) | |
#compute the variance for of y_pred | |
for( i in 1:n){ | |
X_i = matrix( model3_test_data[i,] , 1 , 4 ) # X[i,] creates a vector. Convert it to matrix | |
var_y_hat[i,1] = X_i %*% cov_thetaHat %*% t(X_i) | |
} | |
#get all three variables to order | |
CI = 2 * sqrt(var_y_hat) # Confidence interval | |
y=test_data$y | |
time=test_data$time | |
#create dataframe and order it to plot | |
data = data.frame(y, y_pred, CI, time) | |
data = data[order(data$time), ] | |
#plot prediction, testing data, and confidence intervals | |
plot(data$time, data$y_pred, type = "o", xlim = c(41, 47), ylim = c(-1, 1), col="steelblue1", xlab="Time", ylab="Y", lwd=2) | |
points(data$time, data$y, col="forestgreen", lwd=2) | |
segments(data$time, data$y_pred - data$CI, data$time, data$y_pred + data$CI, col="red1", lwd=3) |