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

012bwght cigs faminc βββμ

=+++

(i) What is the most likely sign for

2

β?

(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 BWGHT.RAW. 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

CIGS 1.000000

-----

-----

FAMINC -0.173045 1.000000

-6.540971 -----

0.0000 -----

1.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＜0.05，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 -0.463408 0.091577 -5.060315 0.0000

FAMINC 0.092765 0.029188 3.178195 0.0015

C 116.9741 1.048984 111.5118 0.0000

R-squared 0.029805 Mean dependent var 118.6996

Adjusted R-squared 0.028404 S.D. dependent var 20.35396

S.E. of regression 20.06282 Akaike info criterion 8.837772

Sum squared resid 557485.5 Schwarz criterion 8.849089

Log likelihood -6130.414 Hannan-Quinn criter. 8.842005

F-statistic 21.27392 Durbin-Watson stat 1.921690

Prob(F-statistic) 0.000000

Dependent Variable: BWGHT

Method: Least Squares

Date: 05/13/13 Time: 19:40

Sample: 1 1388

Included observations: 1388

Variable Coefficient Std. Error t-Statistic Prob.

CIGS -0.513772 0.090491 -5.677609 0.0000

C 119.7719 0.572341 209.2668 0.0000

R-squared 0.022729 Mean dependent var 118.6996

Adjusted R-squared 0.022024 S.D. dependent var 20.35396

S.E. of regression 20.12858 Akaike info criterion 8.843598

Sum squared resid 561551.3 Schwarz criterion 8.851142

Log likelihood -6135.457 Hannan-Quinn criter. 8.846420

F-statistic 32.23524 Durbin-Watson stat 1.924390

Prob(F-statistic) 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cigs影响很小。

五、实验步骤

（1）输入数据