- 2019-09-18 11:21
*views 10*- stata
- stata linear regression Constrained r

One , Basic command of linear regression

regress y x1 x2 （ Red means that the command can be abbreviated to red ）

with Nerlove Data, for example （ The data are attached below ）

regress lntc lnq lnpf lnpk lnpl

The upper part of the table is an analysis of variance , Including the sum of squares of regression , Sum of squares of residuals , mean square ,F Inspection, etc . The goodness of fit is given on the right side of the upper part R2 And adjusted R2.root MSE

Represents the standard error of the equation .

The lower part of the table shows the point estimates and interval estimates of regression coefficients , Standard error sum t Test value .

If the regression does not require a constant term , Can be added after the command noconstant

regress lntc lnq lnpf lnpk lnpl,noc

Two , Regression with constraints

If only the samples satisfying certain conditions are regressed , Conditions can be added if condition

If in this case q>=6000 Identified as a large enterprise , The following commands can be set

regress lntc lnq lnpf lnpk lnpl if q>=6000

Or virtual variables , Define a new variable large , If it's a big business , Then the value is 1, Otherwise 0, The code is

g large=(q>=6000) regress lntc lnq lnpf lnpk lnpl if large

The output is equivalent to the above if Conditional results .

If we return to non large enterprises , It can be expressed as

regress lntc lnq lnpf lnpk lnpl if large==0

If the regression coefficient needs to satisfy some specified conditions , such as a1+a2+a3=1,a1=2a2 etc. , This can be done by setting constraints ：

constraint def 1 lnpl+ lnpk+ lnpf=1 cnsreg lntc lnq lnpf lnpk lnpl,c(1)

constraint def 1 Define the first constraint ,cnsreg Represents a constrained regression ,c(1) Indicates that the constraint condition is satisfied 1

If several conditions need to be satisfied at the same time , Conditions can be further set 2, condition 3, To add constraints lnq=1 take as an example

cons def 2 lnq=1 cnsreg lntc lnq lnpf lnpk lnpl,c(1-2)

Three , forecast , Inspection and related calculation

If you want to calculate the fitting value of the dependent variable , And save to the new variable yhat in , Can be used predict：

Take the prediction of unconstrained regression as an example ：

regress lntc lnq lnpf lnpk lnpl predict yhat

The prediction results are saved in the original data set

The residual is further calculated , And save to e1 in , Then we can （ among residual Can be abbreviated ）：

predict e1,residual

residual e1 The results are stored in the original data

If you want to calculate a coefficient , It can be used directly display Expression mode , Such as computing lnq Square of

di _b[lnq]^2

If it is necessary to test the coefficient under certain conditions , Can be used test condition , To test lnq=1,lnpl+lnpk+lnpf=1 take as an example

te lnq=1 te (lnq=1)(lnpl+lnpk+lnpf=1)

Separate inspection lnq=1,F The test showed that the original hypothesis was rejected ; Joint inspection lnq=1,lnpl+lnpk+lnpf=1, Rejecting the original hypothesis of joint establishment .

For two coefficients at the same time equal to 0 Make assumptions , Commands can be used te variable 1 variable 2 , To test lnpl lnpk Union equals 0 take as an example ：

test lnpl lnpk

F The test showed that both were not rejected 0 The original hypothesis of .

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