Machine Learning Lab Assignment 1

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该博客旨在通过梯度下降算法解决并理解线性回归问题。介绍了实现单变量或多变量线性回归以预测因变量的问题，给出问题的输入（训练数据集）和输出（显示超平面系数、预测因变量值），还列举汽车保险和篮球数据的测试用例，并提及梯度下降算法的停止标准。

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OBJECT OF THE ASSIGNMENT:
To solve and understand linear regression problems by using gradient descent algorithm.
PROBLEM:
Implement linear regression with one or multiple independent variables to predict a dependent (target) variable.
INPUT OF THE PROBLEM:
Training dataset / testing examples
OUTPUT OF THE PROBLEM:
(a) Display the coefficients of the hyperplane, i.e., w = (w0, w1, …, wM).
(b) Predict values of the dependent variable for testing examples.
TESTING CASES:
1. The file data1.txt contains a training set of Auto Insurance (汽車保險) in Sweden. The first column (= x) is the number of claims (索賠) and the second column (= y) is the total payment for all the claims in thousands of Swedish Kronor (瑞典克朗).
  (a) Find the regression line ŷ = w0 + w1x. Thus, use the gradient descent algorithm to find the weight w = (w0, w1).
  (b) Once you have found the regression equation, you can use the model to make predictions.
  (i) What is the predicted value of y when x = 45?
  (ii) What is the predicted value of y when x = 25?
2. The file data2.txt contains a training set of Basketball. Columns 1 – 4 are the feature variables x1, x2, x3, x4, and column 5 is the target variable y. The following data (x1, x2, x3, x4, y) are for each player:
  x1 = height in feet
  x2 = weight in pounds
  x3 = percent of successful field goals (out of 100 attempted)
  x4 = percent of successful free throws (out of 100 attempted)
  y = average points scored per game
  (a) Find the hyperplane ŷ = w0 + w1x1+ w2x2+ w3x3+ w4x4. Thus, use the gradient descent algorithm to find the weight w = (w0, w1, w2, w3, w4).
  (b) Once you have found the hyperplane, you can use the model to make predictions.
  (i) What is the predicted value of y when (x1, x2, x3, x4) = (6.8, 210, 0.402, 0.739)?
  (ii) What is the predicted value of y when (x1, x2, x3, x4) = (6.1, 180, 0.415, 0.713)?
APPENDIX:
REMARKS:
Stopping criteria of the Gradient descent algorithm usually includes:
(a) Stop when a maximum number of iterations has been exceeded.
(b) Stop when some error measure on the training set is small enough.
　　For example: