input: from typing import List
  
  def predict_with_linear_regression(X: List[int], Y: List[int]) -> List[float]:
      """ Perform linear regression for predicting the numbers in a given dataset and then
      predict the value for a new data point.
      >>> predict_with_linear_regression([1,2,3,4,5], [3,5,7,9,13])
      [15.4]
      """
  
output:     n = len(X)
      sum_x = sum(X)
      sum_y = sum(Y)
      sum_xy = sum(x * y for x, y in zip(X, Y))
      sum_x_squared = sum(x ** 2 for x in X)
      
      m = (n * sum_xy - sum_x * sum_y) / (n * sum_x_squared - sum_x ** 2)
      b = (sum_y - m * sum_x) / n
      
      new_x = X[-1] + 1
      predicted_y = m * new_x + b
      
      return [predicted_y]