【文章內(nèi)容簡(jiǎn)介】 Estimator。 Statistic ? standard errors, t statistics, F statistics, and confidence intervals. ? When variables are rescaled, the coefficients, standard errors, confidence intervals, t statistics, and F statistics change in ways that preserve all measured effects and testing outes. ?含 log形式只改變截距，不改變斜率系數(shù)，不改變 R2，不改變檢驗(yàn)結(jié)果 Effects of Data Scaling on OLS Statistics Beta Coefficients ? . test score ? Standardized: Z=(X均值 )/標(biāo)準(zhǔn)差 (sd) ? Advantages: ? The importance of each v.: the scale of the regressors irrelevant, paring the magnitudes ? ? More on Functional Form ?Logarithmic Functional Forms ?Models with Quadratics ?Models with Interaction Terms More on Using Logarithmic Functional Forms ? Approximate Accurate ? Small % change: not crucial ? Large change: mitigate or eliminate heteroskedastic or skewed ? Advantages of using Ln: ? leads to coefficients with appealing interpretations ? when y0, models using log(y) as the dependent v. often satisfy the CLM assumptions more closely than models using the level of y ? taking logs usually narrows the range of the v., in some cases by a considerable amount. This makes estimates less sensitive to outlying (or extreme) observations on the dependent or independent v. Some Standard Rules of Thumb for Taking Logs ? The Log is often taken when the v. being large integer values ? a positive dollar amount, wages, salaries, firm sales, and firm market value。 ? population, total number of employees, and school enrollment ? Variables that are measured in years—such as education, experience, tenure, age, and so on—usually appear in their original form. ? A variable that is a proportion or a percent—such as the unemployment rate, the participation rate in a pension plan, the percentage of students passing a standardized exam, the arrest rate on reported crimes—can appear in either original or logarithmic form, although there is a tendency to use them in level forms. ? a percentage change and a percentage point change More on Taking Logs ? If a variable takes on zero or negative values: ? The percentage change interpretations are often closely preserved, except for changes beginning at y=0 (where the percentage change is not even defined) ? One drawback to using a dependent v. in logarithmic form is that it is more difficult to predict the original v. ? it is not legitimate to pare R2 from models where y is the dependent v. in one case and log(y) is the dependent v. in the other. ? (see Section ) Models with Quadratics ? Decreasing or Increasing Marginal Effects: Quadratic Functions ? parabolic shape and Ushape ? Turning point ? If this turning point is beyond all but a small percentage of the v. in the sample, then this is not of much concern. ? Other forms: ? using quadratics along with logarithms. ? some care is needed in making a useful interpretation with a dependent v. in log form and an explanatory v. entering as a quadratic ? a nonconstant elasticity: doublelog and quadratics ? other polynomial terms: a cubic and even a quartic term Models with Interaction Terms ? Interaction Effects: ? Sometimes it is natural for the partial effect, elasticity, or semielasticity of the dependent v. with respect to an explanatory v. to depend on the magnitude of yet another explanatory v. Example : Effects of Attendence on Final Exam Performance ? Dependent v.: Final Exam Performance Standardized oute on a final exam (stndfnl) ? Be easier to interpret a student’s performance relative to the rest of the class ? Explanatory : ? Percentage of classes attended (atdrte) ? prior college grade point average (priGPA), and ACT score ? Functional Form: ? Quadratics in priGPA and ACT ? class attendance might have a different effect for students who have performed differently in the past, as measured by priGPA. an interaction between priGPA and the atdrte. ? Econometric Model Example : Regression Results, Inference and Interpretations ? Sample Regression Function： ? Jiont Hypothesis: ? What’s the Parti