Homework 1
519021911239 叶航宇
1. Prove. Since we have:
So the left:
2. Solution. Assume a simple regression model as:
for any sample
for the input
, we have:
, we could estimate
by:
the residuals:
since we have
, we need to get optimal solution:
By FOC (first order condition), we have
devided by :
then we have:
so we get
3. Prove.
so we have:
4. Prove. since we have:
we could get:
by averaging:
and substract:
therefore:
so
5.
Since
so we have for any :
and since:
so
6.
1. No. Because the change of study time may cause change of other variale.
2. There is a exact linear relationship among all the independent variables.
3.
7.
1.
is probable to be negative and
nox, the housing price will be
is probable to be positive. With one percent more
percent cheaper.
2. Maybe more nox means less housing area and fewer rooms.
downward
3. Yes.
Computer Exercises
1.
average: 13.46
lowest: 9
highest: 18
2.
black: 120
non-black: 815
percentage of no black: 87.17
3.
1. average wage: 957.95
black average wage: 735.84
non-black average wage: 990.65
2. On average, black men earn less.
3. No. Being black may have effect on one's wage, but is not the only parameters. And the
sample here only shows the causality.
4.
married == 0: 100
the group who are not married has a higher sample mean education.
5.
1. corr: 0.3271
Positive, means that they are positively correlated.
2. The more years of education, the higher sample mean of monthly earnings.
The scatter plot confirm this relation ship.
Code
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*** Program name: Sample Do File.do
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* NOTE:
Whenever a line begins with an asterisk, STATA ignores the whole
line - this is just a comment/note.
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capture log close
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clear /* The 'clear' command gets rid of all data in memory*/
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set memory 60000 /* Allocate 60MB memory to Stata */
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set matsize 150 /*Set the maximum number of variables in a model*/
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set more off /*tells Stata not to pause or display the ” –more–” message
when showing results.*/
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* This line tells Stata where the files are located. USE "" if your folder
names contain spaces.
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* THIS IS THE ONLY LINE YOU NEED TO CHANGE.
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cd "D:\OneDrive\2020学年第二学期\计量经济学\homework\week 1"
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* NOTE:
The next lines set up the .log file.
It will contain all of the
output
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* from this program when it is run. It will be saved in the same directory
as the
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* program and will be replaced with each new run. I have called the log-file
ProblemSet1.
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log using sample.log, replace
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* This line reads in the data set called WAGE1.dta in the same directory (in
my case this is directory "datasets").
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use "WAGE2", clear
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* Type all commands you need below. The commands should NOT contain an
asterisk.
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* 1
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sum educ
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* 2
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tab black
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* 3
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tab black, sum(wage)
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* 4
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tab married, sum(educ)
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* 5
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corr educ wage
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tab educ, sum(wage)
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scatter wage educ
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* To execute all commands in the Do File, click CTRL+D
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log close
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exit, clear
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