一元线性回归的估计、预测和检验

第一题

一、实验目的

（

1

）将数据输入并建立工作文件

（

2

）估计参数

（

3

）进行 假设检验

（

4

）进行点预测和区间预测

（

5

）对简单的问题进行分析

二、实验要求

（

1

）

掌握一元线性回归模型的估计方法

（

2

）

掌握一元线性回归模型的检验方法

（

3

）

掌握一元线性回归模型的预测方法

三、实验原理

普通最小二乘法

四、实验内容

1

．

A

problem

of

interest

to

health

officials

(and

others)

is

to

determine

the

effects

of

smoking

during

pregnancy

on

infant

health.

One

measure

of

infant

health

is

birth

weight;

a

birth

rate

that

is

too

low

can

put

an

infant

at

risk

for

contracting

various

illnesses.

Since

factors

other

than

cigarette

smoking

that

affect

birth

weight

are

likely to be correlated with smoking, we should take those factors into account.

For

example,

higher

income

generally

results

in

access

to

better

prenatal

care,

as

well as better nutrition for the mother. An equation that recognizes this is

bwght

?

?

0

?

?

1

cigs

?

?

2

faminc

?

?

(i) What is the most likely sign for

?

2

?

(ii) Do you think cigs and faminc are likely to be correlated? Explain why the

correlation might be positive or negative.

(iii)

Now

estimate

the

equation

with

and

without

faminc,

using

the

data

in

.

Report

the

results

in

equation

form,

including

the

sample

size

and

R-squared.

Discuss

your

results,

focusing

on

whether

adding

faminc

substantially

changes

the

estimated

effect of cigs on bwght.

(i)

估计

?

2

的值为正数。

(ii)

实验得：

Covariance Analysis: Ordinary

Date: 05/13/13

Time: 19:19

Sample: 1 1388

Included observations: 1388

Correlation

t-Statistic

Probability

CIGS

FAMINC

-0.173045

-6.540971

0.0000

CIGS

1.000000

-----

-----

1.000000

-----

-----

FAMINC

1.< /p>

由实验数据得，二者相关系数为

-0.173045

，可知，二者

负相关。

2 .T

值为

-6.540971

，不等于

0

，可知二者相关。

3.

本题中，假设

cigs

与

faminc

的相关系数为

0

，即二者不

相关，试验数据得，

p

值为

0.0000

＜

0.0 5

，拒绝原假设，所

以二者相关。

(iii)

Dependent Variable: BWGHT

Method: Least Squares

Date: 05/13/13

Time: 19:39

Sample: 1 1388

Included observations: 1388

Variable

Coefficient

Std. Error

t-Statistic

Prob.

CIGS

FAMINC

C

R-squared

Adjusted R-squared

S.E. of regression

Sum squared resid

Log likelihood

F-statistic

Prob(F-statistic)

-0.463408

0.092765

116.9741

0.091577

0.029188

1.048984

-5.060315

3.178195

111.5118

0.0000

0.0015

0.0000

118.6996

20.35396

8.837772

8.849089

8.842005

1.921690

0.029805

Mean dependent var

0.028404

S.D. dependent var

20.06282

Akaike info criterion

557485.5

Schwarz criterion

-6130.414

Hannan-Quinn criter.

21.27392

Durbin-Watson stat

0.000000

Dependent Variable: BWGHT

Method: Least Squares

Date: 05/13/13

Time: 19:40

Sample: 1 1388

Included observations: 1388

Variable

CIGS

C

R-squared

Adjusted R-squared

S.E. of regression

Sum squared resid

Log likelihood

F-statistic

Prob(F-statistic)

Coefficient

-0.513772

119.7719

Std. Error

0.090491

0.572341

t-Statistic

-5.677609

209.2668

Prob.

0.0000

0.0000

118.6996

20.35396

8.843598

8.851142

8.846420

1.924390

0.022729

Mean dependent var

0.022024

S.D. dependent var

20.12858

Akaike info criterion

561551.3

Schwarz criterion

-6135.457

Hannan-Quinn criter.

32.23524

Durbin-Watson stat

0.000000

分析：当增加变量

faminc

后，

cigs

前的系数由

-0.513772

变为

-0.463408

，其变化很小，因 此是否加入变量

faminc

对

cig s

影响很小。

五、实验步骤

（

1

）输入数据

（

2

）输入方程

bwght=c(1)+c(2)*cigs+c(3)*faminc

（

3

）估计参数

Dependent Variable: BWGHT

Method: Least Squares

Date: 05/13/13

Time: 19:48

Sample: 1 1388

Included observations: 1388

Variable

CIGS

FAMINC

C

R-squared

Adjusted R-squared

S.E. of regression

Sum squared resid

Log likelihood

F-statistic

Prob(F-statistic)

Coefficient

-0.463408

0.092765

116.9741

Std. Error

0.091577

0.029188

1.048984

t-Statistic

-5.060315

3.178195

111.5118

Prob.

0.0000

0.0015

0.0000

118.6996

20.35396

8.837772

8.849089

8.842005

1.921690

0.029805

Mean dependent var

0.028404

S.D. dependent var

20.06282

Akaike info criterion

557485.5

Schwarz criterion

-6130.414

Hannan-Quinn criter.

21.27392

Durbin-Watson stat

0.000000

方程为

：

bwght=116.9741-0.463408*cig s+0.092765*faminc

（

111.5118

）

（