List four useful spreadsheet functions and explain what they do.
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Answer:
Check the explanation
Explanation:
Lasso: R example
To run Lasso Regression you can re-use the glmnet() function, but with the alpha parameter set to 1.
# Perform 10-fold cross-validation to select lambda --------------------------- lambdas_to_try <- 10^seq(-3, 5, length.out = 100) # Setting alpha = 1 implements lasso regression lasso_cv <- cv.glmnet(X, y, alpha = 1, lambda = lambdas_to_try, standardize = TRUE, nfolds = 10) # Plot cross-validation results plot(lasso_cv)
Best cross-validated lambda lambda_cv <- lasso_cv$lambda.min # Fit final model, get its sum of squared residuals and multiple R-squared model_cv <- glmnet(X, y, alpha = 1, lambda = lambda_cv, standardize = TRUE) y_hat_cv <- predict(model_cv, X) ssr_cv <- t(y - y_hat_cv) %*% (y - y_hat_cv) rsq_lasso_cv <- cor(y, y_hat_cv)^2 # See how increasing lambda shrinks the coefficients -------------------------- # Each line shows coefficients for one variables, for different lambdas. # The higher the lambda, the more the coefficients are shrinked towards zero. res <- glmnet(X, y, alpha = 1, lambda = lambdas_to_try, standardize = FALSE) plot(res, xvar = "lambda") legend("bottomright", lwd = 1, col = 1:6, legend = colnames(X), cex = .7)
Kindly check the Image below.
