1.Linear Regression with Multiple Variables
转自：https://blog.csdn.net/mupengfei6688/article/details/53098735
1.Suppose m=4 students have taken some class, and the class had a midterm exam and a final exam. You have collected a dataset of their scores on the two exams, which is as follows:
| midterm exam | (midterm exam)^2 | final exam |
| 89 | 7921 | 96 |
| 72 | 5184 | 74 |
| 94 | 8836 | 87 |
| 69 | 4761 | 78 |
You'd like to use polynomial regression to predict a student's final exam score from their midterm exam score. Concretely, suppose you want to fit a model of the form , where is the midterm score and x_2 is (midterm score)^2. Further, you plan to use both feature scaling (dividing by the "max-min", or range, of a feature) and mean normalization.
What is the normalized feature ? (Hint: midterm = 69, final = 78 is training example 4.) Please round off your answer to two decimal places and enter in the text box below.
2.Which of the following are reasons for using feature scaling?
A.It speeds up gradient descent by making it require fewer iterations to get to a good solution.
B.It speeds up solving for using the normal equation.
C.It is necessary to prevent gradient descent from getting stuck in local optima.
D.It prevents the matrix (used in the normal equation) from being non-invertable (singular/degenerate).
迭代次数的减少，加快了正确答案的得出。正规方程对计算只与训练集的大小有关，而与秩无关，不能阻止梯度下降局部最优(ps:正规方程没有局部最优)，第四个答案，除非可以减少特征变量，否则不能解决此问题所以选A
正规方程（normal equation）：
。