中级计量经济学 第六讲
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zeros after a decimal point in an estimated coefficient, so that the results appear prettier. 数据测度单位变换经常被用于减少被估参数小数点后的零的 个数，这样结果更好看一些。 Since this is mainly an action of decoration, we expect nothing essential should change. 既然这样做主要为了好看，我们希望本质的东西不改变。
4
Redefining Variables: An example 重新定义变量：一个例子
Consider a model relating infant birth weight to cigarette smoking and family income:
以下模型反映了婴儿出生体重与孕妇吸烟量和家庭收入之间的关系： (1) b·wght bˆ0 bˆ1cigs bˆ2 fa min c
Consider the following rescaling: 考虑如下单位变换：
(2) Birth weight is changed from ounces to pounds 出生体重单位由盎司变为磅 (3)Number of cigarettes is changed to packs of cigrattes 香烟的支数变为包数 The estimation results is presented in the following table. 估计结果列于下表
5
Y (column) X (rows) Cigs
Packs
Faminc
Intercept
Observations R-squared SSR SER
Table 6.1
(1) bwght
(2)bwghtlbs
-0.4634 (0.0916) --
0.0927 (0.0292) 116.794 (1.049) 1388 0.0298 557,485.51 20.063
Multiple Regression Analysis 多元回归分析
y = b0 + b1x1 + b2x2 + . . . bkxk + u
4. Further Issues 进一步的问题
1
Chapter Outline 本章大纲
Effects of Data Scaling on OLS Statistics 数据的测度单位换算对OLS统计量的影响 More on Functional Form 对函数形式的进一步讨论 More on Goodness-of-Fit and Selection of
8
Impact of changing the scale of the independent variable 改变解释变量测度单位的影响
(1)/16=those in (2) (1)中被估参数的标准差/16＝ (2)中被估参数的标准差
7
Impact of changing the scale of the dependent variable 改变被解释变量测度单位的影响
The t statistics in (1) and (2) are identical. (1)和(2)中 t 统计量相同 The R squared are identical. R平方相同 SSR in (1) /(16*16)=SSR in (2) (1)中SSR/（16*16）＝ (2)中SSR SER (standard error) in (1)/16=SER in (2) (1)中SER(标准差)/16＝ (2)中SER
Regressors 拟合优度和回归元选择的进一步探讨 Prediction and Residual Analysis 预测和残差分析
2
Lecture Notes 课堂笔记
Effects of Redefining variables 重新定义变量的影响
Estimated coefficients 估计系数 R squared R 平方 t statistics t 统计量
-0.0289 (0.0057) --
0.0058 (0.0018) 7.3109 (0.0656) 1388 0.0298 2177.5778 1.2539
(3) bwght
--
-9.268 (1.832) 0.0927 (0.0292) 116.974 (1.049) 1388 0.0298 557.485.51 20.063
6
Impact of changing the scale of the dependent variable 改变被解释变量测度单位的影响
Since 1lbs = 16 oz, the dependent variable is transformed by dividing 16.
因为1磅源自文库16盎司，被解释变量被除以16。
b·wght /16 bˆ0 /16 (bˆ1 /16)cigs (bˆ2 /16) fa min c
We compare columns (1) and (2). 比较第1列与第2列。 The estimated coefficients in (1)/16 = those in (2). (1)中被估参数/16＝ (2)中被估参数 The standard errors of estimated coefficients in
Functional form 函数形式
Logarithmic form 对数函数形式 Models with Quadratics 含二次式的模型 Models with interaction terms 含交叉项的模型
3
Redefining Variables 重新定义变量
Why would we want to do so? 为什么我们想这样做？ Often, data scaling is used to reduce the number of
4
Redefining Variables: An example 重新定义变量：一个例子
Consider a model relating infant birth weight to cigarette smoking and family income:
以下模型反映了婴儿出生体重与孕妇吸烟量和家庭收入之间的关系： (1) b·wght bˆ0 bˆ1cigs bˆ2 fa min c
Consider the following rescaling: 考虑如下单位变换：
(2) Birth weight is changed from ounces to pounds 出生体重单位由盎司变为磅 (3)Number of cigarettes is changed to packs of cigrattes 香烟的支数变为包数 The estimation results is presented in the following table. 估计结果列于下表
5
Y (column) X (rows) Cigs
Packs
Faminc
Intercept
Observations R-squared SSR SER
Table 6.1
(1) bwght
(2)bwghtlbs
-0.4634 (0.0916) --
0.0927 (0.0292) 116.794 (1.049) 1388 0.0298 557,485.51 20.063
Multiple Regression Analysis 多元回归分析
y = b0 + b1x1 + b2x2 + . . . bkxk + u
4. Further Issues 进一步的问题
1
Chapter Outline 本章大纲
Effects of Data Scaling on OLS Statistics 数据的测度单位换算对OLS统计量的影响 More on Functional Form 对函数形式的进一步讨论 More on Goodness-of-Fit and Selection of
8
Impact of changing the scale of the independent variable 改变解释变量测度单位的影响
(1)/16=those in (2) (1)中被估参数的标准差/16＝ (2)中被估参数的标准差
7
Impact of changing the scale of the dependent variable 改变被解释变量测度单位的影响
The t statistics in (1) and (2) are identical. (1)和(2)中 t 统计量相同 The R squared are identical. R平方相同 SSR in (1) /(16*16)=SSR in (2) (1)中SSR/（16*16）＝ (2)中SSR SER (standard error) in (1)/16=SER in (2) (1)中SER(标准差)/16＝ (2)中SER
Regressors 拟合优度和回归元选择的进一步探讨 Prediction and Residual Analysis 预测和残差分析
2
Lecture Notes 课堂笔记
Effects of Redefining variables 重新定义变量的影响
Estimated coefficients 估计系数 R squared R 平方 t statistics t 统计量
-0.0289 (0.0057) --
0.0058 (0.0018) 7.3109 (0.0656) 1388 0.0298 2177.5778 1.2539
(3) bwght
--
-9.268 (1.832) 0.0927 (0.0292) 116.974 (1.049) 1388 0.0298 557.485.51 20.063
6
Impact of changing the scale of the dependent variable 改变被解释变量测度单位的影响
Since 1lbs = 16 oz, the dependent variable is transformed by dividing 16.
因为1磅源自文库16盎司，被解释变量被除以16。
b·wght /16 bˆ0 /16 (bˆ1 /16)cigs (bˆ2 /16) fa min c
We compare columns (1) and (2). 比较第1列与第2列。 The estimated coefficients in (1)/16 = those in (2). (1)中被估参数/16＝ (2)中被估参数 The standard errors of estimated coefficients in
Functional form 函数形式
Logarithmic form 对数函数形式 Models with Quadratics 含二次式的模型 Models with interaction terms 含交叉项的模型
3
Redefining Variables 重新定义变量
Why would we want to do so? 为什么我们想这样做？ Often, data scaling is used to reduce the number of