The derivation proof of least square method

1. Additional questions: Derivation of the linear least squares process

The last step in solving b is to use the sum property , in fact

The same as the evidence of the molecular part, please refer to the introduction of Econometrics (fourth edition) introductory econometrics A Modern approach fourth edition Jeffrey a basic mathematical tool in Appendix A of M-Wood Ridge (Jeffrey M. Wooldridge).

2. Horse racing Problems

Q: 36 Horses, 6 runways, no timers, at least several times to select the top 3?

The answer is 8 times, the idea is as follows:

(1) The 36 horses were divided into 6 groups, and 6 competitions were conducted respectively, and the 1th place in each group could be obtained.

(2) The 1th place in each group will be played 1 times, respectively, to get the rank of the fastest horses in each group.

(3) Select the 1th place in the group of 1th, 2, 3, 2nd name of the group of 1th, 2 (3rd name is not selected, because his best result is the 4th name), the 3rd name of the group's 1th name (Ibid. reasoning), 4th, 5, 6, the group does not have to play (ibid. reasoning), The top 3 will be made up of 6 people and then 1 times.

To sum up, a total of 6+1+1=8 tournaments.

3. Random number

A random number generator of the existing Rand5 (), and so on, may generate a number between the two, requiring it to implement Rand7 (), and so on, which may generate a number between 1~7.

Idea: Mapping 1-5 to a multiple of 7 space, such as Call 2 times Rand5 () multiply can get 1~25 space, each number is equal to 1/25, and then write a judgment function throw away 22-25, leaving 1~21.

Tip:"et" just saying that each number produces equal probabilities does not mean that adding up equals 1.

Def Rand7 (): R = r>21: a = Rand5 () b = Rand5 () R = A * b return R/3

The derivation proof of least square method